OCS Study MMS 2006-059 

 

 

 

 

Alternative Oil Spill Occurrence 

Estimators for the Beaufort/Chukchi Sea 

OCS (Statistical Approach) 

MMS Contract Number 1435 – 01 – 00 – P0 – 17141 

September 5, 2006

Submitted by: TGE Consulting 

Anchorage, Alaska 

Authored by: Ted G. Eschenbach 

 William V. Harper 

MMS U. S. Department of the Interior 

Minerals Management Service 

Alaska Outer Continental Shelf Region
 

Alternative Oil Spill Occurrence 

Estimators for the Beaufort/Chukchi Sea 

OCS (Statistical Approach) 

September 5, 2006 

Submitted by: Dr. Ted Eschenbach, P.E. 

TGE Consulting 

4376 Rendezvous Circle 

Anchorage, AK 99504 

907-333-7817 

fax: 337-2928 

ted1@alaska.net 

Authored by: Dr. Ted G. Eschenbach, P.E. 

Dr. William V. Harper, P.E. 

This study was funded by the U.S. Department of the Interior, Minerals Management Service 

(MMS), Alaska Outer Continental Shelf Region, Anchorage Alaska, under Contract No. 1435 – 

01 – 00 – P0 – 17141, as part of the MMS Alaska Environmental Studies Program. 

The opinions, findings, conclusions, or recommendations expressed in this report or product are 

those of the authors and do not necessarily reflect the views of the U.S. Department of the 

Interior, nor does mention of trade names or commercial products constitute endorsement or 

recommendation for use by the Federal Government. 
Abstract

This study analyzes GOM statistics for pipeline and platform oil spills, and with statistically 

appropriate techniques develops Poisson models for spill rates. These models are tested through 

analysis of exponential inter-spill intervals for several exposure variables. These exposure 

variables include time, oil production, pipeline mile-years, and platform-years. Weibull and 

lognormal models for spill volumes are developed and used to support analyses at spill 

thresholds of 50, 100, 500, and 1000 barrels. In each case confidence limits are calculated and 

reported. The stability of the results has been confirmed for different time periods. 

Significant differences from past MMS publications include Poisson confidence intervals, exact 

binomial confidence intervals, detailed analyses for the exposure variables of pipeline mile-years 

and platform-years, the use of the larger spill data set of spills exceeding 50 barrels to estimate 

rates at higher thresholds, and the inclusion of more recent data (through 2005). A declining rate 

of platform spills is statistically verified, so that platform results are generally based on spills 

1990 to 2005, while pipeline results are based on data from 1972 to 2005. 

Spill causes are analyzed to identify spills with GOM-specific causes, such as hurricanes and 

fishing trawl gear. This is modeled as a binomial proportion for GOM-specific and applicable to 

the Arctic spills at the spill size thresholds. These results are extended to the Arctic with a 

method that provides a conservative confidence interval and a method that provides a minimum 

width confidence interval – both at each spill size threshold. 

For extension from the GOM data to the Arctic using a Beaufort development scenario, spill 

rates per production volume are found to be unreliable as compared with spill rates per pipeline 

mile-year and per platform-year. There was insufficient data on the Beaufort development 

scenario to estimate the spill rates for ice keel gouging, but a rough approximation for strudel 

scour suggested that this was less significant than applicable causes, such as corrosion, human 

error, and operational impacts. 

The estimated rates of Arctic applicable pipeline spills per pipeline mile-year and of platform

spills per platform-year at spill thresholds of 50, 100, 500, and 1000 barrels are presented with 

minimum and conservative confidence intervals. Thus, the existing data from the GOM is 

extended through statistically supported techniques. 

Preliminary results from a new approach to modeling pipeline spill rates based on “platformrelated” spills and pipeline mile-years are presented with the conclusions and recommendations. 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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Table of Contents 

1 Introduction........................................................................................................................... 1

1.1 Overview of Study .......................................................................................................... 1 

1.2 Overview of Data............................................................................................................ 3 

1.2.1 Data for MMS Analyses ......................................................................................... 3 

1.2.2 Data for Bercha Report........................................................................................... 3 

1.2.3 Data Supplied for this Report ................................................................................. 3 

1.3 Methodological Approach for GOM Spill Rate Estimation ........................................... 4 

1.3.1 What Oil Spill Occurrence Rate Measures Should be Considered......................... 4 

1.3.2 Spill Occurrence Drivers that Cannot be Considered............................................. 5 

1.3.3 Recommended Measure of Spill Probability .......................................................... 6 

1.3.4 Spill Sizes and Data Set Size .................................................................................. 8 

1.3.5 Links between Probability Exposure Variables...................................................... 9 

1.3.6 Poisson Distribution used in Previous MMS Models............................................. 9 

1.3.7 Summary on GOM Spill Probability Estimation.................................................. 10 

1.4 Methodology for Extending GOM Spill Rate Estimate to Alaskan OCS..................... 11 

1.5 Recommendations and Conclusions............................................................................. 11 

2 Data ...................................................................................................................................... 12

2.1 Introduction to Data Sets .............................................................................................. 12 

2.2 Pipeline Spill Size and Frequency ................................................................................ 12 

2.2.1 Pipeline Spill Data from MMS ............................................................................. 12 

2.2.2 Pipeline Spill Data from 2000-2005 ..................................................................... 15 

2.2.3 Pipeline Spill Data from Bercha Report ............................................................... 15 

2.2.4 Spills in State Waters............................................................................................ 17 

2.3 Platform Spill Size and Frequency ............................................................................... 18 

2.3.1 OCS Platform Spill Data from MMS for 1964 – 1999......................................... 18 

2.3.2 GOM Platform Spill Data from MMS for 2000 – 2005 ....................................... 22 

2.3.3 GOM Platform Spill Data Set............................................................................... 23 

2.4 Spill Occurrence Exposure Variables........................................................................... 24 

2.4.1 Potential Spill Occurrence Factors........................................................................ 24 

2.4.2 Time as a Spill Occurrence Measure .................................................................... 24 

2.4.3 Volume of Oil Produced ....................................................................................... 25 

2.4.4 OCS Pipeline Exposure......................................................................................... 28 

2.4.5 Number of Platforms and Number of Operating Wells........................................ 31 

2.4.6 Correlation Analysis............................................................................................. 33 

2.5 Spill Cause Analysis..................................................................................................... 34 

2.5.1 Introduction to Spill Cause Analysis.................................................................... 34 

2.5.2 Identifying the Primary Spill Cause...................................................................... 34 

2.5.2.1 Pipeline Spill Causes......................................................................................... 35 

2.5.2.2 Platform Spill Causes........................................................................................ 37 

2.5.3 Statistical Variability and Multinomial Confidence Intervals.............................. 39 

2.5.4 Differences Due to Time and Conditions............................................................. 41 

2.5.5 Statistical Variability and Binomial Confidence Intervals................................... 42 

2.6 Arctic Hazards and Extrapolating to the Arctic Environment...................................... 44 

2.6.1 Ice Keel Gouging .................................................................................................. 45 

2.6.2 Strudel Scour......................................................................................................... 46 
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2.6.3 Upheaval Buckling................................................................................................ 48 

2.6.4 Thaw Settlement ................................................................................................... 49 

3 Gulf of Mexico Spill Rate Estimation................................................................................ 51

3.1 Introduction to Analysis of Data................................................................................... 51 

3.2 Poisson Distribution...................................................................................................... 51 

3.2.1 Poisson Concerns about Exposure Variables........................................................ 51 

3.2.2 Exact Poisson Confidence Intervals...................................................................... 52 

3.2.3 Comparison of MMS and Exact Poisson Confidence Intervals............................ 54 

3.2.4 Compound Poisson Distribution........................................................................... 54 

3.3 Pipeline Spill Analyses Based on Spills ≥ 1000 bbl (1964 – 1999) ............................. 54 

3.3.1 Pipeline Inter-Spill Distribution Analysis............................................................. 55 

3.3.2 Poisson Rate for ≥ 1000 bbl Spills........................................................................ 57 

3.3.3 Pipeline Spill Volume Distribution Analysis........................................................ 57 

3.4 Platform Spill Analyses Based on Spills ≥ 1000 bbl (1964 – 1999) ............................ 60 

3.4.1 Platform Inter-Spill Distribution Analysis............................................................ 60 

3.4.2 Platform Inter-Spill Distribution Analysis with Hypothetical 1/1/1999 Spill ...... 61 

3.4.3 Platform Volume Distribution Analysis............................................................... 62 

3.5 Analyses Based on Pipeline Spills ≥ 50 bbl.................................................................. 64 

3.5.1 Pipeline Inter-Spill Analysis Based on Three Exposure Variables ...................... 64 

3.5.2 Exposure Variable Poisson Confidence Intervals and an Introduction to the 

Poisson – Exponential Relationship...................................................................................... 68 

3.5.3 Pipeline Spill Volume Models.............................................................................. 69 

3.5.4 Comparing Pipeline Spill Volume Models for Different Thresholds................... 75 

3.5.5 Concerns about Non-stationarity of the Poisson Process ..................................... 77 

3.5.6 Alternative Confidence Interval Approaches Applied to Pipeline Spills ............. 77 

3.5.7 Comparison of Through 2005 versus Through 1999............................................ 80 

3.5.8 Summary and Conclusions ................................................................................... 81 

3.6 Analyses Based on Platform Spills ≥ 50 bbl................................................................. 82 

3.6.1 Platform Inter-Spill Analysis Based on Three Exposure Variables...................... 82 

3.6.1.1 Platform Inter-Spill Analysis Based on Time................................................... 83 

3.6.1.2 Platform Inter-Spill Analysis Based on Production Volume (Mbbl)................ 93 

3.6.1.3 Platform Inter-Spill Analysis Based on Number of Platforms ......................... 96 

3.6.2 Platform Spills Comparing a 1971 Start with a 1972 Start................................. 100 

3.6.3 Platform Spill Volume Models........................................................................... 102 

3.6.4 Comparing Platform Spill Volume Models for Different Thresholds................ 105 

3.6.5 Platform Spill Volume Confidence Intervals...................................................... 106 

3.6.6 Summary and Conclusions ................................................................................. 107 

3.7 Chapter Summary ....................................................................................................... 108 

4 Extending to Alaska.......................................................................................................... 110

4.1 Introduction................................................................................................................. 110 

4.2 Development Scenario................................................................................................ 111 

4.3 Extension of Non-GOM Specific Spills to the Arctic ................................................ 113 

4.3.1 Methodology....................................................................................................... 113 

4.3.2 Pipeline Spills..................................................................................................... 115 

4.3.2.1 Pipeline Spills using Method 1 ....................................................................... 115 

4.3.2.2 Pipeline Spills using Method 2 ....................................................................... 117 

4.3.3 Platform Spills .................................................................................................... 118 

4.3.3.1 Applicable vs. GOM-Specific Platform Spills................................................ 118 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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4.3.3.2 Platform Spills using Method 1 ...................................................................... 120 

4.3.3.3 Platform Spills using Method 2 ...................................................................... 122 

4.4 Arctic Specific Hazards for Pipeline Oil Spills.......................................................... 123 

4.4.1 Ice Keel Gouging ................................................................................................ 123 

4.4.2 Strudel Scour....................................................................................................... 125 

4.4.3 Upheaval Buckling.............................................................................................. 125 

4.4.4 Thaw Settlement ................................................................................................. 126 

4.5 Arctic Specific Oil Spill Causes for Platforms........................................................... 126 

4.6 Application of Spill Rates to Development Scenario ................................................. 126 

4.7 Sensitivity Analysis of Platform Spill Rates to Data Adjustment .............................. 129 

4.8 Comparison with Bercha (2006)................................................................................. 129 

4.9 Summary and Conclusions ......................................................................................... 130 

5 Recommendations and Conclusions................................................................................ 131

5.1 Major Conclusions...................................................................................................... 131 

5.2 Cautions in Using and Interpreting the Results.......................................................... 131 

5.3 Suggestions for Future Work...................................................................................... 132 

5.4 Potential New Pipeline Spill Model............................................................................ 133 

5.4.1 Analogy to Fixed and Variable Cost Model vs. Average Cost Model ............... 134 

5.4.2 Determining Pipeline Spill Rates for Fixed and Variable Probability Model .... 135 

5.4.2.1 Platform-Related Pipeline Spills vs. “Pipeline” Spills ................................... 135 

5.4.2.2 Spill Rates for Platform-Related Pipeline Spills vs. “Pipeline” Spills........... 137 

5.4.2.3 Consistency of Spill Rates for “Fixed/Variable” Rate and Average Rate Models

 138 

5.4.3 Applying Spill Rates for “Fixed/Variable” Rate Model..................................... 139 

5.4.4 Summary and Conclusions for Fixed and Variable Cost Model ........................ 141 

6 References.......................................................................................................................... 142

Appendix A. Pipeline Spills ≥ 50 bbl through 1999............................................................... 147

The Department of the Interior Mission................................................................................. 158

The Minerals Management Service Mission .......................................................................... 158
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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List of Figures 

Figure 3.1 Exponential Probability Plot of Pipeline Inter-Spill Times Using Anderson & LaBelle 

(2000) Data ................................................................................................................................... 56 

Figure 3.2 Exponential Empirical CDF Plot of Pipeline Inter-Spill Times Using Anderson & 

LaBelle (2000) data....................................................................................................................... 56 

Figure 3.3 Weibull Probability Plot of Pipeline Spill Volumes Using Anderson & LaBelle 

(2000) Data ................................................................................................................................... 59 

Figure 3.4 Weibull Empirical CDF Plot of Pipeline Spill Volumes Using Anderson & LaBelle 

(2000) Data ................................................................................................................................... 59 

Figure 3.5 Exponential Probability Plot of Platform Inter-Spill times Using Anderson & LaBelle 

(2000) Data ................................................................................................................................... 60 

Figure 3.6 Exponential Empirical CDF Plot of Platform Inter-Spill times Using Anderson & 

LaBelle (2000) Data...................................................................................................................... 61 

Figure 3.7 Exponential Probability Plot of Platform Inter-Spill times Using Anderson & LaBelle 

(2000) Data Supplemented with a Hypothetical Spill on 1/1/1999 .............................................. 62 

Figure 3.8 Weibull Probability Plot of Platform Spill Volumes Using Anderson & LaBelle 

(2000) Data ................................................................................................................................... 63 

Figure 3.9 Weibull Empirical CDF Plot of Platform Spill Volumes Using Anderson & LaBelle 

(2000) Data ................................................................................................................................... 63 

Figure 3.10 Exponential Probability Plot of Pipeline Inter-Spill (Spills ≥ 50 bbl) Times Using N 

= 36 Data Set................................................................................................................................. 65 

Figure 3.11 Exponential Empirical CDF Plot of Pipeline Inter-Spill (Spills ≥ 50 bbl) Times 

Using N = 36 Data Set .................................................................................................................. 65 

Figure 3.12 Exponential Probability Plot of Pipeline Inter-Spill Production Volumes (Mbbl) 

Using N = 36 Data Set (Spills ≥ 50 bbl)....................................................................................... 66 

Figure 3.13 Exponential Empirical CDF Plot of Pipeline Inter-Spill Production Volumes Using 

N = 36 Data Set (Spills ≥ 50 bbl).................................................................................................. 66 

Figure 3.14 Exponential Probability Plot of Pipeline Inter-Spill Pipeline Mile-Years (KMiles) 

Using N = 36 Data Set (Spills ≥ 50 bbl)....................................................................................... 67 

Figure 3.15 Exponential Empirical CDF Plot of Pipeline Inter-Spill Pipeline Mile-Years 

(KMiles) Using N = 36 Data Set (Spills ≥ 50 bbl) ....................................................................... 67 

Figure 3.16 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 50 bbl .................. 70 

Figure 3.17 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 50 bbl............ 71 

Figure 3.18 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 100 bbl ................ 72 

Figure 3.19 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 100 bbl.......... 72 

Figure 3.20 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 500 bbl ................ 73 

Figure 3.21 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 500 bbl.......... 73 

Figure 3.22 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 1000 bbl .............. 74 

Figure 3.23 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 1000 bbl........ 74 

Figure 3.24 Overlay of Weibull Empirical CDFs........................................................................ 77 

Figure 3.25 Exponential Probability Plot of Platform Inter-Spill (Spills ≥ 50 bbl) Times using 

1972-2005 Data Set....................................................................................................................... 84 

Figure 3.26 Exponential Probability Plot of Tie-breaking Adjusted Platform Inter-Spill (Spills ≥

50 bbl) Times using 1972-2005 Data Set ..................................................................................... 85 

Figure 3.27 Weibull Probability Plot of Platform Inter-Spill (Spills ≥ 50 bbl) Times using 1972-

2005 Data Set................................................................................................................................ 86 
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Figure 3.28 Exponential Empirical Distribution Function Fit of Platform Inter-Spill (Spills ≥ 50 

bbl) Times using 1972-2005 Data Set .......................................................................................... 86 

Figure 3.29 Weibull Empirical Distribution Function Fit of Platform Inter-Spill (Spills ≥ 50 bbl) 

Times using 1972-2005 Data Set.................................................................................................. 87 

Figure 3.30 Regression of Inter-Spill time versus Spill Year...................................................... 88 

Figure 3.31 Analysis of Means Comparing Inter-Spill Averages between Data for 1972-1989 

versus 1990-2005.......................................................................................................................... 89 

Figure 3.32 Overlaid Exponential Distribution Fits to Platform Inter-Spill Time for 1972-1989 

versus 1990-2005.......................................................................................................................... 91 

Figure 3.33 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Time for the 

1972-1989 versus 1990-2005........................................................................................................ 91 

Figure 3.34 Panel Displayed Exponential Distribution Fits to Adjusted (Tie Breaking) Platform 

Inter-Spill time for the 1972-1989 versus 1990-2005................................................................... 92 

Figure 3.35 Exponential Probability Plot Platform Inter-Spill (Spills ≥ 50 bbl) Production 

(Mbbl) using 1972-2005 Data Set................................................................................................. 93 

Figure 3.36 Weibull Probability Plot Platform Inter-Spill (spills ≥ 50 bbl) Production (Mbbl) 

using 1972-2005 Data Set............................................................................................................. 94 

Figure 3.37 Exponential Empirical Distribution Function Fit of Platform Inter-Spill (Spills ≥ 50 

bbl) Production (Mbbl) using 1972-2005 Data Set....................................................................... 94 

Figure 3.38 Weibull Empirical Distribution Function Fit of Platform Inter-Spill (spills ≥ 50 bbl) 

Production (Mbbl) using 1972-2005 Data Set.............................................................................. 95 

Figure 3.39 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Production 

(Mbbl) for 1972-1989 versus 1990-2005...................................................................................... 95 

Figure 3.40 Exponential Probability Plot Platform Inter-Spill (spills ≥ 50 bbl) Number of 

Platforms using 1972-2005 Data Set ............................................................................................ 96 

Figure 3.41 Weibull Probability Plot Platform Inter-Spill (Spills ≥ 50 bbl) Number of Platforms 

using 1972-2005 Data Set............................................................................................................. 97 

Figure 3.42 Exponential Empirical Distribution Function Fit of Platform Inter-Spill (Spills ≥ 50 

bbl) Number of Platforms using 1972-2005 Data Set .................................................................. 97 

Figure 3.43 Weibull Empirical Distribution Function Fit of Platform Inter-Spill (Spills ≥ 50 bbl) 

Number of Platforms using 1972-2005 Data Set.......................................................................... 98 

Figure 3.44 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Number of 

Platforms for 1972-1989 versus 1990-2005 ................................................................................. 98 

Figure 3.45 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Time for 

1971-2005 versus 1972-2005...................................................................................................... 101 

Figure 3.46 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Adjusted (Tie 

Breaking) Time for 1971-2005 versus 1972-2005...................................................................... 102 

Figure 3.47 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥ 50 bbl

..................................................................................................................................................... 103 

Figure 3.48 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥ 100 bbl

..................................................................................................................................................... 104 

Figure 3.49 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥ 500 bbl

..................................................................................................................................................... 104 

Figure 3.50 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥ 1000 

bbl ............................................................................................................................................... 105 

Figure 3.51 Overlay of Lognormal Empirical CDFs for Platform Spill Data ........................... 106 

Figure 5.1 Average Cost versus Fixed and Variable Cost Models............................................ 134 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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List of Tables 

Table 2.1 OCS Pipeline Spills of 1000 bbl or More (1964-1999)............................................... 13 

Table 2.2 GOM Pipeline Spills of 50 bbl or More (1972-1999) ................................................. 14 

Table 2.3 GOM Pipeline Spills of 50 bbl or More (2000-2005) ................................................. 15 

Table 2.4 OCS Pipeline Spills Summary (1972-1999)1, 2............................................................ 16 

Table 2.5 OCS Platform Spills ≥ 1000 bbl (1964-1999) ............................................................. 19 

Table 2.6 GOM Platform Spills of ≥ 50 bbl (1971-1999) N = 77 ............................................... 21 

Table 2.7 Comparison of Bercha (2002) and Similarly Selected Spills from Current GOM 

Platform Spill Data Set (1972-1999) N = 21 ................................................................................ 22 

Table 2.8 GOM Platform Spills ≥ 50 bbl (2000-2005) N = 9 ..................................................... 23 

Table 2.9 Summary of GOM Platform Spills ≥ 50 bbl (1972-2005) N = 78............................... 24 

Table 2.10 Yearly GOM Pipeline and Platform Spills of 50 bbl or More (1972-2005).............. 25 

Table 2.11 Oil Production Volume (1972-2005)......................................................................... 27 

Table 2.12 OCS Pipeline Mileage and Segments........................................................................ 29 

Table 2.13 Bercha Pipeline Exposure.......................................................................................... 30 

Table 2.14 GOM Number of Platforms....................................................................................... 32 

Table 2.15 Active Oil Wells from Platforms (Bercha 2006, from Federal Offshore Statistics 

report, MMS, October 2000) ........................................................................................................ 32 

Table 2.16 Correlations between Exposure Variables................................................................. 34 

Table 2.17 Primary Cause of GOM Pipeline Oil Spills............................................................... 36 

Table 2.18 Summary of Primary Cause of GOM Pipeline Oil Spills (N = 36)........................... 37 

Table 2.19 Causes of GOM Pipeline Oil Spills from Bercha (2002 Table 2.2 & 2006 Table 2.2)

....................................................................................................................................................... 37 

Table 2.20 GOM Specific Cause (Hurricanes) Platform Spills................................................... 38 

Table 2.21 Summary of Causes of GOM Platform Spills 1971-2005 (N = 78) .......................... 38 

Table 2.22 Causes of GOM Platform Oil Spills from Bercha (2002 Table 2.4 & 2006 Table 2.5)

....................................................................................................................................................... 38 

Table 2.23 Confidence Intervals for Third Party GOM Pipeline Spill Proportion with Estimated 

Proportion of 25.0% = 9/36 .......................................................................................................... 39 

Table 2.24 95% Confidence Intervals for GOM Pipeline Spill Cause Proportions..................... 39 

Table 2.25 95% Confidence Intervals for Bercha (2002 & 2006) Pipeline Spill Cause 

Proportions.................................................................................................................................... 40 

Table 2.26 95% Confidence Intervals for GOM Platform Spill Cause Proportions.................... 40 

Table 2.27 95% Confidence Intervals for Bercha (2002 & 2006) Platform Spill Cause 

Proportions.................................................................................................................................... 41 

Table 2.28 Binomial Characterization of the Causes of Pipeline Oil Spills (Normal 

Approximation)............................................................................................................................. 43 

Table 2.29 Exact Binomial Characterization of the Causes of Pipeline Oil Spills...................... 43 

Table 2.30 Binomial Characterization of the Causes of Platform Spills (Normal Approximation)

....................................................................................................................................................... 44 

Table 2.31 Exact Binomial Characterization of the Causes of Platform Spills........................... 44 

Table 3.1 95% Confidence Interval Comparison Based on Anderson & LaBelle (2000) Pipeline 

Data with Production Volume as the Exposure Variable ............................................................. 54 

Table 3.2 Spill Rate per Year for ≥ 1000 bbl Spills..................................................................... 57 

Table 3.3 Spill Rates for ≥ 50 bbl Spills (N = 36)....................................................................... 68 
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Table 3.4 Rate Estimates using Exponential Distribution ........................................................... 68 

Table 3.5 Poisson Rates based on Inter-Spill Data (N = 35)....................................................... 69 

Table 3.6 Odds Ratios for the Four Different Threshold Weibull Distributions......................... 75 

Table 3.7 Exact Poisson Confidence Intervals for Different Pipeline Spill Thresholds with 

Production as Exposure Variable.................................................................................................. 78 

Table 3.8 Exact Binomial Confidence Intervals for the Proportion of the ≥ 50 bbl Model Spills 

Exceeding the Larger Threshold with Production as Exposure Variable..................................... 78 

Table 3.9 Spill Rate Estimates and Confidence Intervals Using 2.72 Spill Rate for ≥ 50 bbl 

Times Values in Table 3.8 with Production as Exposure Variable .............................................. 79 

Table 3.10 Confidence Intervals for “Binomial Adjusted” Approach Using (1.91, 3.77) Table 

3.7 Poisson Confidence Intervals from ≥ 50 bbl Model and the Binomial Confidence Intervals in 

Table 3.8 ....................................................................................................................................... 80 

Table 3.11 Confidence Intervals Using (1.91, 3.77) Poisson Confidence Intervals from ≥ 50 bbl 

Model and P(≥ threshold) with Production as Exposure Variable ............................................... 80 

Table 3.12 Predicted Average Inter-spill Times (days) with 95% Confidence and Prediction 

Intervals......................................................................................................................................... 88 

Table 3.13 Comparing 1972-1989 and 1990-2005 Platform Inter-Spill Times........................... 90 

Table 3.14 GOM Platform Spill Rates (Spills ≥ 50 bbls) for 1972-1989 and 1990-2005......... 100 

Table 3.15 Odds Ratios for the Four Lognormal Distributions for Platform Spills.................. 106 

Table 3.16 Exact Binomial Confidence Intervals for Various Platform Spill Volume Thresholds

..................................................................................................................................................... 107 

Table 3.17 Recommend Rate Estimates and Confidence Intervals for Various Platform Volume 

Spill Thresholds (using the 1990 – 2005 Rate)........................................................................... 107 

Table 4.1 Beaufort Sea Development Scenario ......................................................................... 112 

Table 4.2 Method 1 Arctic Pipeline Spill ≥ 50 bbl Poisson Based Rate and 95% Confidence 

Intervals....................................................................................................................................... 115 

Table 4.3 GOM and Applicable Pipeline Spills at Different Thresholds with 95% Binomial 

Confidence Limits (Based on Table 2.17).................................................................................. 116 

Table 4.4 Method 1 Conservative Procedure to Estimate Arctic Pipeline Spill Rates for Various 

bbl Thresholds with Exposure Variable = Production................................................................ 117 

Table 4.5 Method 1 Conservative Procedure to Estimate Arctic Pipeline Spill Rates for Various 

bbl Thresholds with Exposure Variable = Pipeline Mile-Years................................................. 117 

Table 4.6 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for Arctic 

Pipeline Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with Exposure Variable = 

Production................................................................................................................................... 118 

Table 4.7 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for Arctic 

Pipeline Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with Exposure Variable = 

Pipeline Mile-Years.................................................................................................................... 118 

Table 4.8 GOM Platform Spills – Hurricane & Applicable (1990 – 2005)............................... 119 

Table 4.9 GOM and Applicable Platform Spills at Different Thresholds ................................. 119 

Table 4.10 Adjusted GOM and Applicable Platform Spills at Different Thresholds for N = 22 

Spills (Changed Values in Bold Italic) ...................................................................................... 120 

Table 4.11 GOM Platform Spill ≥ 50 bbl Exact 95% Poisson Confidence Intervals for 1990 – 

2005............................................................................................................................................. 120 

Table 4.12 Proportion of ≥ 50 bbl Platform Spills above Different Thresholds with 95% 

Binomial Confidence Limits (1990-2005 Data)......................................................................... 121 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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Table 4.13 Method 1 Conservative Procedure to Estimate Arctic Platform Spill Rates for 

Various bbl Thresholds with Exposure Variable = Production .................................................. 121 

Table 4.14 Method 1 Conservative Procedure to Estimate Arctic Platform Spill Rates for 

Various bbl Thresholds with Exposure Variable = Platform-Years........................................... 122 

Table 4.15 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for Arctic 

Platform Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with Exposure Variable = 

Production................................................................................................................................... 122 

Table 4.16 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for Arctic 

Platform Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with Exposure Variable = 

Platform-Years............................................................................................................................ 123 

Table 4.17 Gouge rate for a burial depth of 2.5 m..................................................................... 124 

Table 4.18 Application of Conservative (Method 1) Extended “Applicable” GOM Spill Rates 

(Spills ≥ 50 bbl) to Beaufort Development Scenario.................................................................. 127 

Table 4.19 Arctic Pipeline Spills for Applicable Causes – Rates and 95% Confidence Limits 

(Spills/KMile-Years)................................................................................................................... 128 

Table 4.20 Arctic Platform Spills for Applicable Causes – Rates and 95% Confidence Limits 

(Spills/KPlatforms-Years)........................................................................................................... 128 

Table 4.21 Sensitivity Analysis for Arctic Platform Spills for Applicable Causes – Rates and 

95% Confidence Limits (Spills/KPlatforms-Years) ................................................................... 129 

Table 4.22 Poisson Rates for Bercha (2006) Data for 1972-1999............................................. 129 

Table 4.23 Poisson Rates for Specific Spill Causes for Bercha (2006) Data for 1972-1999 .... 130 

Table 5.1 Modified Table 2.17 Platform Related Primary Cause of GOM Pipeline Oil Spills. 136 

Table 5.2 Summary of Platform vs. Pipeline Related GOM Pipeline Oil Spills....................... 137 

Table 5.3 Spill Rates for Platform vs. Pipeline Related Applicable Pipeline Oil Spills............ 138 

Table 5.4 Expected Life-of-Field Spill Numbers for Beaufort Development Scenario for 

Pipeline Oil Spills....................................................................................................................... 140 

Table 5.5 Comparing Expected Life-of-Field Spill Numbers for Beaufort Development Scenario 

for Pipeline Oil Spills for Fixed/Variable and Average Models................................................. 140 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Glossary of Acronyms 

Bbbl billion barrels 

ccdf complementary cumulative distribution function 

cdf cumulative distribution function 

KMiles thousands of miles 

KPlatform thousands of platforms 

KWell thousands of wells 

LCL lower confidence limit 

Mbbl million barrels 

pdf probability distribution function 

TLAR that looks about right 

UCL upper confidence limit 

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1 Introduction 

This study is not a comprehensive study of all potential sources of oil spills related to 

development of oil fields in the Beaufort and Chukchi Seas. It does not address for example, the 

probability of oil spills during exploration, the possibility of oil spills during transport in TAPS, 

or from tanker traffic after leaving Valdez. 

What this study emphasizes is the development of statistical measures with confidence intervals 

to describe the uncertainty in the estimate for pipeline and platform spills during production. 

These measures are applied both to the existing MMS data base (mostly Gulf of Mexico) and 

extrapolated to the Beaufort and Chukchi Seas. For statistical robustness and validity these 

measures are linked as closely as possible to causal relationships rather than to simple statistical 

correlations. This study relies on the larger context of other studies for much of the data and 

scenario development. 

1.1 Overview of Study 

There is an extensive history of MMS statistical analysis of oil spill occurrences, for example see 

Smith et al. (1982); Lanfear & Amstutz (1983); LaBelle & Anderson (1985); Anderson & 

LaBelle (1990, 1994, and 2000). For this project to add value to this extensive history, it cannot 

merely refine data by adding or subtracting a spill or three or by relying on a more recent subset 

of the data. Instead this project must evaluate whether alternative statistical approaches can 

improve estimated spill occurrence probabilities for Alaskan OCS areas of the Beaufort and 

Chukchi Seas. 

Current MMS spill occurrences are expressed in terms of spills per billion barrels (Bbbl) 

produced. For example, the rate for US OCS pipeline spills is reported as 1.33 spills of 1000 or 

more bbl per Bbbl handled in Anderson & LaBelle (2000, p. 311). The data base for these 

statistical measures is dominated by operations in the Gulf of Mexico. Thus evaluation of 

possible statistical measures for Alaskan OCS areas of the Beaufort and Chukchi Seas must 

address two questions. 

The first question is “Are alternative measures in terms of spill probabilities per platform-year 

and per pipeline-mile-year more appropriate for this purpose than occurrences measured in spills 

per billion barrels?” These measures represent an approach that is intermediate between the 

single production measure of number of billion barrels produced and a detailed fault-tree 

approach that relies on relatively detailed development scenarios. 

The second question is “How to account for differences between probable Alaskan development 

scenarios and the historical data base?” These differences include: 

1. Given the cost of operating in an Arctic environment, it is reasonable to expect that 

Alaskan prospects must generate higher production levels to be economically justified. 

Thus fewer facilities will be required for the same level of production. For the same level 

of production, the presence of fewer facilities means a lower contribution to the 

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probability of an oil spill occurrence. On the other hand, facilities with larger capacities 

may increase the size of spills if they do occur. 

2. There are substantial differences linked to pigging and maintenance between the historic 

data base and expected Alaskan operating conditions. These can also be linked to general 

differences in the time series in the Gulf of Mexico as the U.S. regulatory and operating 

environment has evolved. 

3. Given the difficulties in operating in the Arctic, at least initial development is likely to be 

at shorter average distances than in the Gulf of Mexico. This will reduce the length of

required pipelines with some reduction in the probability of an oil spill occurrence. On 

the other hand, the Arctic has harsh environmental conditions, which may increase the 

probability of oil spills due to human errors in operations. 

4. Finally, some of the typical causes of spills have substantially different probabilities of 

occurring in the Gulf of Mexico and Arctic environments. For example, fishing gear in 

the Gulf of Mexico has damaged valves and caused spills. On the other hand, in certain 

depths of water in the Arctic Ocean there can be damage from ice keels in moving pack 

ice. 

The difficulty in answering these questions – statistically or with any other approach – is that the 

available data are relatively limited. It is worth noting that since the key data are based on oil 

spills, it is good that the number of data points is not larger – even though this makes the 

statistical analysis more difficult. 

A third question that must be addressed is the robustness of the results as the underlying data are 

refined and extended by time. As the data records are examined there are significant periods 

with no spills – especially at larger spill thresholds, and brief periods with several spills. This is 

intrinsic in the stochastic nature of this problem, but for decision-makers to rely on the study’s 

results; those results should be reasonably stable if analyzed over different periods of time. 

This study addresses this specifically by analyzing spill rates over time. This identifies changes 

and trends in the historical series. Other results and conclusions will be analyzed at three stages. 

The first was represented in the reviewed preliminary analysis, where the time periods were 

chosen to match earlier work (Anderson & LaBelle, 2000; and Bercha, 2002). The second stage 

is the 1972 – 1999 analyses that contained corrections, changes, additions, or deletions identified 

by MMS during review. The level of consistency of the 1972 – 1999 with the third stage is 

discussed as needed and key results are included in an appendix to this report. The third stage 

includes data through 2005, which represents the bulk of the work in this report. 

The balance of Chapter 1 is organized to match the balance of the report. That is Section 1.2 

introduces Chapter 2 on the data, Section 1.3 introduces Chapter 3 on analyzing the existing 

OCS data, Section 1.4 introduces Chapter 4 on extending the results to the arctic environment of 

the Beaufort and Chukchi Seas, and Section 1.5 introduces Chapter 5 on recommendations and 

conclusions. 

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1.2 Overview of Data 

1.2.1 Data for MMS Analyses 

Previous MMS analyses have focused on spills from platforms and pipelines in OCS areas of the 

Gulf of Mexico (GOM) and in the Pacific. Because of the GOM’s much larger operational 

scope, in a statistical sense these data are essentially GOM data. The published portion of the 

MMS analyses has focused on spills of 1000 bbl or more. These data have been carefully 

checked, and they are the best quality data available. The most recent publication (Anderson & 

LaBelle, 2000) covers 1967 to 1999. 

The exposure variable in these MMS analyses has been the volume of crude oil produced, so that 

spill rates are reported per billion bbl (Bbbl) produced. In addition to the exposure data of 

volume of oil production, MMS also has made available data on the number of platforms, the 

number of pipeline segments, and the number of miles of pipeline miles for various product 

codes. Data from 1972 to 2005 has been relied on for this report. 

Both the exposure and spill data supplied by MMS are described in more detail in Chapter 2. 

MMS also maintains a database of “all” spills, but data on the smaller spills have received less 

scrutiny and checking. This larger database is statistically desirable, and it is the foundation for 

much of the analysis in this report. This data base includes information on location, date 

reported, spill volume, primary spill cause, secondary spill cause, spill volume, etc. 

1.2.2 Data for Bercha Report 

Bercha (2002 & 2006) relied heavily on the MMS data, but it also drew upon spill statistics from 

elsewhere in the world. Its analysis of the MMS data identified some discrepancies and some of 

these were corrected at that time, and some have been corrected since. The data on experience in 

other parts of the world are most applicable to the problem of extending results based on GOM 

data to the Arctic. 

Because of the need to construct measures of statistical confidence for the results in this report, 

this report is analyzing the MMS data in more detail. Thus, the results in Bercha (2002 & 2006) 

from the MMS data are used more as a double-check than directly. 

1.2.3 Data Supplied for this Report 

Because this report is being completed after Anderson & LaBelle (2000) and Bercha (2002), it 

has been able to add data for more recent spills. Historical and recent data supplied by MMS are 

identified in Chapter 2. This data has been supplied with extensive discussions as to how to most 

reliably use and adapt it. The more recent data are being used to check the stability of the results 

presented here over different data sets. 

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1.3 Methodological Approach for GOM Spill Rate Estimation 

This study was funded to estimate rates of oil spill occurrences and rates in the Beaufort and 

Chukchi Seas of the Arctic Ocean. Because the data set is drawn almost exclusively from the 

Gulf of Mexico, the authors believe the estimation methodology must first be applied in this 

context. If the methodology does not work with the data from which it was drawn, then 

extrapolating the results to the Arctic Ocean would be questionable. 

1.3.1 What Oil Spill Occurrence Rate Measures Should be Considered 

In estimating oil spill occurrences, one of the first choices is what is the exposure variable. In 

other words, how is the spill occurrence rate measured? All of the possibilities considered are 

spill rates which equal some number of spills per some volume or amount. Thus, to describe a 

spill occurrence rate without referencing a measure, it is simply referred to as a spill rate. 

Choices include the following: 

Spills per billion barrels of production, 

Spills per year, 

Spills per platform-year or per well-year, and 

Spills per pipeline-mile-year. 

The choice must be made by balancing different concerns, and there are reasonable justifications 

for different choices considering the trade-offs between the concerns. These concerns include 

the following: 

The historical MMS measure is spills per billion barrels of production. The measure was 

chosen by knowledgeable professionals for good reasons, and it now has a long history of 

use. Because users are already familiar with the measure, it is easier for them to use in 

the future, and it is much easier to compare past and future uses. 

Much of the data for this problem is available on an annual basis. For example, the 

volume of oil production, the number of platforms, and the total number of pipeline miles 

were supplied as annual data. This means that it is easier to compute occurrences 

annually (per year), than it is to attempt to disaggregate the data into shorter periods. 

The concern over data categorization and occurrence exposure even extends to the 

classification of some spills. For example, a spill from a pipeline riser onto a platform is 

currently classified as a pipeline spill. If the exposure variables include the number of 

platforms and the amount of pipeline mileage, then it might be better classified as a 

platform spill. That is the probability of a spill from the riser is more related to the 

platform than to the length of the pipeline. For example, the probability of a ship 

crushing a riser does not change if the length of a pipeline doubles, but doubling the 

number of platforms would roughly double that probability. 

As much as possible, there should be a sound logic that links spills to the exposure 

variable. This is particularly important when the probability is changing or when the spill 

occurrence is being extrapolated to a different environment. The presence of this logic is 

reflected in a subtle, but important, change in language. The presence of a linking logic 

between exposure and spill probability allows the description of that exposure as a 

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driving variable. In other words, the description is not of just a simple statistical 

correlation, rather a causal linkage is suggested. In general, statistical relationships that 

are based on causality are much more reliable than relationships based on correlation. 

As the data that can be potentially used covers as much as 40 years, one concern is 

changes in spills per each of the occurrence measures over time. Technology, regulatory 

and operating environments, volume of facilities, and the effects of corrosion have not 

been constant – they are changing. Thus, this study does analyze if spill rates are 

homogeneous or inhomogeneous over time, and how fast these rates are changing (if they 

are). 

The choice of occurrence probability drivers involves tradeoffs among the above concerns. 

Moreover the desire to estimate now or in the future the probabilities of different size spills, from

different causes, from platforms and pipelines, at different locations, etc. mean that other 

tradeoffs must also be considered. 

Before discussing which spill occurrence measures are included in this analysis, and which are 

recommended for extrapolation to the arctic environment, the next section briefly discusses some

of the spill occurrence drivers that might be useable – if there were far more data. 

1.3.2 Spill Occurrence Drivers that Cannot be Considered 

If the occurrence of spills is examined for contributing factors from the perspective of the system

of platforms and pipelines, there are a number of factors that can be logically linked to the 

occurrence of spills. Data for some of these exists in some cases, but in general, the MMS 

database that has been made available to the study team, does not support analysis of the 

following potential factors. These are listed with the logical causal link that suggests that each 

would be “nice to know.” 

Each pipeline termination or connection represents another opportunity for human error 

and/or an increased vulnerability to damage. Thus, the number of such points is linked to 

the probability of a spill. It is possible that this may be approximated by the number of 

platforms, wells, and/or pipeline segments. 

As each pipeline ages, it is clearly more likely to have accumulated sufficient corrosion

to either be a problem for pipeline integrity or to increase the vulnerability of the pipeline 

to damage from other causes. Also the age of a pipeline is linked to the technology, 

technical understanding, and regulatory environment that were used for its design, 

construction, and operation. So the date each pipeline was put in service and how old it 

is do contribute to the probability of a spill, which can also be reduced by inspection or 

maintenance activities linked to the age and condition of the pipeline. Note that Bercha 

(2002) includes aggregate mileage placed in service in each year, but the small number of 

corrosion caused accidents and the lack of detailed knowledge of which pipe segments 

were placed in service each year, means that this cannot be linked statistically to 

corrosion. 

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The thicker the wall of a pipeline, the more likely that pipeline will survive impact 

damage from an anchor, ship, or fishing net. The required thickness is also connected 

with the operating pressure and diameter at the design stage. In turn, the diameter, 

operating pressure, and length of pipe between shut-off valves contribute to the size of a 

spill, if a spill occurs. 

The depth of water over the pipeline and the depth of any cover (if any) from trenching, 

backfilling, or deposited sediments affect the vulnerability of the pipe to damage. That 

change clearly impacts the probability of a spill occurring on a segment of pipeline. 

The maintenance and operating regime clearly impacts the probability of a spill. For 

example, if a pipeline is “piggable” and pigging is regularly conducted, then the 

probability of spills due to corrosion is significantly reduced. Weaknesses due to 

corrosion will generally be identified before they can be a threat to pipeline integrity. At 

the same time, spills may be caused by human error or mechanical problems when the pig 

is being loaded into or unloaded from the system. Similarly, the presence and use of 

effective leak detection systems can dramatically reduce the time required to discover a 

spill and the resulting size of the spill. This in turn reduces the probability of a spill of at 

least 500 or 1000 bbls. 

While all of the above conditions influence the probability of a spill, separating out the relative 

impact of multiple factors requires hundreds of data points, rather than the ten to thirty-six to 

seventy-eight spills analyzed here. To analyze multiple factors the already small data set would 

have to be divided into smaller and smaller groups. 

Instead, this study must focus its attention on a few of the most important factors. It is believed 

that the major variables of time, amount of production, number of platforms or wells, and the 

number of pipeline-miles represent the most that can be effectively analyzed here. In addition, 

correctly determining the status of all pipelines for the above data would be problematic at best. 

1.3.3 Recommended Measure of Spill Probability 

In order to choose between spill probability measures, it is helpful to analyze what causes of 

spills are based on volume of production, on time, or on the amount of physical facilities. It is 

also necessary to describe the data that are required about a potential development prospect in 

order to apply the proposed measure. 

It is difficult to identify driving variables for production volume that directly increase the 

probability of an oil spill. However, there is no question that production volume is a proxy 

variable for many other variables that change the probability of an oil spill. More production 

means more platforms, more pipelines, more operators, etc. More importantly, if spill 

probability is based on volume of production, then there is no need for scenarios of development 

with numbers of platforms and miles of pipe. Instead this detail is replaced by the assumption 

that the situation where the probability measure is developed is sufficiently similar to the new 

situation, that the extrapolation from one to the other is valid. 

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As an example of a driving variable that is based on time, consider boats traveling to or from

platforms and the number of fishing days in a season. The first may be linked to the schedule to 

move operators on/off the platform, and the latter determines for how much of the year fishing 

nets are a factor. Scheduled maintenance activities may also be based on time, and there is at 

least some level of increased probability of operator error or equipment malfunction any time 

operational changes are made. Time is also the driving variable behind probabilities due to 

hurricanes and moving pack ice. At extreme examples, there are certainly hurricane forces that 

are possible that would damage virtually any facility and cause a spill. Whether this is the 100-

year, 500-year, or 1000-year storm is a time-based probability measure. 

In order to apply a time-based probability variable to analyze a potential development prospect, 

it is necessary to have some measure of the expected rate of facility development and production. 

This will be required to compare the probabilities to the benefits for the proposed development. 

And it is also needed to prevent logical nonsense, such as, a time based spill probability when 

there are not yet any facilities in place. 

It is reasonable to model exposure to dragging anchors, ice keel gouges, fishing gear from

trawlers, mud slides, etc. with pipeline mileage as a driving variable. However, oil spill 

probabilities from pipelines are not strictly a linear function of mileage, there is a certain 

probability that is linked to the number of pipeline connectors, terminators, etc. However, an 

analysis of the causes of pipeline failures (see Bercha, 2002) suggests that most of the spills are 

linked to modes (corrosion, third party impact, and mud slides) that can be modeled with 

pipeline mileage as a driving variable. 

Similarly, the number of wells or platforms will be a driving variable for the probability of a spill 

from a platform. The data in Anderson & LaBelle (2000) (see also Section 2.3) indicate that 

platform spills have historically typically been larger than pipeline spills. Thus, a complicating 

factor in the possible treatment of riser spills as platform spills is their different size distributions. 

Another reason for using pipeline mileage and the number of platforms as driving variables is an 

observation from other complex systems. Basically as systems become larger and more 

complex, there seems to be a tendency to focus on more common or more controllable causes of 

system failure. Thus, operator and managerial errors of commission or inattention are more 

likely to miss the less common causes of system failure. 

One difficulty in using the number of pipeline miles and the number of platforms as driving 

variables is that the calculation of spill probabilities now requires some level of scenario 

development for potential oil fields to determine how many platforms and how many miles of 

pipeline will be required. In this particular case, that requirement can be satisfied through 

reference to Bercha (2006). 

Thus, the principal choices are the following: 

Spills per billion barrels of production, 

Spills per year, and 

Spills per platform or well-year & per pipeline-mile-year. 

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This study will actually use all of these methods for analyzing the OCS data, and it will test two 

and recommend one of these methods for calculating oil spill probabilities in the Beaufort and 

Chukchi Seas. One of the projection methods will be based on the volume of production. This is 

being chosen because it is more like past MMS practice, thus allowing a better opportunity to 

examine other factors in constructing estimates of oil spill probabilities. Also, it does not require 

the estimation of the development system. So for potential fields where development scenarios 

do not yet exist, some estimation of oil spill probabilities will still be possible. 

The second recommended approach for extrapolation from GOM data to the arctic will be based 

on pipeline mileage and number of platforms. Because the requirement for a development 

scenario can be satisfied through Bercha (2006), it is possible to apply this and to compare the 

results with an extrapolation based on spill rates per production volume. 

It is the professional judgment of the authors that the extrapolation based on pipeline mileage 

and number of platforms is better than the extrapolation based on production volume. This is 

detailed in Chapter 4, but a brief example is illustrative of why this recommendation is made. 

There are substantial differences for example in the average production volume per platform, 

which averaged about 130,000 bbl/year from 1972 to 2005 in the GOM and which are projected 

to average 8.6 Mbbl/year in the Beaufort development scenario. The factor of 66 difference 

means that platform spill rates/bbl of production are less reliable for extrapolation than spill 

rates/platform-year. 

1.3.4 Spill Sizes and Data Set Size

The GOM data are extensive, and they can be analyzed in several ways. In particular, it is 

possible to identify spills of a variety of sizes. For example, Anderson & LaBelle (2000) 

identifies 16 pipeline and 13 platform spills of over 1000 barrels in the interval of 1964-1999. 

Bercha (2002) identifies 31 pipeline spills of over 50 barrels in the interval of 1972-1999. 

Statistically models that are based on larger sets are more reliable, and the larger sample size 

permits tighter confidence intervals about estimated quantities. Also reporting pipeline spill 

probabilities for several different size spills facilitates the use of the results for a variety of 

purposes. Thus, this report estimates spill probabilities for pipeline and platform spills in four 

size ranges: 

50 barrels or greater, 

100 barrels or greater, 

500 barrels or greater, and 

1000 barrels or greater. 

One of the ways that this study offers the opportunity to improve upon past MMS practice is 

through the use of exact confidence intervals for the spill rate parameter of the Poisson 

distribution. This is described in Section 3.2.2. 

While the focus of this study is the probability of a pipeline or platform spill of a particular size, 

the spill data also support statistically derived models for the size of potential spills. This is done 

in Section 3.3.3 for pipelines and in 3.4.3 for platforms. 

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One approach for validating models is to estimate key parameters in several ways and to show 

that consistent results are obtained. In this case, it is possible to connect the estimated spill rates 

for different sizes of spills by using the spill size distribution. A more rigorous definition is 

presented in Chapter 3, but a hypothetical example can illustrate this. Assume that the spill rate 

for 50 or more barrels is 3.6 spills per year. If the spill size distribution indicates that spills of 

1000 barrels or more are 1/3 as likely as the smaller spill, then the indicated rate for the larger 

spill is 1.2 spills per year. 

This approach has the advantage of deriving the results for the larger spill sizes from the larger 

data set available at the smaller spill size. 

1.3.5 Links between Probability Exposure Variables 

As detailed in Section 2.4.6, there are very high correlations (as high as 99%) between 

cumulative production volume, time, and cumulative pipeline mileage for the GOM data. Thus, 

if a Poisson model works with one of these probability drivers, an analogous Poisson model is 

likely to work for the other probability drivers. This is demonstrated in Chapter 3. The high 

correlation between these three probability drivers is also one reason why a Poisson model can 

meet the standards for statistically satisfactory performance. All of the drivers are working 

together, instead of in different directions. 

As detailed in Chapter 3, this does not mean that models based on the drivers are statistically 

equivalent. The length of a year is constant over time, and the annual production volumes are 

relatively stable. However, the amount of pipeline mileage and the number of wells and 

platforms are increasing at a relatively steady rate over time. Thus, the cumulative mileage and 

the cumulative number of pipelines (which are the probability drivers) are non-homogeneous or 

changing over time. 

1.3.6 Poisson Distribution used in Previous MMS Models 

Anderson & LaBelle (2002) nicely describes (thus not repeated here) the Poisson model for the 

relatively uncommon event of an oil spill. As shown in numerous statistics text, this is 

equivalent to modeling the time between events (in this case – oil spills) as an exponential 

distribution. This linkage provides another approach to modeling oil spill probabilities in this 

situation. Using the exponential distribution provides us a way to use a continuous model of 

spill dates, rather than a discrete model of number of spills per year, per interval of a billion 

barrels of production, or per a quantity of pipeline miles or a number of platforms. 

For this study the general approach is to use the year, the production volume per year, or the total 

pipeline mileage (or number of spills) in each year. Thus, there is a clear identification of the 

year, the corresponding production volume, and the corresponding values of pipeline miles or 

platforms in service. This means that others can reproduce our results to try other variations or 

to check our results. 

The previous work reported in Anderson & LaBelle (2000) has used a somewhat different 

approach to modeling spill probability per billion barrels than taken in this study. That approach 

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was to construct “bins” of one billion barrels of production, and then calculate the number of 

spills in each bin. 

The spill rate per billion barrels (Bbbl) of production developed in this study is consistent with 

the results of the above work. In addition, as previously noted, the approach of this study 

supports the construction of exact confidence intervals for the spill probability. The formulas for 

that approach are specified in Chapter 3. While the estimation of the point estimate for spill 

probability does not depend on the assumed distribution – the construction of the exact

confidence intervals does. Thus, the validation of the Poisson model in Chapter 3 is an essential 

step. 

1.3.7 Summary on GOM Spill Probability Estimation 

Chapter 3 of this report entails numerous analyses including statistical distribution fitting to both 

inter-spill and volume data. Section 3.2 covers some initial Poisson probability distribution 

issues including the use of an exponential distribution goodness of fit approach to assess if a 

Poisson distribution is reasonable for spill rates. This issue is also examined in more detail later 

in Chapter 3 when other exposure variables are examined. This section also presents the 

mathematical formulas to compute exact Poisson confidence intervals if the Poisson assumption 

is justified. Exact Poisson confidence intervals are computed for pipeline spill rates and 

compared to those available on the MMS website. 

Section 3.3 focuses on the Anderson and LaBelle (2000) pipeline spill data. This section shows 

that a Poisson distribution adequately fits the observed data based on time as an exposure 

variable (other exposure variables are considered later in Chapter 3). Additionally a Weibull 

distribution is found to fit the pipeline spill volumes for this ≥ 1000 bbl data. 

Section 3.4 examines the Anderson & LaBelle (2000) platform spill data. While a Poisson 

distribution is found to adequately fit the 1964-1980 time interval, it is shown that the likelihood 

of these same Poisson data fitting subsequent years is very low. A Weibull distribution fits the 

platform spill data well.

Section 3.5 has analyses for pipeline spills ≥ 50 bbl. Evidence is presented illustrating that the 

use of the larger ≥ 50 bbl data set adds value to an understanding of OCS pipeline spills. Section 

3.5.1 shows that the exponential distribution fits the inter-spill data well for exposure variables of 

time, production volume in Bbbl, and pipeline mile-years. Thus a Poisson distribution is 

justified for the corresponding pipeline spill rates. Section 3.5.2 provides the exact Poisson 

confidence intervals for the three different exposure variables as well as illustrating some useful 

comparisons related to the Poisson and exponential distributions. Weibull distributions are 

found to fit pipeline spill volumes for the four data sets with thresholds of ≥ 50 bbl, ≥ 100 bbl, ≥

500 bbl, and ≥ 1000 bbl in Section 3.5.3. Section 3.5.4 examines the comparison of the four 

volume data sets including applications of the Weibull distribution. Conditional probabilities are 

introduced in this section to provide additional insights. Section 3.5.5 raises the issue of 

nonstationary Poisson processes in which the spill rates change over time. Alternative ways of 

quantifying spill rate uncertainty are explored in Section 3.5.6. 

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Section 3.6 examines platform spills ≥ 50 bbl. Concerns about the Poisson assumption were 

raised in the discussion of Table 2.5 for the Anderson & LaBelle (2000) platform spills data 

since 11 platform spills of ≥ 1,000 bbl occurred before 1980 and no spills from then until 1999. 

However for this 1971 – 2005 ≥ 50 bbl data set, the lower spill threshold includes more spills. 

Furthermore, the time period is split into two parts and a Poisson is found to fit both parts – with 

a declining spill rate. The 1990 – 2005 time period is the focus of the platform analyses. 

1.4 Methodology for Extending GOM Spill Rate Estimate to Alaskan OCS 

Section 4.1 introduces the structure of the problem and lists the uncertainties that make this a 

challenging problem. Section 4.2 introduces the Beaufort development scenario, which has been 

used by MMS and by Bercha (2006). In this case, it provides a concrete example to test the spill 

rates developed in Section 4.3 for pipelines and platforms. 

The spill rate development methodology described in Section 4.3 includes methods based on 

using the largest possible data base and models of spill size to develop spill rates. It also 

includes methods driven by selecting subsets of spill data and then building a statistical model. 

Section 4.4 introduces the problem of estimating spill rates for major Arctic specific pipeline 

hazards – ice keel gouging, strudel scour, upheaval buckling, and thaw settlement. A less 

quantitative discussion follows on platform hazards such as the impact of cold, dark 

environments or the probability of human error. 

These spill rates are applied to the Beaufort development scenario, which allows for useful 

conclusions about the relative merit for Arctic application of spill rates per bbl of production and 

spill rates per pipeline mile-years and per platform-years. 

1.5 Recommendations and Conclusions 

Much of the final chapter is presented through three sets of “bullets” that succinctly summarize 

the key results, the caveats and cautions, and possible future work. Section 5.4 presents an 

innovative approach to modeling pipeline spill rates that should produce more accurate models. 

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2 Data 

2.1 Introduction to Data Sets 

As the authors of this study are statisticians and not oil field experts, this study has relied on 

previously published works and data bases supplied by MMS. The data bases relevant to the 

statistical estimation questions in Chapter 3 focus on oil spills, oil production, and the associated 

platform and pipeline facilities. In most cases the data focus on OCS operations and production 

in the Gulf of Mexico (GOM), however, some production data from the Pacific and Alaska OCS 

regions were also included. 

As this study has been completed over a period of time, there has been the opportunity to update 

the various data sets. During the preliminary analysis of this study, data sets with an end date of 

1999 were analyzed. The review by MMS of the preliminary analysis allowed the data sets to be 

examined in detail, and some corrections were made. For this final report, it is the current 

corrected version of that data that is reported and analyzed. Most analyzes have been conducted 

with two end dates – 1999 and 2005. 

In most cases the data sets through 1999 and the more recent 2000 to 2005 data are reported 

separately, as there are often some specific issues to be addressed. 

2.2 Pipeline Spill Size and Frequency 

2.2.1 Pipeline Spill Data from MMS 

The OCS or GOM data have been drawn from three sources. Table 2.1 for pipeline spills of 

more than 1000 barrels is drawn from Anderson & LaBelle (2000). For comparison purposes, 

Table 2.2 includes those points from Table 2.1 in the date range of 1972 to 1999. For the 

reviewed preliminary analysis of this report, data for Table 2.2 for pipeline spills of more than 50 

barrels was drawn from PPLrepairs.mdb received from Cheryl Anderson in April 2001. For this 

final report, the data for Table 2.2 for pipeline spills of more than 50 barrels is based on the best

available MMS data provided in OCSGOM50plus17April2006.xls. 

MMS 12 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.1 OCS Pipeline Spills of 1000 bbl or More (1964-1999) 

Spill date Volume

October 15, 1967 160,638

March 12, 1968 6000

February 11, 1969 7532

May 12, 1973 5000

April 17, 1974 19,833

September 11, 1974 3500

December 18, 1976 4000

December 11, 1981 5100

February 7, 1988 15,576

January 24, 1990 14,423

May 6, 1990 4569

August 31, 1992 2000

November 16, 1994 4533

January 26, 1998 1211

September 29, 1998 8212

July 23, 1999 3200

As this analysis and an earlier approach using probabilistic risk assessment (Bercha 2002) both 

estimate oil spill probabilities for the Beaufort and Chukchi Seas, the data used for Bercha is also 

included in Table 2.2. This data was established by matching spill size and cause with 

information in the MMS data. This is intended to support comparison of the results of the two 

different approaches. Where differences in the data exist, in several cases it was the joint work 

of MMS and the Bercha group which supported the cleaner data set on which this report is based. 

MMS 13 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.2 GOM Pipeline Spills of 50 bbl or More (1972-1999) 

 

A&L 

Volume

Spill 

Volumes 

in Bercha

N = 31 

Spill 

Volume

N = 32 

June 13, 1972 100 100 

May 12, 1973 5,000 5,000 5,000 

April 17 1974 19,833 19,833 19,833 

May 21, 1974 65 65 

September 11, 1974 3,500 3,500 3,500 

February 29, 1976 414 414 

December 18, 1976 4,000 4,000 4,000 

March 29, 1977 250 250 

June 5, 1977 50 50 

October 18, 1977 300 300 

April 8, 1978 135 135 

July 17, 1978 900 900 

July 15, 1979 50 50 

January 29, 1980 100 

August 5, 1981 80 80 

December 11, 1981 5,100 5,100 5,100 

January 20, 1983 80 80 

February 16, 1985 323 323 

November 9, 1985 50 50 

February 3, 1986 119 119 

December 30, 1986 210 210 

February 7 1988 15,576 15,576 15,576 

January 24, 1990 14,423 14,423 14,423 

May 6, 1990 4,569 4,569 4,569 

January 3, 1992 190 

August 31, 1992 2,000 2,000 2,000 

June 17, 1993 50 50 

November 16, 1994 4,533 4,533 4,533 

January 22, 1998 800 800 

January 26, 1998 1,211 1,211 1,211 

September 29, 1998 8,212 8,212 8,212 

July 23, 1999 3,200 3,200 3,200 

MMS 14 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

2.2.2 Pipeline Spill Data from 2000-2005 

Table 2.3 summarizes spills over the most recent period. The availability of this data makes it 

possible to test the robustness of the methodology and the results. However, there are some

caveats that are necessary with this data. First, some of the results are preliminary (especially for

2005) and they may be revised over time. As one example of this, the total for Hurricane Ivan 

includes a 1720 barrel spill which is in a pipeline buried under a mudslide. Recovery efforts 

have not yet been successful, but effort is continuing so that spill volume may be reduced. 

However, it was felt that the advantages of including the additional data were larger than the 

uncertainties introduced by potential future changes. 

The second caveat is that the data for hurricanes Ivan (2004), Katrina (August 2005), and Rita 

(September 2005) differ from the data reported in earlier years for other hurricanes. For these 

spills MMS has asked for the reporting of fluids presumed lost with destroyed platforms and the 

linked damage to pipelines. Thus, there are more spills counted as part of each hurricane. 

Specifically, the Ivan total comes from 8 spills from 95 to 1720 bbl, the Katrina total comes from 

6 spills, and the Rita total from 8 spills (note: one 50 bbl spill may be from either so it is counted 

in both the 6 and the 8 count, but as 25 bbl in each total). Undoubtedly, there were similar spills 

in earlier years, but the reporting focused on spills that produced a witnessed oil spill.

Table 2.3 GOM Pipeline Spills of 50 bbl or More (2000-2005)

Spill date Volume

January 21, 2000 2240

September 15, 2004 3445

August 29, 2005 553

September 24, 2005 8162

2.2.3 Pipeline Spill Data from Bercha Report 

Table 2.4 summarizes the 31 OCS pipeline spills from 1972-1999 that were relied on for the 

Bercha report [reproduced from Table 2.1, p. 2.2 and Table A.2.2, p. A.2.6, Bercha, 2002]. This 

data is included because it provides significant information about sub-categories of key 

variables. Fortunately, the number of spills is small enough that more statistically reliable results 

are obtainable if the data set is used as a whole rather than as a collection of sub-categories, such 

as large diameter pipe, that is longer than 5 km and in deep water. 

MMS 15 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.4 OCS Pipeline Spills Summary (1972-1999)1, 2

Spill Statistics 

OCS Pipeline Spills 

By Category 1972-1999 Number 

of Spills

Average 

Volume

(bbl) 

Median 

Volume

(bbl) 

Exposure 

(kmyears) 

Frequency 

(spill per 

104

 kmyr) 

< 10" 16 2,141 173 142,892 1.1197 By Pipe Diameter ≥ 10" 15 4,070 1,211 111,011 1.3512 

Bad Depth Data 14 

< 10 m 6 2,310 1,211 161,966 0.3704 1 By Minimum Depth 

≥ 10 m 11 3,165 1,040 94,641 1.1623 1

< 0.5 km 0 0 0 2,359 0.0000 

.5 ≤ x < 2 km 2 2,335 2,335 25,484 0.7848 

2 ≤ x < 5 km 7 820 100 35,279 1.9842 By Segment Length 

≥ 5 km 22 3,859 850 192,270 1.1442 

Small 6 58 50 253,903 0.2363

Medium 12 317 230 253,903 0.4726

Large 10 4,133 4,267 253,903 0.3939 By Spill Size

Huge 3 16,611 15,576 253,903 0.1182

By Diameter, By Spill Size 

Small 4 58 50 142,892 0.2799

Medium 7 266 135 142,892 0.4899

Large 4 4,436 4,551 142,892 0.2799 <10" 

Huge 1 14,423 14,423 142,892 0.0700

Small 2 58 58 111,011 0.1802

Medium 5 387 312 111,011 0.4504

Large 6 3,932 3,600 111,011 0.5405 ≥ 10" 

Huge 2 17,705 17,705 111,011 0.1802

Small 50 ≤ spill size < 100 bbl 

Medium 100 ≤ spill size < 1,000 bbl

Large 1,000 ≤ spill size < 10,000 

bbl 

Huge 10,000 bbl ≤ spill size 

1

 The frequency rates for different pipeline depths were dropped from Bercha 

(2006) because MMS determined the water depths in the MMS GOM database 

were suspect. The results in Bercha (2002) ignore the 14 spills with missing 

depth data. If these 14 spills are distributed proportionately between the 

shallower and deeper depths, then the frequency rates would be 0.6755 spills per 

104

 km-yr for the shallower category and 2.1195 spills per 104 km-yr for the 

deeper category. 

2

 An early version of a data spreadsheet for Bercha (2002) was found to have 17 

of 33 records (1985+) with segment, date, and general location mismatched with 

rest of data. This may have been corrected after transmission, and Bercha (2002) 

MMS 16 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

does not use spill dates (except to separately analyze 1985+), thus the reported 

results should not be affected but caution should be used if this data source is used 

for further work. 

2.2.4 Spills in State Waters 

Table 2.2 does not include spills that were in state rather than federal waters. These have also 

been omitted from Anderson & LaBelle (2000) and from Bercha (2002). This is of some

consequence for the extension of these results to the Beaufort and Chukchi Seas, as on-shore 

terminations of pipelines seem likely to with some frequency pass through state waters. It also 

seems likely that from the perspective of most stakeholders it is the occurrence of a spill that 

matters – not whether it is in federal or state waters. It also seems likely that distance from spill 

to shore will have impacts on dispersion of any spill. 

There are good reasons for this omission. 

1. MMS does not have quality control over, or legal access to oil industry data in state 

waters. Spill data are incomplete to an unknown extent. Pipeline and platform data, 

especially pipeline mileage data by year, depth, etc. are unavailable. Given the 

incomplete data, it would be misleading to include unknown fractions of the spills, 

pipelines, platforms, and production. It is even possible that including some recorded 

“state” spills could lead to a false “sense of security and completeness” for some users of 

the data. 

2. How do you treat spills of commingled oil? If a pipeline that transports 5% OCS oil 

and 95% state oil, has a spill of 1000 bbl, does this count as 50 bbl OCS spill or 0.05 of a 

1000 bbl OCS spill? Also, given the data problems discussed in the first point, it may 

even be difficult to establish the federal and state shares. 

3. State waters in theory extend either 3 miles or 3 leagues (9 miles). However, offshore 

of Louisiana, this boundary was fixed long ago, before several additional miles of coast 

were eroded away. These differences exacerbate the difficulties of state-to-state 

comparisons and extrapolations. 

From a statistical perspective the difficulty is that for some measures of spill occurrence 

probabilities, it seems inappropriate to remove spills in state waters. For other measures of spill 

occurrence, it may be appropriate to remove the “state” spills. The principle that drives the 

choice is that the event (the spill) and the measure should treat the “state” question the same way. 

The following are suggested as consistent choices: 

Eliminating spills, platforms, and pipeline miles for state waters has the effect of treating 

the event and the variable consistently. Thus, the total of pipeline miles and of platforms 

must also be only in “federal” waters, if only “federal” spills are reported. 

Then the estimation of the probability of spills in state waters would be addressed using 

data bases specific to the pipeline and platform development, hurricane exposure, 

distances, etc. of each state. This is obviously beyond the scope of this study. 

MMS 17 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

The following are inconsistent choices: 

Eliminating spills in state waters for models using oil production or time as the 

occurrence measure is inconsistent. It reduces the event by removing spills in state 

waters from the data set. But there is no corresponding reduction in the measure of spills 

per billion barrels or spills per year. Thus this combination understates the true 

probability of an oil spill for oil that starts in “federal” pipelines but passes through 

“state” pipelines. 

This decision must balance the above principle with the complication and potential confusion 

created by using different data sets for different models. Also in some cases the pipeline and 

platform information may not exist for a proposed development, so that only spill rates based on 

production or time are possible. 

The application of spill rates to the Beaufort and Chukchi Seas is clearly affected by this choice. 

This can be illustrated by comparing the application of a spill rate per pipeline mile with a spill 

rate per Bbbl of production. For MMS’s responsibility for OCS areas, the focus may be on spills 

in that “federal” area. However, for other stakeholders and especially those state residents who 

live on the North Slope and who depend on marine subsistence resources, the question is the 

probability of a spill – not whether it is in state or federal regulated areas. Thus, approach 1 is 

recommended over approach 2. 

1. Applying a spill rate per pipeline mile can be applied to the total length of a pipeline 

through both federal and state areas. This does require the assumption that the 

probability of a spill in the two areas is not statistically different. Different water depths 

and different patterns of activity may imply this is a weak assumption; but, it is clearly 

better than no assumption at all. 

2. Applying the spill rate per Bbbl of production which includes only the “federal” spills 

analyzed in this report would mean that there would be no consideration of spills from

pipelines in state areas. 

MMS applications in oil spill risk analyses for the Alaska OCS Region do include estimates of

spills from existing or permitted offshore State platforms and pipelines. In the recent past, 

spillage estimates have derived from a combination of onshore North Slope spill statistics, TAPS 

experience, and extrapolation of OCS spill rate estimates. 

2.3 Platform Spill Size and Frequency 

2.3.1 OCS Platform Spill Data from MMS for 1964 – 1999 

The OCS platform data have been drawn from two sources. Table 2.5 for spills of more than 

1000 barrels is drawn from Anderson & LaBelle (2000). This table includes the 1969 Santa 

Barbara spill of 80,000 barrels. Table 2.6 for GOM spills of more than 50 barrels is drawn from

OCSGOM50plus17April2006.xls received from MMS in April 2006. Since Table 2.6 is limited 

to GOM spills it does not include any Pacific spills. 

MMS 18 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

A major distinction from the spills reported for pipelines is that many of these platform spills 

involve refined petroleum products such as diesel rather than crude oil or condensate. This will 

be addressed in more detail when spill causes are analyzed. 

Two items from Table 2.5 are worth noting. First Anderson & LaBelle (2000) reasonably 

combined three spills caused by one hurricane into a single spill “event,” which is done 

throughout this report. This can be justified as the three spills have a common cause. However, 

it is also necessary as the Poisson distribution assumes events do not happen simultaneously. 

The exponential inter-spill time is not zero. If needed the time interval is measured more finely. 

Similar statistical issues arise with the multiple spills reported at a common size such as 50 bbl 

(see also, discussion of estimated 50 & 100 values at end of this section). For estimating spill 

events this treatment of a hurricane as a common cause is appropriate, but it would not be for 

modeling the requirements for spill response equipment. 

The second item is that the data in Table 2.5 from 1964 to 1999 reflect a non-homogenous data 

series. There are 11 spills in 17 years and then 0 spills in 19 years. Unfortunately the longperiod without large spills ended in 2005 with spills associated with hurricanes Katrina and Rita. 

Table 2.5 OCS Platform Spills ≥ 1000 bbl (1964-1999) 

Spill date Volume

April 8, 1964 2559

October 3, 1964 11,8691

July 19, 1965 1688

January 28, 1969 80,000

March 16, 1969 2500

February 10, 1970 30,000

December 1, 1970 53,000

January 9, 1973 9935

January 26, 1973 7000

November 23, 1979 1500

November 14, 1980 1456

1

Hurricane Hilda destroyed 3 platforms with 

spill volumes of 5180, 5100, & 1589 bbl. 

The total volume is entered as a single spill. 

Table 2.6 uses a 1971 start date rather than the 1972 start date used with the bulk of the platform

analysis and with the pipeline data. This was done because 1972 happened to be a year with no 

GOM platform spills ≥ 50 barrels, while 1971 has 8 spills of this size. For consistency most 

analyses are done with the 1972 start date, but the inclusion of the 1971 data supports analysis of 

the impact of this choice. 

Table 2.6 with its 77 spills illustrates one of the difficulties with these data. Some of it is 

estimated rather than measured so the round numbers like 50 (10 spills) or 100 barrels (5 spills) 

are vastly over-represented in the data base. 

MMS 19 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

As discussed in Chapter 3, this requires that some values be adjusted by small amounts. With 

continuous probability distributions the probability is zero that two values will be the same if 

measured with sufficient accuracy, such as 50.00 and 50.01. Thus, statistical tests can be 

affected by measurement accuracy in a data set, and some tests require that values not be 

identical. These clusters of estimated values are adjusted so they are not identical so that the 

tests will work. However, these adjustments are much smaller than the variability concealed by 

estimating a spill of 75 to 125 barrels as 100 barrels. Thus, the statistically tested fit of the 

adjusted data to an assumed distribution (such as exponential inter-spill intervals) is worse than 

would be the fit of “measured or real” data. Thus, the statistical tests are more likely to reject the 

“fit” with estimated data than they would be with measured or real data. 

A second complication is that the use of 50 or 100 may have a systematic bias. Those reporting 

spills may round-up to be safe that they are not “under-reporting” or they may round-down to 

minimize the seriousness of the spill. MMS review acknowledged the potential of this bias, but 

suggested that estimating to round numbers is more likely than systematic bias. 

One consequence of the 10 spills estimated at 50 barrels is an unknown amount of overestimation of spill rates. If there is no bias of under- or over-reporting of spill volumes, then 

about half of the 10 spills should be below the 50 barrel threshold; and would thus if measured 

not be part of the data for this study. The impact of this overestimation is limited by the 

unknown number of spills whose reported (estimated) volume was less than 50 bbl, but whose 

actual volume was over the threshold. 

MMS 20 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.6 GOM Platform Spills of ≥ 50 bbl (1971-1999) N = 77 

Spill Date Volume Spill Date Volume Spill Date Volume

1971-04-05 200 1980-01-23 286 1985-01-23 60

1971-05-15 50 1980-03-08 258 1985-02-23 50

1971-05-27 50 1980-03-11 95 1985-06-03 643

1971-05-29 135 1980-05-16 150 1985-07-30 50

1971-07-20 100 1980-06-11 80 1985-09-02 66

1971-08-13 50 1980-10-15 83 1985-09-26 58

1971-10-16 450 1980-11-14 1,456 1986-11-13 52

1971-12-09 50 1980-12-02 118 1987-03-20 60

1973-01-09 9,935 1981-02-15 58 1988-02-19 50

1973-01-26 7,000 1981-04-06 210 1988-11-07 64

1973-06-20 239 1981-08-19 50 1988-11-16 55

1973-12-08 95 1981-11-28 64 1989-02-15 400

1974-07-10 130 1982-01-19 400 1991-10-13 280

1974-09-07 75 1982-04-29 228 1992-12-26 100

1974-10-04 50 1982-08-18 214 1994-11-23 148

1974-11-27 120 1983-01-30 600 1995-01-25 600

1974-12-22 200 1983-02-01 125 1995-07-06 75

1975-03-18 166 1983-03-09 77 1995-10-03 89

1975-09-21 100 1983-03-20 320 1995-12-15 435

1976-10-19 300 1983-04-14 200 1996-09-29 105

1977-12-14 77 1983-05-09 77 1996-12-31 62

1978-05-11 104 1983-05-16 95 1997-12-16 170

1979-01-30 321 1983-08-02 119 1998-04-29 100

1979-01-31 165 1984-06-20 50 1999-01-23 105

1979-04-14 60 1984-07-08 100 1999-09-09 125

1979-11-23 1,500 1985-01-22 107

Table 2.7 compares the Bercha (2002, 2006) spill data set with this data set for platform spills. 

While the individual spills were not identified with dates in Bercha (2002, 2006), the provided 

list of spill sizes and spill causes (Bercha 2002, Table 2.4 and Bercha 2006, Table 2.5) could be 

matched with the current data set. The subset of spills from Table 2.6 that are listed in the last 

column of Table 2.7 was formed by deleting all spills that were not crude oil or condensate (i.e. 

diesel and other refined petroleum products) and all spills that involved a well blowout. 

MMS 21 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.7 Comparison of Bercha (2002) and Similarly Selected Spills from

Current GOM Platform Spill Data Set (1972-1999) N = 21 

Spill Date

Bercha 

Volume

Current 

Volume

1973-01-09 9,935 9,935

1973-01-26 7,000 7,000

1974-07-10 130 130

1974-09-07 75 75

1974-10-04 50 50

1974-11-27 120 120

1978-05-11 104 104

1979-04-14 60 60

1980-11-14 1,456 1,456

1981-02-15 58 58

1983-02-01 125 125

1984-06-20 50 50

1985-09-02 66 66

1988-02-19 50 50

1988-11-16 55 55

1989-02-15 400 400

1991-10-13 280 280

1995-01-25 600 600

1995-07-06 75 75

1995-12-15 435 435

1997-12-16 1701

1998-09-17 1082 5

1

Product spill was mix of condensate and yellow paraffin, and loss 

of control during well shut-in. Either could be why not included in 

Bercha platform spill data set. 

2

Incident explanation noted that 103 bbl of 108 bbl spill recovered, 

so could be classified based on initial or final spill volume. 

2.3.2 GOM Platform Spill Data from MMS for 2000 – 2005 

The 9 spills from 2000 to 2005 included in Table 2.8 are drawn from

OCSGOM50plus17April2006.xls received from MMS in April 2006. Since Table 2.8 is limited 

to GOM spills it does not include any Pacific spills. The 2005 spills from hurricanes Katrina and 

Rita are based on MMS interim working documents with the information provided by Cheryl 

Anderson (personal communication, April 2006). 

While different platforms may have been damaged on different days by the same hurricane, it is 

much more reasonable to treat these as single events. As detailed in the notes to Table 2.8, the 

most recent hurricane spills are each aggregated values that can represent multiple products and 

multiple platforms. 

MMS 22 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

While there is no question about the severity of the hurricanes with spills included in Table 2.8, 

there was a significant difference in how the data were gathered as compared with earlier 

hurricane related spills. Those earlier spills typically were reported as a result of some spill 

response activity. Beginning with hurricane Lili, MMS adopted a much more aggressive 

strategy in identifying spills. Operators were queried about quantities of petroleum products that 

were never recovered as a result of the hurricanes.

For example the 6 individual Ivan spills that were aggregated into a total volume of 1053 barrels 

include 4 platforms that were destroyed or missing. In each case crude oil and refined petroleum

products on the platform before the hurricane are included in the spill total. If a similarly 

aggressive data collection strategy had been started in 1972, we believe that hurricanes would 

have placed more spills into this data base. 

Table 2.8 GOM Platform Spills ≥ 50 bbl (2000-2005) N = 9 

Spill Date Volume

2000-02-28 200

2000-08-09 60

2001-03-30 127

2002-10-03 1,5881

2003-05-09 264

2003-05-10 430

2004-09-15 1,0532

2005-08-29 2,2253

2005-09-24 7,3714

1

 Lili (3 spills of ≥ 50 bbls) 

2

 Ivan (6 spills of ≥ 50 bbls) 

3

 Katrina (14 spills of ≥ 50 bbls) 

4

 Rita (10 spills of ≥ 50 bbls) 

2.3.3 GOM Platform Spill Data Set 

The 78 GOM platform spills combine the data from Table 2.6 (except for the 1971 spills) with 

the data from Table 2.8. A few summary statistics are shown in Table 2.9, as two key decisions 

were required for this data. 

First, after consultation with MMS it was decided to include spills of refined petroleum products, 

as well as spills of crude and condensate. This was done because diesel spills were in many 

years the most common type of spill, and the average volumes were significant. The inclusion of

the refined petroleum product spills is the major difference for platform spills between the 

Bercha (2002 & 2006) reports and this report. That is the main reason why Table 2.7 is a subset 

of Table 2.6. Second, as detailed in Chapter 3, the rate of platform spills has declined over the 

1972 – 2005 time period. 

MMS 23 TGE Consulting
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Table 2.9 Summary of GOM Platform Spills ≥ 50 bbl (1972-2005) N = 78 

Average bbls (#) 

Crude & 

Condensate

Refined 

Petroleum Mixed All

1972-1989 1,005 (20) 215 (36) (0) 498 (56) 

1990-2005 217 (10) 163 (08) 3,059 (4) 714 (22) 

1972-2005 743 (30) 206 (44) 3,059 (4) 559 (78) 

2.4 Spill Occurrence Exposure Variables 

2.4.1 Potential Spill Occurrence Factors 

Section 2.4 describes the data for the exposure variables, which were discussed in Section 1.3.1 

and 1.3.3. These are combined with spill information for measures that include: 

Spills per year, 

Spills per billion barrels of production, 

Spills per pipeline-mile-year, and 

Spills per platform-year or per well-year. 

2.4.2 Time as a Spill Occurrence Measure 

For spill causes such as hurricanes, time seems to be a possibly appropriate spill occurrence 

measure. Each year there is a hurricane season and so each year this is a potential spill 

occurrence cause. This cause is logically related more strongly to the season than to the volume 

of oil production. 

Spills per year is also the most easily understood platform spill occurrence measure, so if it can 

adequately model a situation it is a natural choice. 

MMS 24 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.10 Yearly GOM Pipeline and Platform Spills of 50 bbl or More (1972-2005) 

year Pipeline 

Spills 

Platform

Spills 

1971 8

1972 1 0

1973 1 4

1974 3 5

1975 0 2

1976 2 1

1977 3 1

1978 2 1

1979 1 4

1980 1 8

1981 2 4

1982 0 3

1983 1 8

1984 0 2

1985 2 7

1986 2 1

1987 0 1

1988 1 3

1989 0 1

1990 2 0

1991 0 1

1992 2 1

1993 1 0

1994 1 1

1995 0 4

1996 0 2

1997 0 1

1998 3 1

1999 1 2

2000 1 2

2001 0 1

2002 0 1

2003 0 2

2004 1 1

2005 2 2

2.4.3 Volume of Oil Produced 

For use when scenario information on facilities cannot yet be estimated, this is the only 

probability measure possible. As the measure currently used by MMS, this also facilitates 

comparison with past work. There is one significant difference between how this variable is 

treated in this study and previous work by MMS. This report relies on exact Poisson confidence 

intervals for reported spill rates rather than other approaches used by MMS 

MMS 25 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

For analysis of production volume as a probability measure, this study takes the approach of 

measuring the interval between spills in units of production. Then this interval data can be tested 

as an exponential distribution to validate the Poisson assumption. If the Poisson function is 

acceptable, then the spill rate and exact Poisson confidence intervals can be estimated using the 

number of spills over the total exposure variable.

While this data is dominated by OCS production in the Gulf of Mexico, about 5% and 0.7% of 

the volume in recent years are respectively from the Pacific and Alaska regions. Table 2.11 

summarizes the data extracted from “OCS Crude&Condensate Production 1954 to Estimated 

2005 28April2006.xls” that was received from MMS. 

Since spill statistics are for GOM spills without inclusion of Pacific spills, the most consistent 

choice of production volume is for the GOM. That is what was done for all analyses related to 

platform spills. 

However, the total OCS production volume was used for the calculations of pipeline spills in 

Chapter 3. Key spill rate values were re-calculated using GOM production volume for 

extrapolations to Alaska in Chapter 4. As discussed in Section 2.4.6, these are highly correlated 

values so the statistical validity of Chapter 3 is not affected, although there are differences in 

calculated values. 

MMS 26 TGE Consulting
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach)

Table 2.11 Oil Production Volume (1972-2005) 

Year 

OCS 

Production 

Volume 

(106

 bbl) 

GOM 

Production 

Volume 

(106

 bbl) 

1972 395.9 373.3

1973 384.8 366.0

1974 354.9 338.1

1975 325.3 309.8

1976 314.5 300.5

1977 295.9 283.7

1978 287.9 276.0

1979 334.2 318.2

1980 274.7 264.6

1981 282.9 263.3

1982 314.5 286.1

1983 350.8 320.2

1984 385.1 354.6

1985 380.0 350.3

1986 384.3 355.5

1987 358.6 327.5

1988 332.7 301.2

1989 323.7 290.6

1990 304.4 274.5

1991 326.3 294.7

1992 347.5 304.8

1993 359.2 308.6

1994 372.3 314.0

1995 417.4 345.0

1996 433.1 368.8

1997 466.1 411.6

1998 490.6 444.3

1999 534.4 495.3

2000 559.1 523.0

2001 591.7 558.3

2002 602.3 567.4

2003 594.8 561.1

2004 567.0 535.0

2005 488.0 459.1

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2.4.4 OCS Pipeline Exposure 

Table 2.12 summarizes the number of miles of pipeline and number of pipeline segments for the 

OCS area of the GOM and Pacific. These data were provided by MMS 

[OCSOilPipelines1948to2006.xls, March 2006], and they are limited to those pipelines carrying 

oil. While petroleum spills can occur from other products, such as condensate, these are clearly 

the pipelines that represent a very large share of the spill occurrence rate. While it is better to 

focus on these data, as detailed in Table 2.14 this table of pipeline miles is proportional (r values 

exceed 99%) to the total number of km (miles) of pipeline used in Bercha (2002) and the draft 

data initially supplied with a much broader array of product codes. 

With the large correlations for different mileage measures, the results within the existing GOM 

dominated database would be comparable for all measures. However, when extrapolating to the 

Beaufort and Chukchi Seas, selection of the correct mileage data base is quite important as total 

reported mileage ranges from less than 8000 miles to more than 33,000 miles. 

If a pipeline segment were doubled in length, the spill probability associated with it would not 

double. Some portion of the probability depends on the number of connections to other 

pipelines, risers, and valves the pipeline has. That is probably better measured using the number 

of segments variable in Table 2.12. However, as detailed in Table 2.16, the correlation between 

pipeline segments and pipeline mileage is 0.905, thus both cannot be included in a statistical 

model based on a small data set due to problems with multi-collinearity. 

While the best data available, these values should be treated as estimates and not exact values. 

There are no available data on the accuracy of the estimate. However, it is likely that most errors

in these data would consist of segments that are either erroneously included or excluded, and this 

type of error is likely to be reasonably consistent from year-to-year. Thus for estimating trends 

these data can be treated as being accurate enough that other uncertainties will be far more 

important. 

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Table 2.12 OCS Pipeline Mileage and Segments 

Year 

Number 

of 

Segments 

Miles Year 

Number 

of 

Segments

Miles 

1964 859 537 1985 2,095 4,063

1965 870 565 1986 2,134 4,238

1966 885 654 1987 2,173 4,345

1967 919 742 1988 2,213 4,451

1968 957 887 1989 2,250 4,562

1969 1,002 1,170 1990 2,294 4,737

1970 1,062 1,339 1991 2,345 4,836

1971 1,153 1,504 1992 2,362 4,979

1972 1,249 1,740 1993 2,395 5,030

1973 1,312 1,932 1994 2,436 5,287

1974 1,344 2,049 1995 2,462 5,536

1975 1,389 2,200 1996 2,501 6,148

1976 1,442 2,451 1997 2,531 6,433

1977 1,497 2,563 1998 2,576 6,753

1978 1,568 2,818 1999 2,578 6,996

1979 1,643 2,956 2000 2,584 7,247

1980 1,695 3,120 2001 2,594 7,466

1981 1,766 3,343 2002 2,578 7,651

1982 1,837 3,511 2003 2,463 7,842

1983 1,907 3,703 2004 2,466 8,516

1984 2,012 3,925 2005 2,388 8,369

To support comparison of the results of Bercha (2002 & 2006) with this study, Table 2.13 

summarizes that data. The original data (Bercha 2002, Table A.2.1 (a), 8th column) is stated in 

terms of kilometers of pipeline placed in service in each year with an additional 2% added for 

pipelines with undated origins. This is the second column of Table 2.13. The third column of 

Table 2.13 is simply the cumulative values for each year. For comparison purposes with Table 

2.12 the fifth column of Table 2.13 states these cumulative values in terms of miles rather than 

kilometers, and the last column reports comparable values from Table 2.12. 

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It is suggested that the differences between the last two columns are the result of the additional 

efforts by MMS subsequent to the Bercha work to provide better quality data on the existing 

GOM infrastructure. 

Bercha (2002 & 2006) calculate the spill rate as the number of spills during the total time frame 

divided by the total exposure over the period. Thus, the total number of kilometer-years of 

pipelines represents the total exposure. This is calculated as the sum of the number of 

cumulative kilometers for each year. This exposure is shown in the last row of Table 2.13. 

Table 2.13 Bercha Pipeline Exposure 

Year Pipeline 

(km)

Cumulative 

Pipeline 

(km)

Cumulative 

Pipeline 

Mileage 

Cumulative 

Pipeline 

Mileage 

from Table 

2.12 

1972 435 435 270 1,740

1973 324 759 472 1,932

1974 214 973 605 2,049

1975 358 1,331 827 2,200

1976 526 1,857 1,154 2,451

1977 373 2,230 1,386 2,563

1978 657 2,887 1,794 2,818

1979 339 3,226 2,005 2,956

1980 343 3,569 2,218 3,120

1981 508 4,077 2,533 3,343

1982 400 4,477 2,782 3,511

1983 439 4,916 3,055 3,703

1984 469 5,385 3,346 3,925

1985 425 5,810 3,610 4,063

1986 385 6,195 3,849 4,238

1987 399 6,594 4,097 4,345

1988 610 7,204 4,476 4,451

1989 682 7,886 4,900 4,562

1990 808 8,694 5,402 4,737

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1991 501 9,195 5,714 4,836

1992 394 9,589 5,958 4,979

1993 291 9,880 6,139 5,030

1994 821 10,701 6,649 5,287

1995 667 11,368 7,064 5,536

1996 1358 12,726 7,908 6,148

1997 997 13,723 8,527 6,433

1998 947 14,670 9,116 6,753

1999 667 15,337 9,530 6,996

Total Exposure 185,694 115,385 114,705

The total exposure value shown in Table 2.13, 185,694 km-years does not precisely match the 

value of 187,183 km-years given in Bercha (2006, Table 2.1, spill size exposure). Note the value 

in Bercha (2002) must be lower, as all spill rates reported in 2002 (Table 2.1) are 35.65% higher 

than in 2006 (Table 2.1). While the cumulative mileage reported in each year for this report 

differs from the Bercha reports, the total exposure is very similar and the variables are very 

highly correlated, which will be discussed in section 2.4.6. 

2.4.5 Number of Platforms and Number of Operating Wells 

Table 2.14 summarizes the number of platforms in the GOM. This data was transmitted as 

Fixed_Facilities_production_history.xls by MMS in April 2006. This data included subcategorizations of platforms by type and amount of production and drilling activities. The most 

promising groups were all platforms, platforms with oil production, and all platforms except 

those with no production. For these three groups the minimum correlation was 0.975, so 

statistically their predictive abilities are virtually identical. During consultation with MMS, the 

professional judgment was that the total platform count variable was the most reliable, so that is 

listed in Table 2.14 and used for analysis. 

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Table 2.14 GOM Number of Platforms 

Year 

GOM # of 

Platforms Year 

GOM # of 

Platforms 

1972 1623 1990 3444

1973 1691 1991 3456

1974 1749 1992 3434

1975 1798 1993 3478

1976 1869 1994 3466

1977 1956 1995 3513

1978 2075 1996 3557

1979 2179 1997 3601

1980 2296 1998 3551

1981 2411 1999 3585

1982 2562 2000 3595

1983 2735 2001 3575

1984 2854 2002 3573

1985 3009 2003 3578

1986 3052 2004 3530

1987 3159 2005 3435

1988 3307

1989 3391

Table 2.15 is drawn from Bercha (2002) Table A.3.1, and it presents the data that was used to 

judge the spill rate for platforms in Bercha (2002 & 2006). The final row shows the total of 

well-years (119,714) that was used in both reports as the total exposure over the 1972 – 1999 

time frame. 

Table 2.15 Active Oil Wells from Platforms (Bercha 2006, from Federal Offshore Statistics 

report, MMS, October 2000)

Year 

Active Oil 

Wells Year 

Active Oil 

Wells 

1972 3,744 1986 4,406

1973 3,814 1987 4,543

1974 3,686 1988 4,627

1975 3,477 1989 4,507

1976 3,555 1990 4,515

1977 3,747 1991 4,549

1978 3,648 1992 4,612

1979 2,781 1993 4,774

1980 5,375 1994 4,846

1981 4,522 1995 4,950

1982 4,734 1996 5,040

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1983 4,142 1997 4,727

1984 4,138 1998 4,731

1985 4,321 1999 3,203

Total wellyears 119,714

2.4.6 Correlation Analysis 

There are very high correlations between time, cumulative production volume, and cumulative 

pipeline mileage in the OCS data base. Table 2.16 contrasts data from several sources including: 

Year 1972 – 2005 

Number pipeline segments Table 2.12 

Pipeline mileage Table 2.12 

Platforms Table 2.14

OCS Cumulative production volume Table 2.11 

GOM Cumulative production volume Table 2.11 

Bercha pipeline exposure (km-year) Table 2.14 

Bercha platform exposure (well-year) Table 2.15 

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Table 2.16 Correlations between Exposure Variables

# pipeline 

segments 

Pipeline 

mileage 

# 

Platforms

OCS 

Cum.

prod. 

GOM 

Cum.

prod. 

Bercha 

pipe km1

Bercha 

wells1

Year 0.949 0.990 0.926 0.775 0.711 0.984 0.530

# pipeline segments 1.000 0.905 0.992 0.636 0.548 0.936 0.570

Pipeline mileage 1.000 0.875 0.832 0.783 0.995 0.481

# Platforms 1.000 0.571 0.480 0.890 0.592

OCS cum. prod. 1.000 0.989 0.807 -0.005

GOM cum. prod. 1.000 0.733 -0.176

Bercha pipe km 1.000 0.468

Bercha wells 1.000

1

The correlations with the Bercha data set are only for 1972 – 1999. 

Most of these correlations are strong, and some are very nearly equal to 1.0 or a perfect 

correlation. This has two major implications. First, there is likely to be little or no added value 

to models that have more than 1 predictor variables. Second, results that are true for one 

exposure variable are almost certainly true for other highly correlated exposure variables. 

2.5 Spill Cause Analysis 

2.5.1 Introduction to Spill Cause Analysis 

There are several issues that must be addressed in developing statistically valid estimates for the 

causes of oil spills. These are required for this effort because of the differences between the Gulf 

of Mexico and the Beaufort and Chukchi Seas with respect to exposure to the different causes. 

One frequent cause of pipeline spills in the Gulf of Mexico is “third party impacts,” which are 

predominantly due to dragging anchors and fishing nets. Neither of these will be common in the 

arctic environment. 

These issues can be divided into four major categories. Spills can also be differentiated between 

those occurring on platforms and those from pipelines. Sections 2.5.3 and 2.5.5 include results 

for both pipeline and platform data. 

1. Identifying the primary spill cause 

2. Multinomial statistical variability 

3. Differences due to time and the manner of development 

4. Binomial statistical variability for GOM vs. general causes. 

An additional issue with respect to spill cause is the relationship between cause and size, which 

is analyzed in the final sub-section of this section. 

2.5.2 Identifying the Primary Spill Cause 

During the time span in which the Bercha reports (2002 & 2006) and this report have been 

conducted, MMS has made extensive efforts to improve the quality of information in its 

databases that summarize oil spills. This has included discussions for this analysis of which 

classification would be most appropriate for particular spills. As a result there are some

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significant differences between the causes reported here, the earlier Bercha work, and past 

classifications in the MMS data bases. 

2.5.2.1 Pipeline Spill Causes 

In spite of this work, spill cause classification still requires the exercise of judgment as to which 

of several causes is the primary one. So that others can double-check or modify this work, Table 

2.17 details how each GOM pipeline spill from 1972 – 2005 is classified as to cause. Table 2.17 

divides the causes into two groups, which will be important for the extension of GOM spill rates

to the Beaufort and Chukchi Seas. Some spills have causes that occur in the GOM but not the 

Arctic, such as hurricanes, damage from trawl fishing gear, and damage from the anchors of 

general ship traffic. In some cases it is unclear whether the anchor damage is from a workboat or 

third party traffic. Indicators such as distance from a platform or a greater likelihood that the 

damage from workboats will be noticed and reported have been used as needed. Other spills are 

due to causes such as corrosion and oil field operations that can occur anywhere. Table 2.18 

summarizes this into categories. 

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Table 2.17 Primary Cause of GOM Pipeline Oil Spills

Spill Date 

Spill 

Size 

GOM 

Specific Cause

1972-06-13 100 Corrosion

1973-05-12 5,000 Corrosion

1974-04-17 19,833 GOM Anchor drag

1974-05-21 65 Operational: anchor from derrick barge 

1974-09-11 3,500 GOM Hurricane Carmen

1976-02-29 414 Corrosion: after pipeline kinked by anchor 

1976-12-18 4,000 GOM Shrimp trawl damaged valve 

1977-03-29 250 Natural: mud slide

1977-06-05 50 Operational: lay barge anchor 

1977-10-18 300 GOM Anchor drag

1978-04-08 135 Mechanical/operational

1978-07-17 900 Operational: anchor drag 600’ from platform

1979-07-15 50 Operational: workboat searching for rig anchor 

1980-01-29 100 GOM Trawler drag broke valve 

1981-08-05 80 Corrosion: external or metal fatigue 

1981-12-11 5,100 Operational: service vessel anchor 

1983-01-20 80 Natural: mud slide

1985-02-16 323 Operational: pipeline dented, cracked during construction 

1985-11-09 50 Operational: spud barge anchor

1986-02-03 119 Mechanical/operational: pinhole leak during abandonment 

1986-12-30 210 Mechanical/operational: anchor or original construction 

1988-02-07 15,576 GOM Ship illegally dropped and dragged anchor 

1990-01-24 14,423 GOM Fishing net or anchor

1990-05-06 4,569 GOM Trawler net drag

1992-01-03 190 Unknown

1992-08-31 2,000 GOM Rig broke loose during Hurricane Andrew 

1993-06-17 50 Operational: workboat anchor

1994-11-16 4,533 GOM Trawl net damaged valve 

1998-01-22 800 GOM Mechanical damage: probably anchor

1998-01-26 1,211 Operational: anchor during overboard rescue 

1998-09-29 8,212 GOM Hurricane Georges

1999-07-23 3,200 Operational: jackup rig set down on pipeline 

2000-01-21 2,240 Operational: anchor drag from drill rig 

2004-09-15 3,445 GOM Hurricane Ivan

2005-08-29 553 GOM Hurricane Katrina

2005-09-24 8162 GOM Hurricane Rita

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Table 2.18 Summary of Primary Cause of GOM Pipeline Oil Spills (N = 36)

Number of Spills GOM Specific Cause 

9 Third party damage 

6 Hurricanes 

Non-GOM Specific Cause

14 Operational/mechanical 

4 Corrosion 

2 Natural: mud slide 

1 Unknown 

Table 2.19 summarizes the causes of the pipeline oil spills as previously reported in the Bercha 

reports. The table has been simplified from the original, by reporting on the number of spills in 

each cause classification without breaking these categories down into their sub-categories. For 

the purposes of this report it does not matter whether the corrosion was internal or external or 

whether the third party impact was due to anchors or trawling gear. Also the more aggregated 

data support statistical estimates with tighter confidence intervals due to the larger percentage of 

items in each category. 

One of the major differences between Table 2.19 and the work reported here is the definition of 

third party impact. For example the 3200 bbl spill listed in Table 2.19 under third party cause is 

from a jack-rig or spud barge. Due to the oil field related nature of the cause in the previously 

reported data this is classified as an operational impact. Similarly, several of the “anchor” 

impacts have been from work boats. Thus, the third party category in Table 2.18 contains 

significantly fewer spills than that category in Table 2.19. 

Table 2.19 Causes of GOM Pipeline Oil Spills from Bercha (2002 Table 2.2 & 2006 Table 

2.2)

Cause classification 

 # of 

spills Spill sizes (Bbls) 

 Corrosion 4 80, 100, 5000, 414 

 Third party impact 

 

16 19833, 65, 50, 300, 900, 323, 15576, 2000, 800, 

1211, 3200, 4000, 100, 14423, 4569, 4533 

 Operation impact 4 50, 50, 5100, 50 

 Mechanical 2 135, 210 

 Natural hazard 4 250, 80, 8212, 3500 

 Unknown 1 119 

 Totals 31

2.5.2.2 Platform Spill Causes 

 

The data on platform spills is presented differently than that for pipelines for two reasons. First, 

in several cases it is simply not possible to identify a primary cause. As a simple example, when 

a spill occurs during a diesel transfer from a coupling that breaks or separates is it a mechanical 

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failure or human error because the transfer was unattended. Second, unlike pipelines the only 

GOM specific cause is hurricanes. Thus, the level of detail that was needed to present the 

classification of pipeline spills as operational or third party is not needed here. Thus Table 2.20 

identifies the spills where a hurricane was identified as the primary cause. Table 2.21 

summarizes the number of spills by spill cause. A useful reference on platform spills is Sharples 

et al. (1989). 

Table 2.20 GOM Specific Cause (Hurricanes) Platform Spills

Spill Date 

Spill 

Size Cause

1974-09-07 75 Carmen

1974-12-22 200 repair of Carmen damage

1985-09-02 66 Elena

2002-10-03 1,588 Lili

2004-09-15 1,053 Ivan

 2005-08-29 2,225 Katrina 

 2005-09-24 7,371 Rita 

Table 2.21 Summary of Causes of GOM Platform Spills 1971-2005 (N = 78) 

Cause 

Primary 

Cause GOM Specific Cause (N = 7) 

7 7 Hurricanes 

Non-GOM Specific Cause (N = 71) 

65 35 Equipment failure 

33 23 Human error 

17 6 Sea condition 

13 5 Collision 

2 2 External damage 

Table 2.22 summarizes the causes of the platform oil spills from Table 2.5 of Bercha (2002). As 

indicated in the discussion with Table 2.7, these 21 spills are the crude or condensate spills that 

did not involve a fire or blowout from 1972 – 1999. 

Table 2.22 Causes of GOM Platform Oil Spills from Bercha (2002 Table 2.4 & 2006 Table 

2.5)

Cause classification 

 # of 

spills Spill sizes (Bbls) 

 Process facility release 13 130, 50, 120, 104, 60, 1456, 125, 50, 50, 55, 400, 

280, 75 

 Storage tank release 3 9935, 7000, 435 

 Structural failure 1 58 

 Hurricane/storm 2 75, 66 

 Collision 2 600, 108 

 Totals 21

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2.5.3 Statistical Variability and Multinomial Confidence Intervals 

When examining spill causes the appropriate probability distribution is the multinomial. This is 

a multiple category generalization of the two category binomial distribution which in a set of

random events counts the number of heads or tails, the number of successes or failures, etc. 

Because this is a relatively straight-forward application of descriptive statistics it is included in 

this chapter rather than Chapter 3. 

One large difference from previously published work is the inclusion of confidence intervals on 

the multinomial proportions (Goodman, 1965). This will help clarify realistic limits for the 

accuracy of these proportions and any calculations that might be based on them. Table 2.23 

shows a variety of confidence intervals for a specific cause and Table 2.24 shows 95% 

confidence intervals for all pipeline spill causes. In both tables the estimated proportion is 

simply divides the number of spills for the category (shown in Table 2.18) by the total number of 

spills (N = 36). 

Table 2.23 Confidence Intervals for Third Party GOM Pipeline Spill Proportion with 

Estimated Proportion of 25.0% = 9/36

Confidence 

Level 

Lower 

Confidence 

Limit 

Upper 

Confidence 

Limit 

80% 11.8% 38.2% 

90% 9.6% 40.4% 

95% 7.7% 42.3% 

99% 3.8% 46.2% 

Table 2.23 shows that even at a low or 80% confidence level for a high proportion category; the 

upper confidence limit is about 3.5 times the lower limit. At a high or 99% confidence level the 

upper limit is more than 10 times the lower limit. The 6 listed causes and the relatively small 

number of spills are the reason why these limits are relatively broad. Table 2.23 has been 

included to give a sense of how much difference the choice of a confidence level makes. In 

keeping with typical practice, Table 2.24 reports 95% confidence intervals for all causes. 

Table 2.24 95% Confidence Intervals for GOM Pipeline Spill Cause Proportions

Estimated 

Proportion 

Lower 95% 

Confidence 

Limit 

Upper 95% 

Confidence 

Limit GOM Specific Cause 

25.0% 7.7% 42.3% Third party damage 

16.7% 1.8% 31.5% Hurricanes 

Non-GOM Specific Cause

38.9% 19.4% 58.3% Operational/mechanical 

11.1% 0% 23.7% Corrosion 

5.6% 0% 14.7% Natural: mud slide 

2.8% 0% 9.3% Unknown 

MMS 39 TGE Consulting
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Table 2.25 applies the same statistical approaches to the 31 spills summarized in Table 2.19 from

Bercha (2002 & 2006). 

Table 2.25 95% Confidence Intervals for Bercha (2002 & 2006) Pipeline Spill Cause 

Proportions 

Estimated 

Proportion 

Lower 95% 

Confidence 

Limit 

Upper 95% 

Confidence 

Limit Cause

12.9% 0% 27.3% Corrosion 

51.6% 30.1% 73.1% Third party impact 

12.9% 0% 27.3% Operation impact 

6.5% 0% 17.0% Mechanical 

12.9% 0% 27.3% Natural hazard 

3.2% 0% 10.8% Unknown 

The data in this study for platform spill cause (Table 2.21) is used to construct Table 2.26 which 

reports 95% confidence intervals for all causes. 

Table 2.26 95% Confidence Intervals for GOM Platform Spill Cause Proportions 

Estimated 

Proportion 

Lower 95% 

Confidence 

Limit 

Upper 95% 

Confidence 

Limit GOM Specific Cause (N = 7) 

9.0% 1.2% 16.7% Hurricanes 

Non-GOM Specific Cause (N = 71) 

44.9% 31.4% 58.4% Equipment failure 

29.5% 17.1% 41.8% Human error 

7.7% 0.5% 14.9% Sea condition 

6.4% 0% 13.0% Collision 

2.6% 0% 6.8% External damage 

Table 2.27 applies the same statistical approaches to the 21 spills summarized in Table 2.22 from

Bercha (2002 & 2006). 

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Table 2.27 95% Confidence Intervals for Bercha (2002 & 2006) Platform Spill Cause 

Proportions 

Estimated 

Proportion 

Lower 95% 

Confidence 

Limit 

Upper 95% 

Confidence 

Limit Cause

61.9% 37% 86.6% Process facility release 

14.3% 0% 32.0% Storage tank release 

4.8% 0% 15.6% Structural failure 

9.5% 0% 24.4% Hurricane/storm 

9.5% 0% 24.4% Collision 

2.5.4 Differences Due to Time and Conditions 

While the focus of this study is on the extrapolation of GOM data to the arctic, there are 

additional differences between the data and potential developments which are outside the scope 

of this study. While some of these have been mentioned before, their potential impact on these 

estimates requires some further discussion. 

The GOM database analyzed here includes about four decades of data, and the extrapolation into 

the arctic will extend the time frame by several more decades. Over that period of time, there 

have been and will be advances in technology and regulation that can reasonably be expected to 

reduce the probability of oil spills. However, the effect of this is clearly not uniform across the 

various spill causes. For example, the understanding of corrosion, and the ability to monitor and 

control it are steadily advancing; along with the regulatory environment to improve in this area. 

On the other hand, the ability of an oil pipeline to withstand the impact of a dragging anchor or 

the ice keel of pack ice may not be advancing at the same rate. 

While this study focuses on statistically extrapolating from the experience represented in the 

GOM data base to the arctic environment, this initial study cannot address all issues. This study 

can reasonably be expected to address, and it does address larger issues such as GOM or arctic 

unique hazards, such as trawling gear and strudel scour. The scope of this study does not address 

more subtle impacts. For example, the probability of human error is linked to working 

conditions, such as extreme cold or darkness, which are larger issues in the arctic. 

There are also the impacts due to differences in the manner of development. Such differences 

include the typical platform size, water depth, and distance from shore and the typical pipeline 

diameter, length, water depth, and depth of burial (if any). These details are better addressed 

through engineering studies rather than this type of statistical analysis. 

As these factors are outside the scope of this study, the approach taken is to assume that the net 

effect of them would leave the statistically calculated oil spill risk unchanged. Obviously, this 

assumption is simply for the purposes of this study, as those with greater knowledge of the 

factors will apply that knowledge to move beyond the limitations of this study. 

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2.5.5 Statistical Variability and Binomial Confidence Intervals 

Instead of focusing on the individual spill causes which requires the use of a multinomial 

distribution, this problem can be thought of as involving two binomial probability distributions. 

For the application to the arctic, there is the binomial proportional split between arctic and 

“applicable or general” causes. For the GOM spill data, there is the binomial proportional split 

between GOM-specific causes and “applicable or general” causes. 

Thus, for pipelines the spill cause analysis is simplified to estimating the proportion of GOM 

pipeline spills with causes that are relevant to the Beaufort and Chukchi Seas. Table 2.28 is 

based on a characterization of hurricane and third party impact causes as GOM specific (at least 

as compared with Beaufort and Chukchi Seas spills). Table 2.28 is based on the normal 

approximation to the binomial, which is covered in most introductory statistics texts and courses. 

Exact binomial confidence limits (Clopper and. Pearson, 1934) implemented as Excel functions 

(Harper, 2005) are used to compute exact binomial confidence intervals used in some of the 

tables below and at various parts of subsequent chapters. The lower and upper confidence 

bounds are given below. Unlike the approximate normal based intervals, exact binomial 

confidence intervals are generally not symmetric. Normal based approximations to the binomial 

may not be accurate for small sample sizes or proportions that are close to 0 or 1. 

/2, 2( 1), 2

( , ) ( 1)

( , ) 1 ( , )

L

n B B

U L

B

p n B B n B f

p n B p n n B

α

α

α α

− +

= + − +

= − −

where B is the number of successes in the n Bernoulli trials and is the upper 1 2 , , n n fγ

th γ percentile of the F distribution with n1 and n2 degrees of freedom.

Table 2.29 provides the exact binomial confidence intervals that may be compared to the normal 

approximation intervals in Table 2.28. Since the proportion (p-bar in the table) is close to 50% 

the normal approximation is mainly limited by the small sample size in this case. The normal 

approximation is in this case too optimistic with tighter confidence intervals than given with the 

exact Table 2.29 intervals. 

MMS 42 TGE Consulting
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Table 2.28 Binomial Characterization of the Causes of Pipeline Oil Spills (Normal 

Approximation) 

# general causes 21

# GOM specific causes 15

total 36

p-bar 58.3%

σp 0.082

±conf. int. 

80% 6.9%

90% 10.5%

95% 13.5%

99% 19.1%

Table 2.29 Exact Binomial Characterization of the Causes of Pipeline Oil Spills 

# general causes 21 

# GOM specific causes 15 

total 36 

p-bar 58.3% 

σp 0.082 

Conf. Int. 

80% (46.3%, 69.6%) 

90% (43.3%, 72.3%) 

95% (40.8%, 74.5%) 

99% (35.9%, 78.5%) 

For platforms the spill cause analysis is simplified to estimating the proportion of GOM platform

spills with causes that are relevant to the Beaufort and Chukchi Seas. Table 2.30 uses the normal 

approximation to the binomial, and it is based on a characterization of hurricane causes as GOM 

specific (at least as compared with Beaufort and Chukchi Seas spills). Table 2.31 reports the 

same results but as exact confidence intervals. Once again the normal approximation is too 

optimistic though the main reason in this case is the closeness of the proportion p-bar to 100%. 

As the proportion gets close to 0% or 100%, the normal approximation variance gets 

unrealistically small. 

All binomial confidence intervals used in subsequent chapters are based on the exact binomial 

Excel functions. This results in a more defensible approach to quantifying distribution based 

parameter uncertainty. 

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Table 2.30 Binomial Characterization of the Causes of Platform Spills (Normal 

Approximation) 

# general causes 71

# GOM specific causes 7

total 78

p-bar 91.0%

σp 0.032

±conf. int. 

80% 2.7%

90% 4.1%

95% 5.3%

99% 7.5%

Table 2.31 Exact Binomial Characterization of the Causes of Platform Spills 

# general causes 71

# GOM specific causes 7

total 78

p-bar 91.0%

σp 0.032

Conf. int. 

80% (85.4%, 94.9%) 

90% (83.8%, 95.7%) 

95% (82.4%, 96.3%) 

99% (79.4%, 97.3%) 

2.6 Arctic Hazards and Extrapolating to the Arctic Environment 

Because some readers of this report will be relatively unfamiliar with Arctic specific hazards, 

this section is written at an introductory level. While these Arctic specific hazards are a key part 

of defining oil spill risk in the Arctic, this study’s focus has been on the extension of statistical 

results from the GOM to the Arctic. 

While much of the research cited here dates back to the 1970s and 1980s, there have been 

significant recent advances in knowledge driven by the Northstar and Liberty projects. The 

former is in production (14.4 Mbbl from 2001 to 2005 according to OCS Crude&Condensate 

Production 1954 to Estimated 2005 28April2006.xls transmitted by Cheryl Anderson). 

Northstar involves a subsea pipeline that has some to significant exposure to each of the hazards 

presented here. Because Northstar is placed on a man-made gravel island (Seal Island), the 

recent experience is more relevant to subsea pipelines than it is to oil platforms in the Arctic. 

Example differences between gravel islands and platforms include size, typical ice forces, do 

ships dock or anchor, and the use of ice roads vs. ships and helicopters. 

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A good summary of Northstar can be found in Owen et al. (2001), while more specific topics are 

addressed in Paulin et al. (2001), Leidersdorf et al. (2001), Dickins et al. (2001), and Miller 

(2001). 

2.6.1 Ice Keel Gouging 

As noted in Palmer and Niedoroda (2005), 

“gouges are found almost everywhere in the Arctic, that they occur from shore to 

water depths of at least 40 m, that some gouges are very deep (> 5m) and wide (> 

50 m), and that gouges are contemporary and not relic. A simple calculation 

shows that the force that the ice must apply to cut a deep gouge is very large, 

often of the order of 100 MN. It is not practicable to design a pipeline to 

withstand such a force.” 

While more recent work is also cited, the definitive work on ice keel gouging is still Weeks, et 

al. (1983, 1984). The scale of the effort and some key observations are summarized in the 

following quote from the 1984 reference (p. 229): 

“... between the barrier islands and the 38-m isobath the deepest gouge among 

20,313 measured along 1500 km of sampling track was 3.6m. In protected 

lagoons, on the other hand, the deepest gouge (0.7m) was much shallower (from a 

sample of 41 gouges obtained from 298 km of sampling track) and a large 

percentage of the 1-km segments examined (92%) contained no gouges at all.” 

The spatial distribution for this data is from Smith Bay in the west to near Camden Bay in the 

east with the heaviest concentration off-shore of the current North Slope on-shore infrastructure. 

This is the most likely area for initial off-shore developments. 

One important parameter for ice keel gouging is the number of gouges per mile or per kilometer. 

For the gouge density, Weeks et al. (1983, p. 20) obtained an average of 5.2 gouges/km-year 

(with a range from 2.4 to 7.9 over 3 years). In addition, no relationship with water depth was 

found (for deeper water). The shallower segments in the lagoons had fewer gouges. 

From 1974 to 1990 data on 5329 gouges was gathered in the Canadian Beaufort Sea (reported in 

Chayes et al. (2006). This showed a decreasing rate of gouging in deeper water (from about 1.5 

gouges/km in about 8 m to about 0.22 gouges/km in 30 m of water). There are a variety of 

explanations that could be advanced for the differences between the Weeks and Chayes results, 

but resolution of this is outside the scope of this study. As the Weeks data represent a larger 

sample in the right spatial location, this study relies on the Weeks data set. 

A second important parameter for ice keel gouging is the depth of the incision. Weeks et al. used 

the exponential distribution to model the probability of different incision depths. The parameter, 

λ, which is the inverse of the average incision depth, was found to depend on water depth. 

Specifically, the deeper the water was, then the deeper was the average incision depth (and the 

smaller was the λ). The relationship between water depth, z, and λ (both measured in meters) is 

shown in Equation 2.1. Note this equation is shown with the data it is derived from in Weeks et 

al. (1983, Figure 10 & 1984, Figure 4). 

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λ = 9.97e– 0.04z (2.1) 

More recently between 1996 and 1999, 48 ice gouges exceeding the minimum measurement 

threshold of 0.1 m were detected in the Northstar pipeline corridor (Leidersdorf, et al., 2001). 

These were all in shallower waters (< 12 m) and the maximum incision depth was 0.4 m. “In all 

four years, however, measurable gouges were confined to water depths exceeding 5 m.” These 

results are consistent with the earlier work, and these results are limited to shallow water. Thus, 

this study will rely on the earlier work by Weeks et al. which includes deeper gouges and deeper 

water depths. 

The work by Weeks et al. included the development of a probabilistic model for an ice keel 

gouge contacting the pipeline. Thus, rather than attempting to summarize a voluminous and 

detailed analysis, this study will simply rely on that probabilistic model. However, one key 

parameter of the probabilistic model is addressed in the data included in that original work. A 

key question is: what is the orientation of the ice gouge relative to the pipeline? If the ice gouge 

is angled to the pipeline then a gouge of a given length has a smaller probability of contacting the 

pipeline. Thus, the original example application is done at angles of 90o

 and 20o. This appears 

to have been done for illustrative purposes, and an angle must be chosen for this study. 

In shallower waters the gouge orientation has more variability. However, “because the fast ice 

edge generally parallels the isobaths, ice-ice interactions tend to force the nearshore ice to drift 

parallel to the coast even when the free-drift direction is not exactly parallel with the coast.” 

Since the principal ice movement in deeper waters is parallel to the coast and pipelines will 

generally be perpendicular to the coast, the angle between the pipeline and the ice gouge is best 

modeled as nearly perpendicular. 

Other work on ice keel gouging includes 

• Croasdale et al. (2005) which focuses on failure modes for the ice in ice keel gouging, 

• Croasdale et al. (2001) which focuses on design for icebergs (on the Grand Banks), 

• Morrison and Marcellus (1985) comparing Alaskan & Canadian Beaufort Sea scour data 

and methodologies, 

• Wadhams (1977) which describes ice keels in the Arctic. 

2.6.2 Strudel Scour 

Strudel scours represent the removal of bottom material by the drainage of fresh water on top of 

the ice during the spring. The most thorough study and modeling of the phenomenon was done 

in May 2000 to support the proposed Liberty Development Pipeline (Blanchet, Cox, Leidersdorf, 

and Cornell, 2000) with review by Eschenbach (2001). 

Based on that study and review, the following observations are made: 

1. Concerns about strudel scour are the largest directly in front of river mouths, as the rivers 

are the source of the water on top of the ice. During spring flows not all of the water 

flows under the ice. Thus, the more distant pipeline routes are from river mouths, the less 

of a concern there is with strudel scour. 

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2. The width and depth of the strudel scour depends on the water depth. 

a. While scours do occur under ice that is bottom-fast, those scours are smaller in 

size. While their relative significance has not been verified, there are at least two 

limiting factors for shallow water strudel scours. First, because the ice is bottomfast or nearly so, it cannot be depressed by the weight of water on top of the ice to 

form a pool of significant depth. Second, the limited space under the ice, can 

limit the ability of water to flow away from the strudel scour. 

b. For the Liberty Pipeline Data Set, the majority of the strudel scours occurred in 5 

to 10 feet of water. In water deeper than this, the strudel scours were shallower. 

Essentially, the water between the ice and the bottom is dissipating the erosive 

force of the water draining through the scour. A second possible effect is the 

“relief” provided by water draining through strudel features closer to shore. 

While the water depth limits may vary with the volume of water being discharged 

by a particular river in a particular year, further data gathering and analysis could 

define whether a 12’, 15’, or 20’ water depth represents a limit to the area of

concern for strudel scour. Note that in strudel scour studies linked to the 

Northstar development (Leidersdorf, 2001) “all of the strudel scour depths greater 

than 1.5 m were found to occur in water depths less than 4 m.” 

c. A second limit for the water depth in which strudel scour can occur is the 

maximum extent of the “over-flood” limit. For example, Blanchet et al. (2000, p. 

130) identifies a maximum over-flood extent of 3.3 miles off-shore with an 

average over 11 years of 2.59 miles (2.79 typo in final draft). This was in the area 

of the Sagavanirktok, Kadleroshilik, and Shaviovik Rivers. As another example 

measured a different way, Walker (1974) reported that overflood off of the 

Colville River extended only to the 3-6 m water depth in the Colville delta in 

three years of observations. 

3. While scour occurrence statistics can be calculated, the water depth limits imply that only 

a limited portion of any pipeline length is truly exposed to strudel scour. A pipeline from 

an off-shore platform generally starts at the deepest depth it is exposed to and goes 

relatively directly to shore. Thus, it is much more nearly perpendicular to the shore, than 

parallel with it. Thus, the question for determining the concern with strudel scour, is how 

much of this pipeline is in for example, 5 to 12 or 15 or 20 feet of water?

More recent work by Leidersdorf, Hearon, and Swank (2006) included data that suggests 

pipelines with hot oil may induce strudel scours – at least in shallow waters. “Given this 

relatively low frequency, an unexpected finding was the occurrence of five scour depressions in 

close proximity to the Northstar pipeline alignment. Four of the depressions were relatively 

small features in water depths less than 1.5 m, suggesting that the heat radiating from the 

pipelines predisposes the ice to strudel formation in shallow water.” While not advanced in the 

paper, another possible explanation is the trapping of along-shore flow of overflood waters when 

an ice road is built over the pipeline (see Trefrey et al., 2004, Figure 3-28b, p. 45). 

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Strudel scour alone does not cause a pipeline spill. Rather it represents the possibility of 

uncovering enough of a buried pipeline, which could lead to failure modes such as upheaval 

buckling, or even digging out underneath a pipeline to create a free-span. Thus, probability 

models must consider the density of strudel scours and the probability of scours of sufficient 

dimension to uncover a critical length of pipeline. 

Blanchet et al. (2000, Table 3.10) calculated a density at the Liberty location of 4.0 scours/mile2

-

year for 1997 data, 1.1 for 1998 data, and 2.9 for the combined data. 

There are several issues that cannot be addressed in this study for these data from Blanchet et al. 

First, it is not known how representative these values are of other potential pipeline locations. 

Second, while detailed strudel scour information from other years was not available, analysis of 

photo imagery indicated that in 11 years of data, the 1997 and 1998 years had the smallest extent 

of overflooding at this location. (Overflooding extent represents how far out to sea the 

freshwater has flowed on top of the ice.) See also Dickins et al. (2001) for more discussion of 

overflooding. 

To calculate the probability of uncovering a “critical length,” it is also necessary to know 

(Liberty values used shown in parentheses) the following: 

Depth of burial (8’) 

 Probability distribution for width of scour (see Blanchet et al. 2000) 

Relationship between width and depth of scour (assumed 45o

 slope) 

Length of pipeline vulnerable to strudel scours (1.8 miles) 

Critical length of uncovered pipe (100’). 

In the sensitivity analysis, use of a 27o

 slope rather than 45o was tested, and it reduced the 

probabilities by an order of magnitude. Perhaps due to granular sediments in the area of the 

Liberty pipeline route for those data points with width and depth measurements, the calculated 

average slope values were much lower. These were average slopes for individual scours ranging 

from 1o

 to 27o off the Sagavanirktok River, 1o to 14o off the Kadleroshilik River, and 1o to 5o off 

the Shaviovik River (Blanchet et al., 2000, p. 90). 

As a first order approximation within the limits of that data, it is reasonable to believe that 

likelihood of larger scours from years with more overflooding is balanced by the conservatism

between the 45o

 assumed average slope, and the measured average slopes that were typically 

much less than 27o

 value used in the sensitivity analysis. 

With these parameters the probability of a free span greater than 0’ was calculated to be 3.8x10-4

and the probability of a free span ≥ 100’ was calculated to be 5.2x10-5 (Blanchet et al., 2000, p. 

ix). 

 

2.6.3 Upheaval Buckling 

Upheaval buckling is more of an issue in the Arctic than in other locations, because the principal 

force is due to thermal expansion of the pipeline when filled with warmer oil as compared to its 

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temperature during construction – which is colder in the Arctic. However, for a spill to occur, 

this must result in fracture or buckling – not just result in pipe movement. 

As the engineering expertise and assumptions to model this are not within the scope of this 

study, it is assumed that the critical length defined for the probability of a strudel scour has 

appropriately considered the probability of upheaval buckling. Thus, the probability of upheaval 

buckling is assumed to equal the probability of a strudel scour. 

Assuming that the probability of upheaval buckling is equal to the probability of a problem due 

to strudel scour requires the assumption that design and construction of any buried pipeline has a 

sufficient margin of safety that upheaval buckling does not occur on its own. Note that if a 

pipeline is not restrained by burial in a trench, thermal expansion can be accommodated by side 

to side rather than vertical movements. 

2.6.4 Thaw Settlement 

Thaw settlement has been an issue for portions of the Trans-Alaska pipeline, where warm oil has 

melted permafrost and ice lenses below the pipe. This sinking of the pipe can be likened to an 

electric line that sags due to the weight of ice on it until the line snaps. 

Erosion due to the melting of permafrost is common along the North Slope of Alaska, thus the 

problems with thaw settlement start on-shore, can be high at pipeline landing sites, and can 

extend off shore due to subsea permafrost. This subsea permafrost off the North Slope of Alaska 

has long been recognized as a potential problem for oil and gas infrastructure. Nearest to the 

shore, the ice is frozen to the bottom and permafrost can form just as it does on-shore, but as 

detailed in Miller (2001) salt concentrations may be high and large ice lens and ice bonding may 

be rare. Farther off-shore permafrost does not extend all the way to the soil/water boundary. 

More importantly, the further off-shore that you are the deeper into the soil are the boundaries 

between unfrozen soil, seasonally frozen soil, and permafrost. It is only in permafrost that you 

find ice lens which when they melt lead to the most extreme cases of thaw settlement. 

This suggests that once a pipeline is “far” enough off-shore, then thaw settlement is not likely to 

be a problem. While more data and engineering analysis of heat flows is required to determine

how “far” off-shore this is, there is substantial work on subsea permafrost that has been done. 

For example one approach to defining the problem is the mapping of permafrost depths. Work 

of this type for the North Slope includes Osterkamp and Harrison (1977 and 1976), Neave and 

Sellman (1982), Rogers et al. (1975), Sellman et al. (1989), and Barry (1989). 

Paulin et al. (2001) describes how thaw settlement was an issue near-shore for the Northstar 

project, and the modeling and over-trenching with thaw stable backfill that was done (see also

Owen and Miller, 2001). 

A potential complication in some less expected locations may be the presence of relic 

permafrost. In the Laptic Sea of eastern Siberia, where the OCS is wider than is Alaska’s, relic

permafrost from when the sea levels were lower and the shelf was land has been found 

(Romanovsky, 2006). 

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As there is no statistical basis for estimating the probability of an oil spill due to thaw settlement, 

this study will not attempt to do so. 

While it is outside the scope of this study, it is worth noting that if a clear design standard will be

applied to this phenomenon, then the design standard is potentially another way to establish a 

spill probability. For example, suppose that the design standard is for 1 spill every 100 or every 

1000 years. Such values can be converted into the probability of a spill. 

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3 Gulf of Mexico Spill Rate Estimation 

3.1 Introduction to Analysis of Data 

This chapter covers numerous statistical analyses and often involves fitting theoretical statistical 

distributions to the data sets described in Chapter 2. The primary focus of the distribution fitting 

is either on modeling the inter-spill distributions or on the volume of the spills. The inter-spill 

distributions lead directly to assessing if the assumption of a Poisson distribution is appropriate 

for the OCS and GOM data. The Poisson process assumption has been attacked in some reviews 

(Givens 2002 & Zeh 2002) of the Anderson & LaBelle (2000) publication. Because of the 

criticality of the Poisson assumption, Section 3.2 will focus on the general use of the Poisson 

distribution before subsequent sections assess the applicability of the Poisson for the OCS data. 

After the initial Poisson section, the data from Anderson & LaBelle (2000) are analyzed for both 

inter-spill and volume aspects in Section 3.3. Applications of the exact Poisson confidence 

intervals described in Section 3.2 are applied to these data. Pipeline spills are covered in Section 

3.3, and platform spills are covered in Section 3.4. 

Sections 3.5 and 3.6, respectively for pipelines and platforms, introduce extensions to the work 

in Anderson & LaBelle (2000). One form of extension is using smaller thresholds, such as spills 

≥ 50 bbls, for data selection as described in Chapter 2. Results of integrating distributions based 

on differing thresholds is given, as it may be more accurate to use larger data sets to predict even 

just those spills of at least 1000 bbl. These sections also address a key issue of different 

exposure variables and tests if the Poisson assumption is relevant over time, production volumes, 

pipeline miles, and platform numbers. 

Minor adjustments in spill volumes are sometimes made to avoid duplicate values. For example 

if there are four spill volumes of 50 bbl, these are changed to 50 bbl, 51 bbl, 52 bbl, and 53 bbl. 

If many volume ties are found at say 50 bbl, these are changed to 50 bbl, 50.1 bbl, 50.2, etc. 

Theoretically, the probability of any two continuous values being identical is zero, and these 

minor adjustments avoid some technical issues such as the stacking of points on a probability 

plot and do not impact the relevance of the findings presented here. 

3.2 Poisson Distribution 

3.2.1 Poisson Concerns about Exposure Variables

The Poisson distribution is often used in counting processes in which events occur over some

elapsed exposure variable. Often the exposure variable is time and the Poisson is used to 

estimate the likelihood of so many events over a time period of interest. For example, what is 

the likelihood of 15 phone calls in a 1⁄2 hour time period at a call center? Even if a Poisson is 

appropriate, does the mean arrival rate of phone calls change over time? If the arrival rate 

changes over time, such as spills becoming less likely due to better regulation and management, 

then the Poisson process is defined by statisticians as non-stationary. 

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Time is only one of many potential exposure variables. One of the beauties of the Poisson is that 

it is flexible over both time and space, and that it can be measured in units of produced oil, 

pipeline-miles, or number of platform-years. 

One issue with testing the Poisson assumption is that few discrete distributions are in common 

practice compared to the many continuous distributions used. Additionally fewer methods exist 

to test discrete distribution assumptions than for continuous distributions. The approach 

undertaken in Chapter 3 indeed relies on a link between the Poisson and a continuous 

distribution. 

Generally found in calculus based probability and statistics text is the relationship between the 

discrete Poisson distribution that can realize only values of 0, 1, 2 ... for counting events and the 

continuous exponential distribution that can realize any observed values > 0. In such texts it is 

shown that if and only if the inter-event times are exponentially distributed then the process 

generating the discrete events is a Poisson process. Thus one can test the inter-event times to see 

if a theoretical exponential distribution adequately fits the observed data. If so, then the 

assumption of a Poisson distribution for the events is justified. As discussed earlier there are 

generally more ways to test a goodness-of-fit question when the distribution is continuous. 

In the context of the OCS data, inter-event is inter-spill for each of the potential exposure 

variables. For both pipeline spills and platform spills, three exposure variables are analyzed. 

Time is the first exposure variable and is tested in subsequent sections of Chapter 3. A second 

exposure variable has been production volume in Bbbl. A third exposure variable is pipeline 

mile-years in thousands of miles (KMiles). For platforms the third exposure variable is 

platform-years. 

Testing the Poisson assumption via an exponential goodness-of-fit requires that the days between 

spills, or the production volume between spills, or the number of pipeline mile-years between 

spills, etc. be computed. If these inter-spill amounts are found to be adequately modeled by an 

exponential distribution, then using a Poisson for the spill events is justified. 

Data given in Chapter 2 show the annual production volumes and annual pipeline miles. To 

compute the volume and pipeline mile-years between spills, the number of days in each year of 

the study horizon that capture the inter-spill time is computed. Assuming that the production 

volumes and mileage are relatively constant with any given year, the Bbbl of production and 

KMiles of pipeline mile-years represented by the inter-spill time period are computed. These 

numbers are then input to the corresponding exponential goodness-of-fit tests. If the exponential 

fits these inter-spill amounts, then a Poisson assumption is justified for that exposure variable. 

3.2.2 Exact Poisson Confidence Intervals 

Once a Poisson distribution has been justified, one can begin to estimate the spill rate. The rate 

is merely the mean of the Poisson distribution. Concern still must exist to see if a time varying 

Poisson mean (also known as a non-stationary Poisson process or a non-homogeneous Poisson 

process) is needed. For the time being in this section it is assumed that the assumption of a 

stationary non-changing mean is appropriate though this assumption is examined in Section 3.6. 

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Bounding the uncertainty in a parameter estimate is standard statistical practice, and it has been 

mentioned in several reviews. Quantification of this uncertainty is based on the level of 

confidence desired and the appropriate method for the parameter of interest. The parameter of 

interest for OCS is the estimate of the mean of the Poisson process. This is the rate at which 

events (spills) are estimated to occur. As discussed earlier this rate depends on the selection of 

an exposure variable (time, production volume, pipeline mile-years, platform-years are used in 

Chapter 3). 

While not mandatory it is common practice to develop 95% confidence intervals. For the 

Poisson distribution the corresponding interval should not be developed using standard normal 

based confidence interval approaches. That is, one should not break an exposure variable – say 

the continuous variable production volume in Bbbl into individual bins from which a mean and 

standard deviation are computed to form a confidence interval. Exact methods for Poisson 

confidence intervals have been documented (in obscure places admittedly) for many years and 

are given below. These may easily be computed in Excel though with a caution (Buchan, 2004 

on the web at http://www.nwpho.org.uk/sadb/Poisson%20CI%20in%20spreadsheets.pdf) due to 

an Excel function inaccuracy that does not impact the OCS application. 

From Johnson and Kotz (1969, pp. 96) are the formulas in Equation 3.1 where λ (the more 

common Poisson mean notation) is used instead of the θ used in Johnson and Kotz. The first 

formula for λ L represents an exact lower confidence interval for the mean spill rate λ while the 

second for λU is the formulation for the upper confidence interval. Taken together these form

the 95% confidence interval used later in Chapter 3 where α is set to 0.05. These confidence 

intervals are based on the chi-square (χ

2

) distribution. 

2 2

2 , 2( 1),1 2

1 1

2 2

; 2

ExposureVariable ExposureVariable

x

L U

χ χ α

λ λ

⎛ ⎞ ⎛ ⎜ ⎟ ⎜

⎜

⎜

⎜

⎜ ⎝ ⎠ ⎝

+ − = = ∑ ∑x α

⎞

⎟

⎟

⎟

⎟

⎟

⎠

 (3.1) 

Generally in statistics increasing the sample size decreases the width of confidence intervals. In 

this case, the subscript x is the number of spills, and the basis for the number of degrees of 

freedom for the chi-square variable. Then the amount of the exposure variable is in the 

denominator of Equation 3.1. To check that this formula behaves as expected, assume that the 

number of spills and the amount of exposure are both doubled (which keeps the spill rate 

constant). Doubling the number of degrees of freedom more than doubles the lower χ

2

 value, so 

the lower limit goes up and is closer to the estimated average, since the exposure doubled. In 

like fashion doubling the number of degrees of freedom less than doubles the upper value, so the 

upper limit has decreased. Thus, a larger sample at the same spill rate has a tighter or narrower 

confidence interval. 

The resulting confidence interval will generally be tighter than the inaccurate intervals based on 

dividing the exposure variable into artificial subunits. 

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3.2.3 Comparison of MMS and Exact Poisson Confidence Intervals 

Below is a comparison of the 95% confidence intervals found on the web at 

http://www.mms.gov/eppd/sciences/osmp/pdfs/ConfidenceIntervals2.pdf and exact Poisson 

confidence intervals. Both are endeavoring to create 95% confidence intervals for the pipeline 

spill rates between the time periods given in the below Table 3.1. 

Table 3.1 95% Confidence Interval Comparison Based on Anderson & LaBelle (2000) 

Pipeline Data with Production Volume as the Exposure Variable 

OCS 

Pipelines 

# 

Spills 

Volume

(Bbbl) 

Rate 

(Spills/Bbbl) 

MMS Confidence 

Interval 

Exact 95% Poisson 

Confidence Interval 

1964-

1999 16 12.00 1.333 (0.54, 2.12) (0.76, 2.17) 

1985-

1999 8 5.81 1.377 (0.00, 2.77) (0.59, 2.71) 

The intervals reported on the web are based on dividing the production volume into 1 Bbbl units 

and then computing the confidence intervals based on N = 12 (for 1964 – 1999) assumed 

independent observations. With small sample statistics, this approach would also typically 

assume that the data are from a normal distribution. This introduces an unnecessary binning 

process and one that may be inaccurate for non-integer Bbbl. The associated statistical 

procedure may allow the possibility of negative values in the confidence intervals which are then 

set to zero. The exact approach with results seen in the final column of Table 3.1 is based on 

sound conceptual theoretical underpinnings and is also easier to compute. 

3.2.4 Compound Poisson Distribution 

A topic worth mentioning is the compound Poisson distribution (also called a mixture of Poisson 

distributions). Clark & Harper (2000, beginning pp. 113) discuss this topic from an application 

perspective while Johnson & Kotz (1969, beginning pp. 111) provide a more theoretical 

foundation. 

For example, if there are multiple spill modes each represented by a Poisson, then the combined 

spill probability may be represented by a combination of individual Poisson distributions. The 

weighting function for each individual Poisson depends on the appropriate assumptions that 

should be based on sound engineering and/or statistical rationale. In future work, this could 

potentially be employed in the GOM to Arctic transition. It would have to fold in both the 

uncertainty in the Poisson rates and the uncertainty in the proportions (weighting functions) for 

the different spill modes. 

3.3 Pipeline Spill Analyses Based on Spills ≥ 1000 bbl (1964 – 1999) 

Section 3.3 covers pipeline spills using the data found in Anderson & LaBelle (2000). Both 

inter-spill and volumes are analyzed. In a similar vein Section 3.4 examines platform spills 

using the data from Anderson & LaBelle (2000). 

MMS 54 TGE Consulting
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3.3.1 Pipeline Inter-Spill Distribution Analysis 

A variety of statistical hypothesis tests and graphical procedures were used in the analyses 

supporting Chapter 3; however, the presentation in this chapter will often be limited to the two 

graphical based procedures found to be the most understandable and informative. These figures 

will be supplemented by other results when felt necessary to support a given situation. We note 

for the non-statistician that fitting statistical distributions to data is both an art and a science. 

Different statistical tests may give differing results and an engineering statistician must be 

willing to blend these sources to find the most logical choice.

Figures 3.1 and 3.2 are based on the 16 pipeline spills of at least 1000 bbl found in Table 2 of 

Anderson & LaBelle (2000) (also in Table 2.1 of this report). For each spill the inter-spill time 

in days was computed resulting in 15 inter-spill times. As this is approximately a 31 year time

interval (1967 – 1998), the mean inter-spill time is 773.6 days (a little over 2 years). This 

excludes an inter-spill time for the final spill of July 23, 1999 as there is no subsequent spill date. 

Figure 3.1 is a probability plot for an exponential distribution. The blue lines represent 95% 

confidence limits on the modeled exponential distribution while the red circles represent the 

actual observed data. The AD (Anderson-Darling) goodness-of-fit test statistic of 0.337 is not 

meaningful by itself; however, the associated p-value of 0.739 clearly indicates that an 

exponential distribution adequately fits the data based on this test statistic. P-values ≥ 0.05 

indicate that the associated goodness-of-fit test is not rejected at the 95% confidence level. 

Statistical tests are aids and should not be relied on in isolation. Graphical assessments are more 

important and some language is needed to represent the application of professional assessment. 

While somewhat colloquial, this report uses the acronym of TLAR (That Looks About Right) in 

line with what may be approaching nearly a century of use. In Clark and Harper (2000a) the 

acronym is credited to Walt Giffin who introduced it to the authors in their graduate statistical 

work. The TLAR (That Looks About Right) is a visual assessment of how the empirical or 

observed data fits a given theoretical model. Data analysis should always involve visual 

assessments as this provides a medium easily understood by almost anyone and the human 

pattern recognition capability is a needed tool for identifying trends, outliers, and data requiring 

detailed analyses. While it does take a trained eye with necessary experience to fully assess such 

visual goodness-of-fit measures, it allows the selection of statistical distributions in those cases 

where numerical statistics are not sufficient to make a final determination. Figure 3.1 along with 

the Anderson-Darling results support an exponential distribution. 

Figure 3.2 further supports an exponential distribution for the inter-spill times based. The 

smooth line represents the theoretical cumulative distribution function (cdf) for the hypothesized 

distribution (exponential in this case) versus the step function empirical cdf. A visual TLAR 

comparison finds these two lines in good agreement. Since these inter-spills times are 

adequately modeled by an exponential, as explained in Section 3.2.1, the assumption of a 

Poisson distribution over time is justified. 

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Days Since

Perc

ent

10 100 1000 10000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Mean 773.6

N 15

AD 0.337

P-Value 0.739

Probability Plot of Days Since

Exponential - 95% CI

Figure 3.1 Exponential Probability Plot of Pipeline Inter-Spill Times Using Anderson & 

LaBelle (2000) Data 

Days Since

Perc

ent

0 1000 2000 3000 4000

100

80

60

0

40

20

Mean 773.6

N 15

Empirical CDF of Days Since

ponential

n

& LaBelle (2000) data

Ex

Figure 3.2 Exponential Empirical CDF Plot of Pipeline Inter-Spill Times Using Anderso

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3.3.2 Poisson Rate for ≥ 1000 bbl Spills 

is justified. 

L

The last section examined and affirmed the validity of the Poisson assumption for larger spills 

when using time as the exposure variable. Table 3.2 defines the rate and confidence intervals for

that data set and a later subset. The later subset 1985-1999 inter-spill times have also been found 

to be well fit by an exponential distribution (though the results are not shown) and thus the 

application of the Poisson distribution for quantification of spill rates

Table 3.2 Spill Rate per Year for ≥ 1000 bbl Spills 

Time Period # Spills Exposure 

Variable 

Sum Exposure 

Variable 

Rate 

(Spills/year) LCL UC

1964-1999 16 Integer Years 36 0.444 0.254 0.722 

1985-1999 8 Integer Years 15 0.533 0.230 1.051

Intuitively, one would expect the average rate for the Poisson distribution (spills/year) to be the 

inverse of the average rate for the exponential inter-arrival time between spills. This is only 

approximately true, because the inter-arrival distribution d

ig

ata have 1 less data point, and it 

nores the time before the first spill and after the last spill. Thus for 1964-1999 inverting the 

 days to years equals 0.472 spills/year (= 

tinuous

distributions such as the exponential and Weibull distributions used often in this report. No 

goodness of fit for a Poisson existed in Mintab until summer 2005 in which a downloadable 

patch that upgrades the user to Minitab 14.2 adds a chi-square goodness of fit test for the 

60 spills for a quality application of the Chi square test. This 

average 773.6 days between spills, and converting from

365/773.6) rather than the 0.444 spills per year shown in Table 3.2.

Because of its importance, the exact relationship between the Poisson and exponential is detailed

and illustrated for three exposure variables in Section 3.5.2. This important relationship allows 

the better set of statistical tools for continuous distributions to be used effectively; otherwise, less

precise goodness of fits goodness of fit tests for discrete distributions such as the Poisson would 

require binning of the data and more serious sample size concerns. 

For example, Minitab 14 (the current version of this well known statistical package) does 

probability plots along with the Anderson-Darling goodness of fit test for numerous con

Poisson. However chi-square goodness of fit tests requiring binning of the data, which is 

somewhat arbitrary, so that different users may get varying results. Additionally the chi-square 

goodness of fit tests requires minimum expected bin frequencies to be valid. A common 

standard is an expected bin count of at least 5 observations. Thus, 12 bins of one Bbbl of 

production would require roughly

is likely to be a problem for the small data sets available. 

3.3.3 Pipeline Spill Volume Distribution Analysis 

A brief overview of the Weibull distribution is included here. The cumulative distribution 

function (cdf) in all of the empirical cdf plots, such as Figure 3.2, is the probability of the 

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random variable being ≤ some value. The cdf is represented in the statistical literature by F(x). 

For continuous distributions such as the exponential or Weibull, this is the integral of the f(x) 

that represents the probability density function (pdf). The random variable x in F(x) is whatever 

variable is being modeled such as spill volumes. For example F(5000) = P(x ≤ 5000) or 

probability that a spill volume would be less than or equal to 5000 bbl. For the Weibull 

distribution F(x) is given below where ν , , α β represent the threshold (or Thresh on the plots), 

scale, and shape parameters given in the Minitab probability and empirical cdf Weibull plots. 

.

exp .

( ) 1 exp , ; 0

where implies e raised to a power

for x otherwise x F x

β

ν ν

α

⎡ ⎤ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦

> − = − −

The complementary cumulative distribution function (ccdf) is 1 – F(x). For example P(x > 5000 

bbl) = 1 – F(5000), and it is the probability that a given spill will exceed 5,000 bbl. Since each 

Weibull Minitab plot gives us values for Thresh, Scale, and Shape or ν , , α β it is relatively easy 

to compute either F(x) or 1 – F(x). 

The analysis reported here supports the Weibull distribution (parameters for shape, location, and 

threshold given in figures) as an adequate model for the sixteen pipeline spill volumes in 

Anderson & LaBelle (2000). This fit of a Weibull distribution is not as good as subsequent 

Weibull fits for volumes in other sections of this chapter primarily due to the inclusion of the 

1967 spill volume of 160,638 bbl that is not in the time period covered in other sections. The 

Weibull is the best fit based on the Input Analyzer’s Squared Error criterion (Kelton, Sadowski, 

and Sturrock, 2004, chapter 4), is not rejected by the Input Analyzer’s Kolmogorov-Smirnov 

goodness-of-fit test (p-value > 0.15), and looks reasonable visually in the probability plot below 

in Figure 3.3 as well as the empirical cdf plot in Figure 3.4. It does not pass the AndersonDarling test as seen in Figure 3.3; however, the other evidence leads to the overall acceptance of 

the Weibull distribution. 

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A&L Volume - Threshold

Perc

ent

100 1000 10000 100000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape

1.032

0.6509

Scale 9944

Thresh 1000

N 16

AD

Probability Plot of A&L Volume

3-Parameter Weibull - 95% CI

P-Value <0.010

Figure 3.3 Weibull Probability Plot of Pipeline Spill Volumes Using Anderson & LaBelle 

(2000) Data

A&L Volume

Perc

ent 100

80

60

40

20

0

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Shape 0.6509

Scale 9944

Thresh 1000

N 16

Empirical CDF of A&L Volume

3-Parameter Weibull

Figure 3.4 Weibull Empirical CDF Plot of Pipeline Spill Volumes Using Anderson & 

LaBelle (2000) Data 

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The Weibull distribution will be used considerably later in this chapter to provide linkages 

between various thresholds (e.g. 50 bbl, 100 bbl, 500 bbl, & 1000 bbl) choices in data sets.

3.4 Platform Spill Analyses Based on Spills ≥ 1000 bbl (1964 – 1999) 

3.4.1 Platform Inter-Spill Distribution Analysis 

The OCS Platform Inter-spill data are examined in this section using the data from Anderson & 

aBelle (2000, p. 306) (also Table 2.6 in this report). Eleven platform spills occurred between 

1964 and 1980. None occurred between 1980 and the publication of the Anderson & Labelle 

2000 article. The assumption of a Poisson distribution for the frequency of spills based on time 

is tested in this section. This is addressed by examining if the exponential distribution 

adequately fits the inter-spill times. 

Figures 3.5 and 3.6 show that the inter-spill times in days between 1964 and 1980 are reasonably 

fit by an exponential distribution implying the Poisson arrivals are reasonable over this time 

frame. In addition to the visual assessment, the Anderson-Darling goodness-of-fit test (p-value = 

0.496) is not rejected. Thus modeling the process (at least based on time) by a Poisson 

distribution for this time period is justified, but there have been no platform spills between 1980 

and the publication of Anderson & LaBelle (2000). How this lack of platform spills impacts the 

Poisson assumption is addressed in Section 3.4.2. 

L

Days Between

P

erc

ent

1 10 100 1000 10000

99

90

80

70

60

20

Mean 606.4

N 10

AD 0.474

P-Value 0.496

Probability Plot of Days Between

Exponential - 95% CI

50

40

30

10

5

3

2

1

Figure 3.5 Exponential Probability Plot of Platform Inter-Spill times Using Anderson &

LaBelle (2000) Data 

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Days Between

Perc

ent

0 500 1000 1500 2000 2500 3000

100

80

60

40

20

0

Mean 606.4

N 10

Empirical CDF of Days Between

Figure 3.6 Exponential Empirical CDF Plot of Platform Inter-Spill times Using Anderson 

& LaBelle (2000) Data

3.4.2 Platform Inter-Spill Distribution Analysis with Hypothetical 1/1/1999 Spill 

Gi

(2000), it is necessary to examine the on distribution. A hypothetical spill 

as added on 1/1/1999 to examine this issue. Figure 3.7 clearly shows that the exponential 

distribution no longer adequately fits the data with this hypothetical platform spill added. 

nderson-Darling test (p-value = 

latform spills over the 16.61 year time frame in Anderson & LaBelle (2000) 

e annual spill rate is 0.662 platform spills/year. For a 19 year time period after this, the 

y

r

n

s may be appropriate) for spills ≥ 1,000 bbl. 

Exponential

ven that no spills have occurred between 1980 and the publication of Anderson & LaBelle 

applicability of a Poiss

w

Supplemental statistical support is provided by the failing A

0.017) though more weight should be given to failing the TLAR comparison. 

Another way to approach this issue is to ask if a Poisson adequately fits the 1964-1980 data, 

what would that particular Poisson distribution tell us about the subsequent 19 years through 

1999? For the 11 p

th

expected number of spills would be 12.58 spills versus the 0 spills observed. More specificall

using a Poisson distribution with this mean, the probability of 0 spills in 19 years would be only 

0.000003, i.e., a very unlikely situation. Thus it is concluded that the use of a single Poisson fo

platform spills over the time period from 1964 to 1999 is not currently justified (separate Poisso

distributions for different interval

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99

90

80

70

60

50

Mean 1153

N 11

AD 1.653

P-Value 0.017

40

30

20

10

5

Perc

ent

3

2

1

10 100 1000 10000

Days Between_1

Probability Plot of Days Between_1

Exponential - 95% CI

Figure 3.7 Exponential Probability Plot of Platform Inter-Spill times Using Anderson & 

LaBelle (2000) Data Supplemented w l Spill on 1/1/1999 

.4.3 Platform Volume Distribution Analysis 

A Weibull distribution fits the platform spill volumes as illustrated in Figures 3.8 and 3.9. This 

is supplemented by the Anderson-Darling goodness-of-fit (p-value > 0.25) seen in Figure 3.8. 

The Weibull distribution is a flexible distribution compared to several common continuous 

distributions, and we use the Weibull distribution extensively (see Section 3.5) to generalize the 

work seen in Anderson & LaBelle (2000). 

It is not uncommon to see p-values, such as in Figure 3.8, given as either > some value or < some

value in goodness of fit applications. The underlying null hypothesis sampling distribution of 

the test statistic has not been fully solved for all potential statistical distributions being tested 

with goodness of fits tests such as the Kolmogorov-Smirnov and the Anderson-Darling. In such 

cases as seen in Figure 3.8 for a three parameter Weibull distribution current statistical methods 

are unable to give an exact p-value but can assess that the p-value is greater than 0.25 which is 

all that is needed for most hypothesis testing. 

ith a Hypothetica

3

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Volume - Threshold

Perc

ent

1000 10000 100000 1000000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape 0.6082

Scale 11569

0.385

P-Value >0.250

Thresh 1000

N 11

AD

Pro e

3-Parameter Weibull - 95% CI

Figure 3.8 Weibull Probability Plot of Platform Spill Volumes Using Anderson & LaBelle 

(2000) Data 

bability Plot of Volum

Volume

Perc

ent

0 20000 40000 60000 80000 100000 120000 140000 160000

100

80

60

40

20

0

Shape 0.6082

Scale 11569

Thresh 1000

N 11

Empirical CDF of Volume

3-Parameter Weibull

Figure 3.9 Weibull Empirical CDF Plot of Platform Spill Volumes Using Anderson & 

LaBelle (2000) Data 

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3.5 Analyses Based on Pipeline Spills ≥ 50 bbl 

Section 3.5 extends published MMS work by including smaller spills. The reasons for adding 

extra data by lowering the threshold of 1,000 bbl include providing additional insights, testing if 

such extended data provides further support of the analyses based on the 1,000 bbl threshold, 

searching for other ways to estimate spill rate uncertainty, and examining the statistical value of

a larger data set. 

Another key extension is in the area of exposure variables. As mentioned before the Poisson 

distribution has tremendous flexibility, but it should be tested to see if it fits the actual observed 

data. Earlier in Chapter 3 this was examined only for the time between spill events. Does the 

Poisson assumption hold when the exposure variable is no longer time, but instead production 

volume or pipeline mile-years? 

3.5.1 Pipeline Inter-Spill Analysis Based on Three Exposure Variables 

A data set with 36 observations (Table 2.2 combined with Table 2.3) starting with June 13, 1972 

was used to see if a Poisson process can be justified based on time, on production volume (Table 

2.11) in millions of barrels (Mbbl), and from Table 2.12 on thousands of pipeline mile-years 

(KMiles). The rationale for this start date was due to the availability of both production volume 

and pipeline miles data. 

T

exam

ays in 1972 and the re roduction volume

nd pipeline miles were fairly constant throughout a given year, the total production volume and 

a

igures 3.10 through F dequately fits all

ree exposure variables (time, production volume, and pipeline mile-years) for this data set. 

Both visual a nts and th g -fit upp s de .

Thus now it i le to take is tio stim the

spills. Having said that a Poisson le, it essa xam ity 

of tio

his analysis required that the number of days in each year between each spill be computed. For

ple the first inter-spill time from June 13, 1972 to May 12, 1973 covered 333 days with 202

d maining 131 days in 1973. Then assuming that the p

a

the tot l pipeline mile-years between spills were computed. 

The inter-spill data for time, production volume, and pipeline mile-years are then tested to see if 

an exponential distribution fits the observed data. As before, if an exponential fits the inter-spill 

data for a given exposure variable (time, production volume, or pipeline mile-years) then a 

Poisson may be used to estimate the likelihood of the number of spills per unit of the exposure 

variable.

F

th

igure 3.15 illustrate that an exponential distribution a

ssessme

s possib

e Anderson-Darling

advantage of the Po

oodness-of

son distribu

is still nec

tests s

n for e

ort thi

ating

cision

number of 

fit is acceptab

n 3.5.5).

ry to e ine the stationar

the Poisson process (see Sec

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Days InterSpill

Perc

ent

1 10 100 1000

99

90

80

70

60

50

Mean 347.3

N 35

AD 0.499

P-Value 0.493

Probability Plot of Days InterSpill

Exponential - 95% CI

40

5

3

2

1

30

20

10

Figure 3.10 Exponential Probability Plot of Pipeline Inter-Spill (Spills ≥ 50 bbl) Times 

Using N = 36 Data Set

Empirical CDF of Days InterSpill

Days InterSpill

Perc

ent

0 200 400 600 800 1000 1200 1400 1600 1800

Mean 347.3

N 35

Exponential

Using N = 36 Data Set

100

80

60

0

40

20

Figure 3.11 Exponential Empirical CDF Plot of Pipeline Inter-Spill (Spills ≥ 50 bbl) Times

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Prod Interspill Mbbl

Perc

ent 0.001 0.010 0.100 1.000 10.000

99

90

80

70

60

50

40

30

20

Mean 0.3781

N 35

AD 0.648

P-Value 0.314

Exponential - 95% CI

10

5

3

2

1

Probability Plot of Prod Interspill Mbbl

Figure 3.12 Exponential Probability Plot of Pipeline Inter-Spill Production Volumes 

(Mbbl) Using N = 36 Data Set (Spills ≥ 50 bbl)

Mean 0.3781

Exponential

Empirical CDF of Prod Interspill Mbbl

100

N 35

olumes

80

60

Pe

40

rc

ent

20

0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Prod Interspill Mbbl

Figure 3.13 Exponential Empirical CDF Plot of Pipeline Inter-Spill Production V

Using N = 36 Data Set (Spills ≥ 50 bbl) 

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KMiles Interspill

Perc

ent

0.01 0.10 1.00 10.00 100.00

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Mean 4.539

N 35

AD 0.652

P-Value 0.310

Probability Plot of KMiles Interspill

Exponential - 95% CI

F

(KMiles) Using N = 36 Data Set (Spills ≥ 50 bbl)

igure 3.14 Exponential Probability Plot of Pipeline Inter-Spill Pipeline Mile-Years

KMiles Interspill

Perc

ent

0 10 20 30 40

100

80

60

40

20

0

Mean 4.539

N 35

Empirical CDF of KMiles Interspill

Exponential

Figure 3.15 Exponential Empirical CDF Plot of Pipeline Inter-Spill Pipeline Mile-Years 

(KMiles) Using N = 36 Data Set (Spills ≥ 50 bbl)

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3.5.2 Exposure Variable Poisson Confidence Intervals and an Introduction to the Poisson 

– Exponential Relationship 

Once the Poisson assumption has been validated by testing exponential inter-arrival measures, it 

is possible to compute spill rates with exact Poisson confidence intervals (LCL, UCL) or (lower 

confidence limit, upper confidence limit) for each exposure variable. The results are shown in 

Table 3.3. 

Table 3.3 Spill Rates for ≥ 50 bbl Spills (N = 36) 

Label Exposure Variable

Sum

Exposure 

Variable 

Rate LCL UCL 

Pipeline Spills/KMile-year KMile-years 161.80 0.223 0.156 0.308 

Pipeline Spills/Bbbl Bbbl Production 13.5 2.660 1.863 3.682 

Pipeline Spills/year Time, whole years 34 1.059 0.742 1.466 

As detailed in earlier chapters, the relationship between the discrete Poisson distribution and the 

continuous exponential distribution allows the testing of the Poisson assumption for small data 

sets that could not directly be assessed from a discrete distribution approach. 

Typically in modern statistics booksλ is used to represent the true unknown Poisson mean and 

λ

ˆ represents its estimate based on the observed data. Computationally λˆ is simply computed by 

div

one in Table 3.3 above. Since

iding the number of events (spills) by the sum of the relevant exposure variable such as was 

d λ

ˆ is only a sample estimate of the true population parameterλ it 

is critical to bound this estimate with a confidence interval as done in Table 3.3 to convey the 

uncertainty in the estimation. In what follows below the concern is not on the associated 

confidence interval but instead on using the Poisson and exponential relationship to provide an 

estimate ofλ . 

Each of the Minitab plots for the exponential distribution showed the value of the mean,1/ λ . 

Examining these exponential means and inverting them, one might intuitively expect to get the 

same Poisson rates seen in Table 3.3. Instead the following is obtained. 

Table 3.4 Rate Estimates using Exponential Distribution 

Exposure Variable Exponential Mean Rate 

Pipeline Spills/KMile-year 4.539 0.220 

Pipeline Spills/Bbbl 0.3781 2.645 

Pipeline Spills/year 347.3 days 1.051 per year 

While the agreement is close between the two sets of rates shown in Tables 3.3 and 3.4, there are 

minor differences. These minor differences are based on the use of the data set. In this case the 

exponential analysis deals with the 35 intervals between the 36 spills used for the Poisson 

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approach. Thus the exponential data set does not use the time (or amount of some other 

exposure variable) before the first spill or after the last spill which is part of the Poisson data set. 

If the Poisson approach focuses in on these same data, that is the interval between the first and 

last spill, then an exact match to the exponential rate is found. This has one less spill, since “the 

clock starts” with the first spill (now spill 0) and ends with the last one. Thus, the rates in Table 

3.5 match the rates in Table 3.4. 

Table 3.5 Poisson Rates based on Inter-Spill Data (N = 35) 

Label # Spills Exposure 

Variable 

Sum 

Exposure 

Variable

Rate LCL UCL 

Pipeline Spills/KMile-year 35 KMile-years 158.861 0.220 0.153 0.306 

Pipeline Spills/Bbbl 35 Bbbl Production 13.235 2.645 1.842 3.678 

Pipeline Spills/year 35 Time, years 33.304 1.051 0.732 1.462 

Table 3.5 also allows a clear statement of how the exponential mean for the inter-arrival interval 

is estimated. It is simply the sum of the exposure variable divided by the number of spills. For 

KMile-year this is 158.861 divided by the 35 inter-spill observations. This gives the same exact 

expo

tatistics, empirical CDF, and probability plot require the computation of all the inter-spill 

exposure variables. 

s

2005), it is not true that the final data sets end with significant spans of time without spills. 

Thus, it is left to further research and other spill data sets whether it is desirable to consider a 

final long-period without spills as a “censored” application for the exponential distribution. For 

example, suppose the period of no platform spills exceeding 1000 bbl from 1980 were to have 

continued through 2005. This is the same issue faced in mortality estimation when some people 

in a study are still alive, which is handled by using censored data techniques. If a person is still 

alive, that period is known, even if their life span is not. It is a direct analogue to the last spill 

and thus the methods used on biostatistics could be applied to spill data. 

3.5.3 Pipeline Spill Volume Models 

In examining the pipeline spill volumes there are some ties for spills sizes ≤ 100 bbl and minor 

adjustments were made to break the ties. Of the 36 pipeline spill volumes, 31 (86%) were 

unchanged, 3 (8%) were increased by 1 bbl, 1 (3%) was increased by 2 bbl, and 1 (3%) was 

increased by 3 bbl. There were four spills listed as 50 bbl and two of these were the ones 

changed by 2 or 3 bbl. The average increase was 0.222 bbl. These changes are minor and do not 

impact the statistical results in this report. However, avoiding ties is important for some of the 

statistical work. 

This section shows that Weibull distributions fit Pipeline spill volumes for draft spill volumes in 

the left-hand column of Table 2.2 with thresholds of 50 bbl, 100 bbl, 500 bbl, and 1000 bbl. 

nential mean seen in Table 3.4 of 4.539. While this is straightforward, the goodness-of-fit

s

A there are large pipeline and platform spills near the end of the studied time frame (1972 – 

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Sub

 1972 to 2005, 

rows from 16 with a threshold of 1,000 bbl, to 19 with a threshold of 500 bbl, to 29 with a 

threshold of 100 bbl, and to 36 spills with a threshold of 50 bbl. 

he authors believe that the more complete data set (spills ≥ 50 bbl) offers the opportunity for 

further insight and possibly better estimation. Even this larger (N = 36) data set ignores pipeline 

data set. What is 

nderson-Darling goodness-of-fit results in each probability plot 

upport the selection of the Weibull distribution. Data sets with labels that include text such as 

n

sequent sections use these results to present some conceptual approaches that extend the 

work of Anderson & LaBelle (2000). The dataset used here, based on data from

g

T

spills less than 50 bbl and hence cannot be considered a complete pipeline spill

the impact of ignoring spills less than 50 bbl? It depends on what proportion of the full 

population of pipeline spills are less than 50 bbl. The 50 bbl data set is used to estimate what 

conditional proportion of the ≥ 50 bbl population falls into the ≥ 1,000 bbl population. The 

results are encouraging. 

Figure 3.16 through Figure 3.23 show that the Weibull distribution is a reasonable fit for all four 

thresholds shown. Visual TLAR assessments of both the probability plots and empirical cdf

plots supplemented by the A

s

50_1 have been very slightly modified to break the lower level ties. For example rather tha

leaving say three values at 50 bbl, a label such as 50_1 implies that ties have been broken as 

discussed in the first paragraph of this section. Such modifications allow better visual 

distributional assessments as well as aiding the statistical goodness of fits tests. 

Spill >= 50_1

Perc

ent

100000.000

0.000

100

0

0

.000

10.0

1.0000.100

.010

1000

.000

10

00

0

0

.001

99

90

80

70

60

50

40

30

20

Shape 0.4398

Scale 1391

Thresh 50.00

N 36

AD 0.376

P-Value 0.434

3-Parameter Weibull - 95% CI

Probability Plot of Spill >= 50_1

10

5

3

2

1

Figure 3.16 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 50 bbl

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Spill >= 50_1

40000 50000

Sha

3-Parameter Weibull

Empirical CDF of Spill >= 50_1

100

Perc

ent

0 10000 20000 30000

80

60

40

20

0

pe 0.4398

Scale 1391

Figure 3.17 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 50 bbl

Thresh 50.00

N 36

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Spill >= 100_1

P

erc

ent

100000.00

10000.00

1000.00

100.00

10.00

1.00

0.10

0.01

99

90

Shape 0.5140

3-Parameter Weibull - 95% CI

Scale 2250

Thresh 99.99

N 29

AD 0.431

P-Value 0.329

Probability Plot of Spill >= 100_1

80

70

60

50

40

30

20

10

5

3

2

1

Figure 3.18 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 100 bbl

Spill >= 100_1

3-Parameter Weibull

Empirical CDF of Spill >= 100_1

100

Perc

ent

0 10000 20000 30000 40000 50000

80

60

40

20

0

Shape 0.5140

Scale 2250

for Spills ≥ 100 bbl

Thresh 99.99

N 29

Figure 3.19 Weibull Empirical CDF Plot of Pipeline Spill Volumes

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Spill >= 500_1

Perc

ent

100 1000 10000 100000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape 0.9194

Scale 4953

Th 500

N 19

A 0.267

P- >0.250

3-Parameter Weibull - 95% CI

Pr

resh

D

Value

obability Plot of Spill >= 500_1

Figure 3.20 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 500 bbl

1

0

Shape 0.9194

Scale 4953

Thresh 500

N 19

3-P ull

Empirica

arameter Weib

l CDF of Spill >= 500_1

00

80

60

c

ent r Pe

40

20

0 5000 10000 15000 20000 25000 30000

Spill >= 500_1

Figure 3.21 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 500 bbl

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Spill >= 1000_1

Perc

ent

100 1000 10000 100000

99

90

80

70

60

50

40

Shape 1.089

Scale 5754

Thresh 1000

N 16

AD 0.383

P-Value >0.250

3-Parameter Weibull - 95% CI

Probability Plot of Spill >= 1000_1

30

10

3

20

5

2

1

Figure 3.22 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 1000 bbl

 

Spill >= 1000_1

Perc

ent

0 5000 10000 15000 20000 25000

100

80

60

40

20

0

Shape 1.089

Scale 5754

Empirical CDF of Spill>=1000_1

3-Parameter Weibull

Thresh 1000

N 16

Figure 3.23 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 1000 bbl

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3.5.4 Comparing Pipeline Spill Volume Models for Different Thresholds 

Fitting the four Weibull (see Section 3.3.3 for explanation of Weibull) distributions to the four

data sets, allows the computation of some measures of consistency. That is because with any of 

the spill distributions it is also possible to comp ity For example, 

for the spill distribution for ≥ 50 bbls it is also possible to compute the probability of ≥ 100 bbls, 

≥ 500 bbls, and ≥ 1000 bbls. Table 3.6 is a table of odds ratios comparing the four models. 

Notice that the blan lls corres size comp that canno e with a probability

distribution at a hig reshold distribution for spills ≥ 500 bbl cannot be used to 

predict spills of ≥ 50 bbl). 

or example, consider the row comparing 100 bbl spills vs. 500 bbl spills. In the ≥ 50 bbl 

he odds

stimating the likelihood of spills exceeding 2000 bbl to spills exceeding 15,000 bbl. It is not 

tainty; however, it is 

e 1000 bbl models have led to less 

ute the probabil of larger spills.

k ce pond to arisons t be mad

her th (e.g., the

F

column the odds ratio is 1.46 implying that the odds of spilling more than 100 bbl compared to 

500 bbl is 1.46 to 1. In the ≥ 100 bbl column of this row, the odds of spilling more than 100 bbl

compared to spilling more than 500 bbl is estimated to be 1.51. Note the consistency of t

ratios in the ≥ 50 bbl and ≥ 100 bbl columns. This implies that these two Weibull models are 

providing similar predictions. 

While the odds ratios for the ≥ 500 bbl and ≥ 1,000 bbl columns are similar to the other rows for 

some values, these two columns have much higher odds ratios for the last row 2000 vs. 15000 

e

unusual to find the extremes (tails) of a distribution having the largest uncer

believ d that the smaller data sets available for the ≥ 500 and ≥

reliable results. It seems to be a better approach to use a larger data set (e.g., ≥ 50 bbl) to more 

completely estimate the spill distribution. Indeed if data were available for all spills regardless

of size, then those data should be examined to assess their potential worth. 

Table 3.6 Odds Ratios for the Four Different Threshold Weibull Distributions 

Thresholds for the four Weibull models 

Spill sizes compared ≥ 50 bbl ≥ 100 bbl ≥ 500 bbl ≥ 1,000 bbl 

50 vs. 100 1.25 

100 vs. 500 1.46 1.51 

500 vs. 1000 1.27 1.24 1.13 

1000 vs. 2000 1.37 1.34 1.24 1.16 

2000 vs. 15,000 5.37 5.62 10.50 12.00 

Another w o l)

to estimate e much of the ≥ 100 bbl distribution should represent 

giv t r vein the ≥ 50 bbl distribution was used to do the 

same for th rtions

(pro b onditional probabilities are then

used to adj s to

allow a gra ic four cdfs as given in Figure 3.24.

This paragraph and the next detail how this is done. The conditional probability of one event 

happening given another will happen is just the ratio of two probabilities. The numerator is the 

ay t compare these four Weibull distributions is to use the largest data set (≥ 50 bb

th conditional proportion of how

en hat the spill is ≥ 50 bbl. In a simila

e ≥ 500 bbl and ≥ 1000 bbl distributions. These conditional propo

ba ilities) are 0.793, 0.544, and 0.429, respectively. These c

ust the cumulative distribution functions of these three larger threshold distribution

ph al overlay comparison of the

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joint proba

conditioned n bl

given that the s f the required ratio is P(x ≥ 1000 bbl and x ≥ 50 

bbl h x ≥ 50 bbl) where x is the spill size. 

Unfortunat

approach th p

the full spill si bl. Thus

hen this model is used to compute P(x ≥ 1,000 bbl), it is instead computing the probability of a 

bility that both events will occur. The denominator is the probability that the event 

o will occur. For example, what is the conditional probability of a spill ≥ 1,000 b

pill is ≥ 50 bbl? The top half o

) w ile the bottom probability is the probability that P(

ely we have no way with the available data of assessing P(x ≥ 50 bbl). Instead we 

e roblem from a different perspective. Our Weibull distribution for ≥ 50 bbl is not 

ze distribution. It is a conditional distribution for only those spills ≥ 50 b

w

spill being ≥ 1,000 bbl given that the spill size is at least 50 bbl and hence a conditional 

probability. Jumping ahead to compute this probability which is one of three conditional 

probabilities in the next paragraph, 1- F(1000 bbl using the ≥ 50 bbl model) is the desired 

conditional probability. The math for this example is: 

0.4398

x v 1000 50 β ⎡ ⎤ ⎡ ⎤ ⎛ ⎞ − − ⎛ ⎞ 1 (1000) 1 1 exp exp 0.429 1391 F

α

⎢ ⎥ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦

− = − − − = − =

represents the likelihood that a spill will 

e ≥ 500 bbl given that the spill is ≥ 50 bbl. The ≥ 50 bbl model covers any spills of at least 50 

f this

ell the Weibull for ≥ 50 bbl fits the other data sets based on larger 

resholds is that the theoretical conditional proportions (0.793, 0.544, 0.429) based solely on the 

ual data which are

0.8 0.52

smaller sam f

observation se results are very encouraging. This supports the belief that 

the 

Figure 3.24 100 bbl cdfs are similar, but with some differences 

from urther

away,” for

differences of 2000 vs. 15,000 bbl spills in Table 3.6.

The main i be

bala d w

that it is pr

The next paragraph provides such conditional probabilities for ≥ 100 bbl, ≥ 500 bbl, and ≥ 1,000

bbl thresholds given that the spill is ≥ 50 bbl. As another example, what happens to the 

conditional probability of a spill of ≥ 500 bbl when it is conditioned on the ≥ 100 bbl model? 

Conceptually consider what should happen, i.e., should this probability increase or decrease from

a computed 0.544? What does the 0.544 represent? It

b

bbl. If a smaller range of potential spills is examined, such as at least 100 bbl, the proportion of 

this distribution that represents ≥ 500 bbl should be larger than the corresponding ≥ 500 bbl 

proportion of the ≥ 50 bbl distribution. Hence this new conditional probability should be larger

than 0.544. Indeed it is larger and is 0.663 using the ≥ 100 bbl Weibull model as the base o

calculation. 

One measure of how w

th

≥ 50 bbl Weibull distribution are close to the proportions based on the act

06, 8, 0.444 respectively. Given that the larger threshold data sets have progressively 

ple sizes and these latter numbers are based on small integer values (number o

s in the data sets), the

≥ 50 bbl data set can be used to make predictions for larger thresholds. 

shows that the ≥ 50 bbl and ≥

 the curves for the 500 & 1000 bbl spills. Also the curve for the ≥ 500 bbl spills is “f

smaller spills so it is not a logical progression as the sample size is reduced. These 

are also seen in the comparison

mplication of these results is that the reliability offered by a larger data set must

nce ith the reliability offered by a data set that has seen greater scrutiny. It is believed 

udent to examine the statistical results from both approaches. 

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CDF Comparison

1

0.6

0.8

0.9

0.7

>= 50bbl

>= 100bbl 0.5

F(x)

>= 500bbl

>= 1000bbl

0.2

0.3

0.4

0

0.1

0 2000 4000 6000 8000 10000 12000 14000 16000

Barrels Oil Spilled

ts over time visually seems to show a potential decrease in spill 

tes over time, Bbbl, and KMiles. Efforts using moving averages and regression with different 

ays

nd may 

.5.6 Alternative Confidence Interval Approaches Applied to Pipeline Spills 

nalyzed here. Spill rate confidence intervals are initially developed for all four thresholds as a 

mating 

Figure 3.24 Overlay of Weibull Empirical CDFs

3.5.5 Concerns about Non-stationarity of the Poisson Process 

Examination of various data se

ra

exposure variables have yielded inconsistent results. For example a regression of inter-spill d

versus spill year does not result in a statistically significant slope (p=0.155). While a tre

exist, the data is noisy enough that it cannot be confirmed for the GOM pipeline spills. When 

more evidence exists of a non-stationary process (as will be found for platforms) more

sophisticated approaches are used to quantify the relationship of the changing rate. 

3

This section examines the development of confidence intervals for spill rates using different 

methods. The analysis in this section is based on the 36 spills ≥ 50 bbl shown in Tables 2.2 and 

2.3. Three subsets of these data using higher spill thresholds form the set of four models 

a

function of production volume. The same methodology can be applied to other exposure 

variables. 

One reason for pursuing this approach is to establish a statistically credible basis for esti

the probabilities of larger spills, such as ≥ 10,000 bbl or ≥ 100,000 bbl. At these spill levels 

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there are respectively only 3 pipeline spills and 0 pipeline spills, which are too small for any 

reliable estimation process.

sed 

ller

than 

be

results from other approaches that are based on the larger data set for spills ≥ 50 

bl. The disadvantage of the Table 3.7 results is the reduction in sample size as the spill 

 

Table 3.7 Exact Poisson Confidence Intervals for Different Pipeline Spill Thresholds with 

eshold N for Bbbl Lower Upper 

Using the four thresholds with the exposure variable of Bbbl of production volume, Table 3.7 

gives the four pipeline spill rates with their exact Poisson confidence intervals. These are ba

on the formulation given in Section 3.2.2. The confidence intervals below are based on sma

and smaller data sets as the threshold size increases. Thus, the Poisson spill rate falls faster

the upper limit on its value as the threshold increases. 

These results are useful in estimating the probability of different size spills, but they can also

compared with

b

thresholds increase. 

Production as Exposure Variable 

Thr

Poisson Rate Exact Poisson CI Exact Poisson CI 

50 36 2.72 1.91 3.77

100 29 2.19 1.47 3.15

500 19 1.44 0.86 2.24

1000 16 1.21 0.69 1.96

Table 3.8 presents the fraction of the ≥ 50 bbl spills that are ≥ the higher thresholds using the 

previously developed Weibull probability distribution. More formally, the Weibull based model 

the conditional probability of

ely

Lower Binomial 

Confidence 

Upper Binomial 

Confidence Actual 

100 0.7932 .9181 0.8060 = 29/36

for pipeline spill volumes for ≥ 50 bbl is used to estimate

exceeding larger thresholds. Then assuming this probability represents a binomial proportion for

the N = 36 observations in the ≥ 50 bbl data set, exact binomial confidence intervals are given in

the last two columns. While the assumption that the conditional probability may be treated as a 

binomial in this manner may be questioned, it does provide one way of bounding the lik

proportion of the ≥ 50 bbl population that would exceed the larger thresholds indicated and thus

is useful information in its own right. 

Table 3.8 Exact Binomial Confidence Intervals for the Proportion of the ≥ 50 bbl Model 

Spills Exceeding the Larger Threshold with Production as Exposure Variable 

Threshold P(≥ Threshold) Interval Interval Proportion 

0.6398 0

500 0.5440 0.3810 0.7206 0.5280 = 19/36

1000 0.4293 0.2551 0.5924 0.4440= 16/36

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The models and the confidence intervals in Tables 3.7 and 3.8 can be used in three ways to 

estimate confidence intervals for spills ≥ the different thresholds. The three approaches are 

summarized in Tables 3.9 through 3.11. 

Table 3.9 uses the values in Table 3.8 in two ways. First the P(≥ Threshold) column of Table 3.8 

is used to estimate the spill rate per Bbbl for larger threshold based strictly on the > 50 bbl 

Weibull model. This is done by multiplying the value in the P(≥ Threshold) column by the 

estimated spill rate based just on the ≥ 50 bbl data. For example, the estimated spill rate for ≥

100 bbl spills is 2.16 (= 2.72*.79). 

Note how closely these spill rates match the ones developed separately based on their individual 

data sets. This is encouraging and lends strength to the concept of basing spill probabilities for 

any threshold on the largest possible data set. The last two columns of Table 3.9 are the same

2.72 spills per Bbbl rate for the ≥ 50 bbl data multiplied by the corresponding lower or upper 

column in Table 3.8. Thus, this represents one way to bound uncertainty at any threshold level 

by using only the ≥ 50 bbl data. 

One of the benefits of using the full data set is the ability to tighten the confidence intervals 

around the Poisson rates. While Table 3.7 does give exact Poisson confidence intervals for the 

four thresholds, each increasing threshold uses a smaller data set. This results in wide 

confidence intervals as the number of data points decreases. Using the full N = 36 data set in 

ta

thresholds of interest. resulting in the 

bility to reduce the width of the corresponding confidence intervals compared to the Table 3.7 

bbl

Threshold P(≥ Threshold) Adjusted Poisson Adjusted LCL Adjusted UCL 

100 0.79 2.16 1.74 2.50 

bles such as Table 3.9 does more than provide alternative confidence interval approaches for 

These tables more completely uses the larger data set

a

intervals based on reducing sample sizes as the thresholds increase in magnitude. 

Table 3.9 Spill Rate Estimates and Confidence Intervals Using 2.72 Spill Rate for ≥ 50

Times Values in Table 3.8 with Production as Exposure Variable 

Rate per Bbbl 

500 0.54 1.48 1.04 1.96 

Table 3.10 might be in some sense considered a worst case for the spill rate per Bbbl production 

volume in that it works with the exact Poisson confidence intervals in Table 3.7 for the ≥ 50 bbl 

spill and combines this information with the binomial proportion uncertainty given in Table 3.8. 

Table 3.10 has the widest intervals because it assumes for example, that the lower confidence 

interval rate for ≥ 50 bbl (1.91 in Table 3.7) and the lower confidence interval proportion for ≥

100 bbl (0.64 in Table 3.8) occur simultaneously. Thus, 1.22 (= 1.91*0.64) is the tabulated 

value. While this is not the recommended approach for GOM volumes, the method has 

applicability in the extension from the GOM to the Arctic where both the proportion of GOM 

spills that may be applicable to the Arctic (the binomial component) and the rate (the Poisson 

component) are quite uncertain. 

1000 0.43 1.17 0.69 1.61

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Table 3.10 Confidence Intervals for “Binomial Adjusted” Approach Using (1.91, 3.77) 

Table 3.7 Poisson Confidence Intervals from ≥ 50 bbl Model and the Binomial Confidence 

Intervals in Table 3.8

Threshold Adjusted LCL Based on both 

Confidence Intervals 

Adjusted UCL Based on 

both Confidence IntervalsI 

100 1.219 3.457 

500 0.726 2.714 

1000 0.486 2.231 

Table 3.11 also uses the (1.91, 3.77) exact Poisson confidence interval for ≥ 50 bbl. It multiplies 

this by the estimated proportion of the ≥ 50 bbl population that would exceed the larger 

thresholds (see Table 3.8). This provides a third approach to estimating the confidence interval 

for any threshold directly from the largest data set based on the 50 bbl threshold. 

Table 3.11 Confidence Intervals Using (1.91, 3.77) Poisson Confidence Intervals from ≥ 50 

bbl Model and P(≥ threshold) with Production as Exposure Variable

Threshold P(≥ threshold) Adjusted LCL Adjusted UCL 

50 1.0000 1.9052 3.7658

100 0.7932 1.5112 2.9872 

.,

e

e

Chapter 4 for the extension from the GOM to the Arctic. 

gives analogous Figures and Tables to 

e pipeline information in Section 3.5 using a numbering scheme to make the matching of the 

through 1999 analysis figure/table to the through 2005 figure/table seen in the main body of the 

500 0.5440 1.0364 2.0487 

1000 0.4293 0.8179 1.6167 

What is nice about the approaches summarized in Tables 3.9 to 3.11 is that a new subset of the 

data is not required each time a question arises about a different threshold. The quality of these 

estimates does depend on how well the ≥ 50 bbl data can be used to model the censored 

population above this threshold. These results are encouraging. While each approach has its 

own appeal, the Table 3.9 method is recommended for this section in which the proportions, i.e

P(≥ threshold), are thought to be reasonably estimated. If such proportions are more speculativ

than data based estimates, then the broader intervals of Table 3.10 are recommended. The Tabl

3.10 is related to the approach used in

3.5.7 Comparison of Through 2005 versus Through 1999 

Appendix A parallels the pipeline analysis in Section 3.5. In Section 3.5, analyses for pipeline 

spills ≥ 50 bbl are documented for data through 2005. Since the preliminary analysis submitted

in the fall of 2005 analyzed data only through 1999, it was felt important to provide the reader an 

opportunity to see what has changed by adding six additional years of pipeline spill data. While 

some of the results in Appendix A are the same as given in the earlier preliminary analysis, 

others reflect changes due to corrected data. Appendix A

th

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report obvious. For example Figure A3.10 is Appendix A may be compared to Figure 3.10 in 

Section 3.5. 

The comparison between the Appendix A through 1999 and Section 3.5 through 2005 analyses 

may be summarized in the following areas: 

• Pipeline Exposure Variable Goodness of Fit Distribution Analysis 

o All fits are very good and there are no major differences between the through 

1999 and through 2005 data. 

• Poisson Exposure Variable Rates 

o Spill rates have dropped somewhat in the through 2005 data. 

• Weibull Distribution Volume Goodness of Fit Analysis 

o All fits are very good and there are no major differences between the through 

1999 and through 2005 data. 

• Comparison of the four Weibull Volume Threshold Data Sets 

o Results compare well between the through 1999 and through 2005 data with the 

through 2005 data visually showing a somewhat better match between the four 

curves at low spill thresholds. 

• Alternative Spill Threshold Confidence Intervals 

o Following the pattern in the 2nd bullet above, spill rates have dropped somewhat 

in the through 2005 data. Slightly higher probabilities of larger spills are found in 

th this.

3.5.8

ection 3.5 has analyzed pipeline spil n inter-spill perspective as well as 

ill volume. The three exposure variables studied (time, volume, and pipeline miles) were all 

found to be adequate y e tial utio us isso mption for the spill 

rates for each exposu ble fie al e c of oisson confidence

intervals based on all OM sure bles

ipeline spill volumes wel a W dis on. F hresholds (50 bbl, 100 bbl, 

ta

s.

e through 2005 data though the reduction in spill rate dominates

The second and fifth bullets above mention the reduced spill rates in the through 2005 data 

versus the through 1999 data. This is not a major change and the resulting spill rates easily fall 

into the confidence intervals of the other time period’s spill rates. Additionally the earlier 

mentioned regression analyses among other things in Section 3.5.5 do not point to a nonstationary system. The major conclusion that can be supported is that the methodology and the

results are robust enough that the addition of 6 years of data has not led to significant changes. 

Summary and Conclusions 

S ls ≥ 50 bbl from both a

sp

ly fit b

r

xponen distrib

d

ns. Th

l

the Po

rea

n assu

e varia is justi . This ows th tion exact P

three G expo varia .

P were l fit by eibull tributi our t

500 bbl, and 1,000 bbl) were used to develop the approach given in this part of the report. The 

results of using a larger database of ≥ 50 bbl are very encouraging. Several methods were also 

derived for using the larger ≥ 50 bbl data to estimate spill rates and associated confidence 

intervals for the larger thresholds. These new methods make more complete use of the full N =

36 data set for spills ≥ 50 bbls, rather than depending on increasingly smaller subsets of spill da

for larger threshold

The following conclusions may be made from the results in this section:

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1. The use of the larger data set for pipeline spills ≥ 50 bbl adds remarkable modeling

flexibility and improves the validation of the conceptual underpinnings of the 

statistical modeling. 

2. Production and pipeline mile-years are useful exposure variables to help understand

and model not only the GOM but will be advantageous in the Chapter 4 extension 

from the GOM to the Arctic. 

3. Exploiting the relationship between the Poisson and exponential distributions 

provides a natural path to test whether the Poisson distributions is applicable to spill 

s

d

posure

line spill volumes ≥ 50 bbl provides a more complete 

use of available data and reduces uncertainty of spill rate confidence intervals. 

7. The Table 3.9 approach to assessing pipeline production spill rate confidence 

Table 3.10 approach that ncertainty will be applied in 

Chapter 4 for the extension from the GOM to the Arctic. This table expands earlier 

s.

bbl

ns

ts,

ded data provides further support of the analyses based on the 1000 bbl

resho ng the

atistic

Another key extension is in the area of exposure variables, where three are tested – time, 

produ nd the num of platfo After t e spill analyses were 

completed in Section 3.5, it was h d that the orm spills would easily fo the same

pattern ll v th

3.6.1 rm Inter-Spill Analysis Based on Three Exposure Variables 

A data starting with April 5, 1971 was

constr ne, and that some effort was 

needed to test the impact of includin he 1971 d s not in . This an ysis is

docum 3.6.2.

To be consistent with pipeline analysis that started with 1972 and the analysis in the Bercha 

report 006), a subset spi focus of na Thi includ s

examination of whether a Poisson process can be justified based on time, on production volume 

rates for an exposure variable. 

4. The application of exact Poisson confidence intervals for differing exposure variable

provides a more firm foundation for uncertainty quantification and prediction. 

5. Table 3.3 for pipeline spill rates for all three exposure variables is the recommende

source for spill rates ≥ 50 bbl. The rates are given separately for each of the ex

variables and are for ≥ 50 bbl rate estimates. 

6. A Weibull distribution for pipe

intervals for thresholds ≥ 50 bbl is recommended for GOM application, while the 

folds in other sources of u

work for just the exposure variable production that was based on ≥ 50 bbl prediction

8. Table 3.9 allows the generalization to predictions for 100 bbl, 500 bbl, and 1,000

as well as other desired thresholds. 

3.6 Analyses Based on Platform Spills ≥ 50 bbl 

Section 3.6 extends the published MMS work by including smaller platform spills. The reaso

for adding extra data by lowering the threshold of 1000 bbl include providing additional insigh

testing if such exten

th ld, searching for other ways to estimate spill rate uncertainty, and examini

st al value of a larger data set. 

ction volume, a ber rms. he pipelin

ope platf llow

. However platform spi s have pro ed more difficult an envisioned. 

Platfo

set with 86 observations (Table 2.6 + Table 2.8)

ucted. The year 1971 had 8 spills and 1972 had no it was felt

g t ata versu cluding it al

ented in Section

s (2002 & 2 with 78 lls was the a lysis. s e

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in Mbbl, and on number of platf rs. sis requ r of days in

ach year between each spill be computed. Then assuming that the production volume and 

rved data. As 

efore, if an exponential fits the inter-spill data for a given exposure variable then a Poisson may 

d

A Weibull distribution is a generalization of the exponential distribution. Unlike the 

ensored (each had a lower threshold of 50 bbl, 100 bbl, 500 bbl, or 1000 bbl) Weibull 

r

hold 

reliability theory the hazard function (defined further below) is often used to assess the failure 

rate as a function of time. The hazard function may increase or decrease dynamically (i.e., 

showing time dependence) indicating a rising or dropping failure rate. A horizontal hazard 

function is time independent (i.e., static) so the failure rate is not changing. This static or 

constant hazard function is the special case of the Weibull distribution that is the exponential 

distribution. The Weibull (Weibull, 1951) distribution allows a non-constant failure rate (or 

hazard function), so that the Weibull distribution is one of the major tools used in reliability 

assessments. 

The hazard function or conditional failure function is defined as: 

orm-yea This analy ired that the numbe

e

number of platforms were fairly constant throughout a given year, the total production volume 

and the number of platform-years between spills were computed. 

The inter-spill data are then tested to see if an exponential distribution fits the obse

b

be used to estimate the likelihood of the number of spills per unit of the exposure variable. 

While the exponential distribution did pass relevant goodness of fit statistical measures an

visual TLAR approaches some of the time, a Weibull distribution often fit the inter-spill data 

better.

c

distributions used for the pipeline spill volumes in Section 3.5, most Weibull distributions fo

inter-spill time have a lower bound of 0 and not some higher value. In such cases the thres

parameter ν = 0. 

In

( ) ( ) 1 ( )f t h t

F t = −

where h(t) is the hazard function, f(t) is the probability density function, and F(t) is the 

cumulative distribution function. Thus 1 – F(t) is the probability that the component will survive 

to time t. 

When the Weibull distribution shape parameter β = 1 we have a constant hazard function and 

thus an exponential distribution. When β < 1, the Weibull has a hazard function that is 

decreasing with time. When β > 1, the Weibull has a hazard function that is increasing with 

time. In the Weibull analyses that follow in this section, the shape parameter β < 1 and thus a 

decreasing spill rate is indicated. This also matches the Anderson and Labelle platform data 

d

3.6.1.1 Platform Inter-Spill Anal

ft hand portion of the curve sh blem. There were numerous 

es especially among the smaller values. Out of the 77 inter-spill days, 62 (81%) were 

unchanged, 8 (10%) were lengthened by 1 day, 5 (6%) were lengthened by 2 days, and 2 (3%) 

iscussion for platforms in Section 3.4.2.

ysis Based on Time

Figure 3.25 shows an exponential distribution fit to the inter-spill exposure time in days. The pvalue of 0.304 is not rejected by the Anderson-Darling goodness of fit test; however, the initial 

le ows a common (in this section) pro

ti

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were lengthened by 3 days to remove all the ties. The maximum change was 3 days and the 

average change was 0.31 days. A revised version based on tie breaking adjustments results in 

Figure 3.26. The p-value is higher (improved) though the main improvement is visual. Similar 

changes would be possible for other exposure variables but were not done as it is more difficult 

to adjust them. 

Days Interspill

Perc

ent

0.1 1.0 10.0 100.0 1000.0

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Mean 155.1

N 77

AD 0.665

P-Value 0.304

Probability Plot of Days Interspill

Exponential - 95% CI

0.1

Figure 3.25 Exponential Probability Plot of Platform Inter-Spill (Spills ≥ 50 bbl) Times 

using 1972-2005 Data Set 

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Probability Plot of Days fixed

Exponential - 95% CI

99.9

99 M

N

Days fixed

Perc

ent

0.1 1.0 10.0 100.0 1000.0

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

ean 155.5

Figure 3.26 Exponential Probability Plot of Tie-breaking Adjusted Platform Inter-Spill 

(Spills ≥ 50 bbl) Times using 1972-2005 Data Set 

Figure 3.27 fits a Weibull distribution to the same data as used in Figure 3.25, i.e., not adjusted 

for ties. Two things are worth noting; 1) more of the data points are within the 95% confidence 

limits; 2) the shape parameter (labeled β in the mathematics given earlier) is 0.8756 < 1.0. 

Again, this shape parameter implies that the inter-spill time is increasing and that the spill rate is 

decreasing. 

77

AD 0.482

P-Value 0.511

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Days Interspill

Percent

0.01 0.10 1.00 10.00 100.00 1000.00

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

Shape 0.8756

Scale 145.4

N 7

AD 0.160

P-Value >0.250

Probability Plot of Days Interspill

Weibull - 95% CI

7

Figure 3.27 Weibull Probability Plot of Platform Inter-Spill (Spills ≥ 50 bbl) Times using 

igures 3.28 and 3.29 show good empirical distribution function fits of the exponential and 

Weibull, respectively. A better fit for the Weibull is seen for smaller spill sizes. 

1972-2005 Data Set 

F

Days Interspill

Percent

0 200 400 600 800 1000

100

80

60

40

20

0

Mean 155.1

N 77

Empirical CDF of Days Interspill

Exponential

Figure 3.28 Exponential Empirical Distribution Function Fit of Platform Inter-Spill (Spills 

≥ 50 bbl) Times using 1972-2005 Data Set 

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Days Interspill

Perc

ent

0 200 400 600 800 1000

100

80

60

40

20

0

Shape 0.8756

Scale 145.4

N 77

Empirical CDF of Days Interspill

Weibull 

Figure 3.29 Weibu ter-Spill (Spills ≥

50 bbl) Times using 1972-2005 Data Set 

re 3.29 shows a better fit

r the Weibull than Figure 3.28 for the exponential. The major discussion of a new approach 

e

he shape parameter for the Weibull fit for all three exposure variables is < 1. This means the 

hazard of spills is declining over time. The significance of the decline is demonstrated through 

h

ll Empirical Distribution Function Fit of Platform In

While the exponential distribution does not fare too badly in this section for time as the exposure

variable, its performance is not as good for the other two platform exposure variables. This in

turn led to the analysis that follows in this section. Even with time, Figu

fo

based on the Weibull and a dropping failure rate will be detailed in this section but relevant 

applications for production volume and the number of platforms as exposure variables will b

given in Sections 3.6.1.2 and 3.6.2.2. 

T

linear regression, and by dividing the time span into two parts. 

Figure 3.30 is a straight line regression of the inter-spill days versus spill year. While the R^2 is 

small the regression slope is statistically significant (p-value 0.009). The positive slope says that 

over the time period the average increase in inter-spill days is 5.774 each year. This is not a hig

rate but over periods of 5 to 10 years or more, it adds up. 

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Spill year

Da

ys Interspill

1970 1975 1980 1985 1990 1995 2000 2005

1000

800

600

400

200

0

S 166.697

R-Sq 8.7%

R-Sq(adj) 7.5%

Fitted Line Plot

Days Interspill = - 11309 + 5.774 Start year

Figure 3.30 Regression of Inter-Spill time versus Spill Year

Table 3.12 summarizes the predicted inter-spill time, which is found by using the equation at the 

top of Figure 3.30. The table also lists 95% confidence limits for the average inter-spill time

95

confidence limits make it clea gh to matter on average. 

The prediction intervals are so broad that it is clearly impossible to expect to see the 

Table 3.12 Predicted Average Inter-spill Times (days) with 95% Confidence and

Prediction Intervals 

Year 

Interspill LCL UCL LPL UPL 

2000 239.0 166.1 311.9 0.0 579.0 

2005 267.9 176.0 359.7 0.0 614.4 

2010 296.7 184.9 408.5 0.0 647.1 

While potentially very useful for prediction in the GOM, this technique is clearest using time as 

the variable. It is possible that similar results might be obtained if inter-spill intervals are 

measured in production units or platform-years. To convert these calculated inter-spill values 

and limits to spill rates they are simply inverted. This may be a desirable approach for longerrange predictions. 

Given the difficulty of implementing and explaining this approach, a better starting point for 

analyzing changes in platform spill rates is to simply divide the 1972 to 2005 interval into two 

 and 

% upper and lower prediction limits (LPL, UPL) for a single inter-spill time in that year. The

r that the interval is increasing by enou

improvement by looking at individual inter-spill times. 

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parts. Without examining the data, it was decided that 1990 would be a good break point for 

analysis purposes. It was felt that this was a nice round year to work with and broke the full time 

interval into fairly equal parts. Thus the question is: Is there a statistically significant difference 

in the inter-spill data for 1972 to 1989 versus 1990 to 2005? To avoid losing a data point the 

inter-spill time between 1989 and 1990 was included in the earlier interval. This is one of the 

longest inter-spill times; thus including it in the earlier interval is a conservative approach to 

estimating the rate of improvement. 

Figure 3.31 is an Analysis of Means (ANOM) comparing the 1972 – 1989 average inter-spill 

days to the 1990 – 2005 average. The centerline shows an overall average over the full 1972 – 

2005 time frame of 155.1 inter-spill days. The “stairstep” lines represent upper or lower bounds 

around this grand average. The interval is tighter for the earlier data due to more data points 

falling into the earlier time period. Since both averages fall outside the bounds, both are 

significantly different from the overall grand average. Hence we have a non-stationary system

without a constant failure rate over time. 

StartCat

Mean

Y1972 - Y1989 Y1990 - Y2005

250

200

150

225.6

155.1

100

50

84.7

One-Way ANOM for Days Interspill by StartCat

Alpha = 0.05

972-

1989 versus 1990-2005 

ill

ays have approximated doubled in the latter time interval implying that the spill rate is roughly 

nce

s

Figure 3.31 Analysis of Means Comparing Inter-Spill Averages between Data for 1

Similar statistical result may be seen in the two sample t-test (p-value of 0.012) comparing the 

two means and the nonparametric Kruskal-Wallis test (p-value of 0.001) comparing the two 

corresponding medians. The two rounded inter-spill sample means of 122 days for 1972 – 1989 

and 243 days for 1990 – 2005 are seen below in the two sample t-test output. The inter-sp

d

one half of the 1972 – 1989 time interval. This will be further quantified later with a confide

interval for the ratio of these two rates. The Kruskal-Wallis shows the median inter-spill day

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are approximately three times (218 days versus 69.5 days) for the 1990 – 2005 versus 1972 – 

1989 time intervals. 

Table 3.13 Comparing 1972-1989 and 1990-2005 Platform Inter-Spill Times 

Two-sample T-test

N Mean Std. Dev. SE Mean 

Y1972-Y1989 56 122 159 21 

Y1990-Y2005 21 243 183 40 

Estimate for difference -120.280 95% Conf. Int. (212.688, -27.871) 

T-test t = -2.65 P-value = 0.012 DF = 31 

 

Kruskal-Wallis Test of Median Inter-spill Times 

 N Median 

Average 

Rank z 

Y1972-Y1989 56 69.50 34.0 -3.23 

Y1990-Y2005 21 218.00 52.4 3.23 

Overall 77 39.0 

H = 10.40 DF = 1 P = 0.001 

H = 10.41 DF = 1 P = 0.001 (adjusted for ties) 

All of this implies that the rate of spills varies significantly across these two time periods. Thus, 

the next step is to test if the two time periods can be shown to be adequately modeled separately 

by exponential distributions. If so, then separate Poisson distributions could be fit to each time

interval. There is also a statistical test to directly compare the two Poisson rates. 

Figures 3.32 and 3.33 show the two different exponential fits to the inter-spill days for the two 

time intervals. The main point to be made is that both exponential distributions adequately fit 

each interval based on the p-values. Hence there is no reason here to discard the Poisson 

assumption. For the other two exposure variables only the panel display style of Figure 3.33 is 

used. 

Figure 3.34 can be compared with Figure 3.33 to examine how “breaking ties” (as in Figure 

3.26) improves the resulting fits. This is shown primarily for illustration and to hopefully 

convey the idea that the ties in the lower end of the distributions are not as important as they may 

visually appear to be. 

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Days Interspill

Perc

ent

1 10 100 10 0 10000

99

30

0

.9

99

90

80

70

60

50

40

20

10

5

3

2

1

122.3 56

Mean N

0.804 0.20

AD P

1

242.6 21 0.552 0.412

Y1

Sta

972 -

0 -

rtCa

Probability Plot of Days Interspill

Figure 3.32 Overlaid Expo er Ti 1

1 -200

Y1989

t

Y199 Y2005

Exponential - 95% CI

nential Distribution Fits to Platform Int 972-

5

-Spill me for

989 versus 1990

Days Interspill

Perc

ent

1 10 100 1000

1 10 100 1000

Y1972 - Y1989 Y1990 - Y2005

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

M

N

A

ean 3

6

D 4

Va

Y1972 - Y1989

a

D

P-Value 0.412

9

ab s Int l

% CI

Panel variable: StartCat

r

122.

5

0.80

P- lue 0.201

Me

Y1

n 242.6

90 - Y2005

N

A

21

0.552

Prob ility Plot of Day erspil

Exponential - 95

Figure 3.33 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Time fo

the 1972-1989 versus 1990-2005 

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Days fixed

Perc

ent

1 10 100 1000

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

1 10 100 1000

Y1972 - Y1989 Y1990 - Y2005

Mean 122.7

Y1972 - Y1989

N 56

AD 0.676

P-Value 0.292

Mean 242.9

N 21

AD 0.524

P-Value 0.449

Y1990 - Y2005

Exponential - 95% CI

Panel variable: StartCat_1

Figure 3.34 Panel Displayed Exponential Distribution Fits to Adjusted (Tie Breaking) 

Platform Inter-Spill time for the 1972-1989 versus 1990-2005 

Building on the work of Przyborowski and Wilenski (1940), Chapman (1952) illustrates the 

development of an exact confidence interval for the ratio of two Poisson rates. In this case it is 

desired to know how the Poisson rate drops going from 1972 – 1989 to 1990 – 2005. First keep 

in mind that the higher average inter-spills days for the exponential distribution for 1990 – 2005 

gives the mean inter-spill time, w ber of spills per time (or per unit 

f another exposure variable).

mean rate for X be λ ple size will be the 

um of x and y where there are x inter-spill and y inter-spill values in the 1972 – 1989 and 1990 

Probability Plot of Days fixed

versus 1972 – 1989 implies the Poisson rates will vary in the opposite direction. The exponential 

hile the Poisson rate is the num

o

Let X and Y be two Poisson random variables with x and y spills, respectively. Let the Poisson 

 and let the Poisson mean rate for Y be γλ. The total sam

s

– 2005 time intervals, respectively. Let 

1 (1 ) 1

τ λ γ and ρ λ= + = +

. Then X has a binomial (n, 

ρ) distribution. Using the exact Excel binomial confidence interval function described in Section

2.5.5, ( , ρ ρ) may be developed. As given in Chapman (1952), a confidence interval for the rat

γ of the two Poisson mean rates is 

io

1 1 1, 1

ρ ρ

⎛ ⎞ ⎜ ⎟ − −

⎝ ⎠

. Thus we can compute an exact confidence 

interval for the ratio of the two Poisson mean rates. If the resulting interval does not contain the 

value 1.0 at a given level of confidence, then the two Poisson rates are significantly different. 

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Implementing this results in a 95% two sided confidence interval for the Poisson mean rate ratio 

to

rly in the exponential results. But now this ratio is bounded by confidence limits. 

section the exponential fails the Andersonarling goodness of fit test (p = 0.017) at the 95% confidence level. Hence even more reason to 

e is

d version of the same procedure given 

Section 3.6.1.1 for time as the exposure variable. A more direct approach is used in this 

section as the major concepts and concerns have been given in the prior section. The 1972 – 

1989 versus 1990 – 2005 comparison is also presented. Fundamentally, the conclusion is the 

same. Modeling the entire interval with one distribution is better done with the Weibull, but the 

increasing inter-spill production volume and decreasing spill rate can be modeled with two 

exponential distributions for the two time periods. 

γ of (0.3051, 0.8330) with the point estimate of 0.5041 for γ. Since 1.0 is not in this Poisson 

mean rate ratio confidence interval, this implies at the 95% confidence level that the two rates 

are significantly different and the 1990 – 2005 rate is significantly lower. Thus we have 

statistical backing for claiming that platform spill rates have dropped from the 1972 – 1989

1990 – 2005 time interval. Indeed the rate is roughly 1⁄2 of the earlier time period rate as

indicated ea

3.6.1.2 Platform Inter-Spill Analysis Based on Production Volume (Mbbl) 

This section analyzes production volume in millions of barrels (Mbbl) as an exposure variable 

for platform spills. As seen in Figures 3.35 through 3.38, the Weibull distribution fits inter-spill 

production better than an exponential. Indeed in this

D

move away from fitting an exponential to the full time period. Also note the Weibull shap

0.8224 < 1. Again, this shape parameter implies that the inter-spill production volume is 

increasing and that the spill rate is decreasing 

This section with production volume follows an abbreviate

in

Mbbl Interspill

Percent

0.1 1.0 10.0 100.0 1000.0

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

Mean 155.2

N 77

AD 1.741

P-Value 0.017

Probability Plot of Mbbl Interspill

Exponential - 95% CI

F

(Mbbl) using 1972-2005 Data Set 

igure 3.35 Exponential Probability Plot Platform Inter-Spill (Spills ≥ 50 bbl) Production

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Mbbl Interspill

Perc

ent

0.01 0.10 1.00 10.00 100.00 1000.00 10000.00

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

Shape 0.8224

Scale 139.7

N 7

AD 0.281

P-Value >0.250

Probability Plot of Mbbl Interspill

Weibull - 95% CI

7

Figure 3.36 Weibull Probability Plot P Inter-Spill (spills ≥ 50 bbl) Production 

(Mbbl) using 1972-2005 Data Set 

latform

Mbbl Intersp

Per

ill

c

ent

0 100 200 300 400 500 600 700 800 900

Mean 155.2

N 77

E

Empirical CDF of Mbbl Interspill

xponential

100

80

60

40

20

0

Figure 3.37 Exponential Empirical Distribution Function Fit of Platform Inter-Spill (Spills

≥ 50 bbl) Production (Mbbl) using 1972-2005 Data Set 

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Mbbl Interspill

Perc

ent

0 100 200 300 400 500 600 700 800 900

100

80

60

40

20

0

Shape 0.8224

Scale 139.7

N 77

Empirical CDF of Mbbl Interspill

Figure 3.38 Weibull Empirical Distribution Function Fit of Platform Inter-Spill (spills ≥ 50 

bbl) Production (Mbbl) using 1972-2005 Data Set 

Weibull 

Mbbl Interspill

Perc

ent

1 10 100 1000

99.9

99

90

80

70

60

50

40

10

5

30

20

3

2

1

1 10 100 1000

Y1972 - Y1989 Y1990 - Y2005

Mean 103.7

N 56

AD 0.920

P-Value 0.144

Y1972 - Y1989

Mean 292.4

1

P-Value 0.442

Y1990 - Y2005

Probability Plot of Mbbl Interspill

Exponential - 95% CI

Figure 3.39 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill 

Production (Mbbl) for 1972-1989 versus 1990-2005 

N 2

AD 0.530

Panel variable: StartCat

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Separate exponential distributions fit the to the two time periods 1972 – 1989 and 1990 – 2005 

pass the Anderson-Darling Goodness of fit test as seen in Figure 3.39. The corresponding interspill means are 103.7 Mbbl and 292.4 Mbbl. This is even more evidence that the time based 

sults that the spill rate has dropped in the 1990 – 2005 time interval. 

3.6.

This section analyzes the number of platfo osure variable for platform spills. As 

en in Figures 3.40 through 3.43, the Weibull distribution fits inter-spill production better than 

an exponential. As seen with ex tion n-Darling

goodness of 0.01 n ce o move 

away from fitting an exponential to the full tim

1. The 1972 – 1989 versus 1990 – 2005 comparison is presented below. 

mentally, the conclusion is the same as with the other exposure variables. Modeling the 

ntire interval with one distribution is better done with the Weibull, but the increasing inter-spill 

pl

e period

re

The point estimate for the ratio of the two Poisson means rate is 0.3547 indicating the rate over 

the 1990 – 2005 time interval is only around 1/3 that of the 1972 – 1989 time interval. The 

corresponding 95% confidence interval for this ratio is (0.1997, 0.5930). With 1.0 not falling 

into the confidence interval it is seen that the two Poisson mean rates are significantly different. 

1.3 Platform Inter-Spill Analysis Based on Number of Platforms 

rms as an exp

se

production the

1) at the 95% co

ponential distribu

fidence level. Hen

e period. Also note the W

fails the Anderso

even more reason t

eibull shape is 0.8007 < 

fit test (p =

Funda

e

atform-years and decreasing spill rate can be modeled with two exponential distributions for 

the two tim s.

NumPlatforms Interspill

Perc

ent

1 10 100 1000 10000

Me 67

N 77

AD 907

P-V .011

t ill

5%

Set

an 12

1.

alue 0

Probability Plot of NumPla

Exponential - 9

forms Intersp

 CI

99.9

60

1

99

90

80

70

50

40

30

20

10

5

3

2

0.1

Figure 3.40 Exponential Probability Plot Platform Inter-Spill (spills ≥ 50 bbl) Number of

Platforms using 1972-2005 Data

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Probability Plot of NumPlatforms Interspill

Weibull - 95% CI

NumPlatforms Interspill

Perc

ent 99.9

99

0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

Shape 0.8007

F ure

Scale 1116

N 77

AD 0.172

P-Value >0.250

ig 3.41 Weibull Probability Plot Platform Inter-Spill (Spills ≥ 50 bbl) Number of

Platforms using 1972-2005 Data Set 

NumPlatforms Interspill

Perc

ent

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

1

0

00

80

60

40

20

Mean 1267

N 77

Exponential

Empirical CDF of NumPlatforms Interspill

Figure 3.42 Exponential Empirical Distribution Function Fit of Platform Inter-Spill (Spil

≥ 50 bbl) Number of Platforms using 1972-2005 Data Set 

ls

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NumPlatforms Interspill

Empirical CDF of NumPlatforms Interspill

Weibull 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

100

80

60

40

20

0

Shape 0.8007

Scale 1116

N 77

Perc

ent

Figure 3.43 Weibull Empirical Distribution Function Fit of Platform Inter-Spill (Spills ≥

50 bbl) Number of Platforms using 1972-2005 Data Set 

NumPlatforms Interspill

Percent

10 100 1000 10000

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

10 100 1000 10000

Y1972 - Y1989 Y1990 - Y2005

Mean 861.2

N 56

AD 1.450

P-Value 0.035

Y1972 - Y1989

Mean 2349

N 21

AD 0.558

P-Value 0.405

Y1990 - Y2005

Probability Plot of NumPlatforms Interspill

Exponential - 95% CI

Panel variable: StartCat

Figure 3.44 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Number 

of Platforms for 1972-1989 versus 1990-2005 

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Separate exponential distributions fit the to the two time periods 1972 – 1989 and 1990 – 2005 

are seen in Figure 3.44. Technically the 1972 – 1989 time period does not quite pass the 

d est at the 95% confidence level since its p-value is < 0.05. 

However the visual TLAR assessment is reasonable. Keep in mind also that if the ties were 

ted for time as the exposure variable) both the visual fit and the 

e

ponding 95%

con nfidence 

inte 005

tim

The

rati oisson 

con approach to 

test

200

num (commonly 

use

pow

An erson-Darling goodness of fit t

adjusted (as was illustra

Anderson-Darling results would improve. Using Arena’s Input Analyzer the exponential 

distribution passes the Kolmogorov-Smirnov Test with a p-value > 0.15. Hence an exponential 

distribution can be used for the 1972 – 1989 interval. The corresponding inter-spill means are 

861.2 platform-years and 2349 platform-years. This indicates that spill rate has dropped in th

1990 – 2005 time interval since the average number of platform-years between spills has 

increased. 

The point estimate for the ratio of the two Poisson means rate is 0.3666. The corres

fidence interval for this ratio is (0.2157, 0.6292). With 1.0 not falling into the co

rval it is seen that the two Poisson mean rates are significantly different with the 1990 – 2

e frame having the lower spill rate with number of platforms as the exposure variable. 

above binomial based confidence intervals provide an exact confidence interval for the 

os of the two Poisson rates. Table 3.14 based on inter-spill data shows the exact P

fidence intervals for each time period and for all exposure variables. An inexact

ing whether the Poisson mean rates are different would be to see if the UCLfor the 1990 – 

5 falls below the LCLof the 1972 – 1989 time period. This does occur for production and

ber of platforms, but not quite for time as an exposure variable. Such a method

d but incorrect) for comparing Normal means is well documented to be ad hoc and not 

erful; however, it is still used in practice by many. 

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Table 3.14 GOM Platform Spill Rates (Spills ≥ 50 bbls) for 1972-1989 and 1990-2005 

.874

CL

0 4.040 

990-2005 Using Inter-Spill Exponential Distribution 

xposure Variable

Sum Exposure 

Variable Rate LCL UCL 

Production Bbbl 6.141 3.420 2.117 5.227 

0

l 6.766 3.252 2.038 4.923 

2

re variable.

is expected that the other two exposure variables would respond in similar fashion. 

und

Platforms 1972-1989 Using Inter-Spill Exponential Distribution 

Label # 

Spills Exposure Variable Sum Exposure Variable Rate LCL UCL 

Spills/Bbbl 56 Production Bbbl 5.806 9.645 7.286 12.52

Spill/(Number of Platforms) 56 KPlatforms-Years 48.23 1.161 0.8771 1.508 

Spills/year 56 Time, years 18.77 2.984 2.254 3

Platforms 1972-1989 Using Full Years 

Label # 

Spills Exposure Variable Sum Exposure Variable Rate LCL U

Spills/Bbbl 56 Production Bbbl 5.680 9.860 7.448 12.80

Spill/(Number of Platforms) 56 KPlatforms-Years 43.72 1.281 0.9677 1.663

Spills/year 56 Time, years 18 3.111 2.35

 

Platforms 1

Label # 

Spills E

Spills/Bbbl 21

Spill/(Number of Platforms) 21 KPlatforms-Years 49.34 0.4257 0.2635 0.6507

Spills/year 21 Time, years 13.96 1.504 0.931 2.30

 

Platforms 1990-2005 Using Full Years 

Label # 

Spills Exposure Variable Sum Exposure Variable Rate LCL UCL

Spills/Bbbl 22 Production Bbb

Spill/(Number of Platforms) 22 KPlatforms-Years 56.37 0.3903 0.2446 0.5909

Spills/year 22 Time, years 16 1.375 0.862 2.08

3.6.2 Platform Spills Comparing a 1971 Start with a 1972 Start 

A data set with 86 observations (Table 2.6 + Table 2.8) starting with April 5, 1971 was 

constructed. The year 1971 had 8 spills and 1972 had none, and it was felt that some effort was 

needed to test the impact of including the 1971 data versus not including it. This section 

analyzes the impact on including versus dropping 1971 using time as the only exposu

It

Figures 3.45 and 3.46 show that an exponential distribution is not rejected by the AndersonDarling goodness of fit test since all p-values are > 0.05. Figure 3.46 has broken the ties fo

in the original data resulting in better fits both visually and based on p-values. The difference in 

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the exponential inter-spill mean days is small with the 1971 – 2005 inter-spill mean slightly 

smaller. The difference is NOT statistically significant, as is detailed at the end of this section

While the difference might be significant if comparing 1971 – 1989 with 1972 – 1989, that 

comparison does not matter because the earlier time period is not used for any projections to th

Beaufort and Chukchi Seas which is the focus of this study. Thus, only analysis for the entire 

time sp

.

e

an was done. Perc

ent

0.1 1.0 10.0 100.0 1000.0

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

0.1 1.0 10.0 100.0 1000.0

99

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

.9

99

Days InterSpill_1971 Days InterSpill_1972

Mean

N

AD

Days In

148.1

85

1.110

ue 0.087

terSpill_1971

n 155.1

77

0.665

lue 0.304

nterSpill_1972

Probability ill_1972

Exponential - 95% CI

Figure 3.45 Panel yed Expon tial Dist ion Fits latform r-Spill Time for

1971 005 vers 72-200

P-V

Days I

al

Mea

N

AD

P-Va

Plot of Days InterSpill_1971, Days InterSp

Displa en ribut to P Inte

-2 us 19 5

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P

erc

ent

0.1 1.0 10.0 100.0 1000.0

99.9

99

90

80

70

60

50

40

30

20

10

5

3

2

1

0.1

0.1 1.0 10.0 100.0 1000.0

99.9

99

90

80

70

60

50

0.1

40

30

20

10

5

3

2

1

Days InterSpill_1971_1 Days InterSpill_1972_1

Mean 148.6

N 85

AD 0.834

Days InterSpill_1971_1

P-Value 0.186

Mean 155.6

Days InterSpill_1972_1

Probability Plot of Days InterSpill_1971_1, Days InterSpill_1972_1

ted

eans rate is 0.9550. The corresponding 95% 

onfidence interval for this ratio is (0.6066, 1.56338). With 1.0 falling into the confidence 

ger 

resholds well, but did not fit as well as the lognormal distribution for the smaller two 

Exponential - 95% CI

N 77

AD 0.443

P-Value 0.562

Figure 3.46 Panel Displayed Exponential Distribution Fits to Platform Inter-Spill Adjus

(Tie Breaking) Time for 1971-2005 versus 1972-2005 

The point estimate for the ratio of the two Poisson m

c

interval it is seen that the two Poisson mean rates are not significantly different. 

Since exponentials fit both the 1971 – 2005 and the 1972 – 2005 time intervals and there is no 

statistically significant difference in the corresponding Poisson rates, it is felt that there is no 

reason to further analyze platform data using a 1971 start. The platform volume spill analysis 

that follows uses the 1972 – 2005 data. 

3.6.3 Platform Spill Volume Models 

This section shows that three parameter lognormal distribution fits platform spill volumes with

thresholds of 50 bbl, 100 bbl, 500 bbl, and 1000 bbl. Subsequent sections use these results to

present some conceptual approaches that extend the work of Anderson & LaBelle (2000). A 

three parameter Weibull distribution (as was used for the pipeline spills) fit the two lar

th

thresholds. 

It is our belief that the more complete data set (spills ≥ 50 bbl) offers the opportunity for further 

insight and possible better estimation. Even this larger data set ignores pipeline spills less than 

50 bbl and hence cannot be considered a complete pipeline spill data set, but as discussed earlier 

it is a reasonable choice given data quality issues. 

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Figure 3.47 through Figure 3.50 show that the three parameter lognormal distribution is a 

reasonable fit for all four thresholds shown. Visual TLAR assessments of the probability plots 

supplemented by the Anderson-Darling goodness-of-fit results in each probability plot suppo

the selection o

rt

f the three parameter lognormal distribution. In this section all the ties were broken 

along the lines of breaking volume ties for pipeline spills. 

Spill >= 50_1 bbl - Threshold

Perc

ent

1000000.00

100000.00

10000.00

1000.00

100.00

10.00

1.00

0.10

0.01

99.9

99

95

90

80

70

60

50

40

Loc 4.267

Scale 2.083

Thresh 49.99

N 78

AD 0.647

P-Value 0.088

Probability Plot of Spill >= 50_1 bbl

3-Parameter Lognormal - 95% CI

30

20

10

5

1

0.1

Figure 3.47 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥ 50 

bbl 

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Probability Plot of Spill >= 100_1 bbl

3-Parameter Lognormal - 95% CI

99

100000.00

10000.00

1000.00

100.00

0.00

1.00

0

0

Spill >= 100_1 bbl - Threshold

Perc

ent

1

.10

.01

Loc 4.511

Scale 2.447

Thresh 99.99

N 49

AD 0.572

P-Value 0.130

95

90

80

70

60

50

40

30

20

10

5

1

Figure 3.48 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥

100 bbl 

Spill >= 500_1 bbl - Threshold

Perc

ent

100 1000 10000 100000

99

60

95

90

80

70

50

40

30

20

10

5

1

Loc 6.862

1.5

5

0.

P-Value 0.261

3-Paramete - 95% CI

9 Three Parameter LogNormal Probability Plot of Platform Spills for Spills ≥

500 bbl 

Probability Plot of Spill >= 500_1 bbl

r Lognormal

Scale

Thresh

73

00

N 1

AD

1

423

Figure 3.4

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Spill >= 1000_1 bbl - Threshold

Perc

ent

100 1000 10000 100000 1000000

99

95

90

80

1

70

60

50

40

30

20

10

5

Loc 7.044

Scale 1.633

Thresh 1000

N 8

AD 0.407

P-Value 0.262

Probab 1 bbl

3-Parameter Lognormal - 95% CI

Figure 3.50 Three Parameter LogNormal Probabi t of Plat ills fo

0 bbl

3. arin atform Spill Volum odels for ent Thr

itting the four lognormal distributions to the four data sets, allows a comparison of consistency 

l spills. In the ≥ 50 bbl 

column the odds ratio is 3.02 implying that the o ds of spilling more than 100 bbl compared to 

l

on of the

ng

. Thus the value of a larger data set (e.g., ≥ 50 bbl) may be used to reasonably 

redict the likelihood of larger platform spill sizes. 

The consistency of the four lognormals is rather striking. Following the approach that led to the 

pipeline Figure 3.24, Figure 3.51 illustrates the excellent match between the four cumulative 

distribution functions based of the conditional probability approach detailed in Section 3.5.4 for 

pipelines. 

ility Plot of Spill >= 1000_

lity Plo form Sp r Spills ≥

100

6.4 Comp g Pl e M Differ esholds

F

across the models. Table 3.15 presents the odds ratios comparing the four models. Notice that 

the blank cells correspond to size comparisons that cannot be made with a probability 

distribution at a higher threshold (e.g., the distribution for spills ≥ 500 bbl cannot be used to 

predict spills of ≥ 50 bbl). 

For example, consider the row comparing 100 bbl spills vs. 500 bb

d

500 bbl is 3.02 to 1. In the ≥ 100 bbl column of this row, the odds of spilling more than 100 bb

compared to spilling more than 500 bbl is estimated to be 3.67. With the minor excepti

5.76, note the consistency of the odds ratios in the all columns. This is done by looking at each 

row separately. If the values in the row are in the same ballpark, then the models are predicting 

similar outcomes. The results in this table imply that these lognormal models are providi

similar predictions

p

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Table 3.15 Odds Ratios for the Four Lognormal Distributions for Platform Spills 

Thresholds for the four lognormal models 

> 50 bbl > 100 bbl > 500 bbl > 1,000 bbl 

50 vs. 100 1.76 

100 vs. 500 3.02 3.67 

500 vs. 1000 1.76 1.56 1.52

1000 vs. 2000 1.91 1.63 1.70 1.88 

2000 vs. 15000 10.91 5.76 9.24 8.51 

CDF Comparison for Platform Lognormal Distributions

0

0.1

0.2

0.3

0 2000 400

0.4

0.5

0.6

0.7

0.8

0.9

1

0 6000 8000 10000 12000 14000 16000

Barrels Oil Spilled

F(x)

>= 50bbl

>= 100bbl

>= 500bbl

>= 1000bbl

As

nded approach for confidence intervals for varying volume

s

e

he volume was well modeled by the lognormal distribution, but this was based on the full set of 

spills independent of which time frame the spill fell into. The two volume means for the time 

periods are not be significantly different (p-value = 0.591) in a two sample t-test. Thus the full

volume data set is used regardless of the spill date. 

Figure 3.51 Overlay of Lognormal Empirical CDFs for Platform Spill Data 

3.6.5 Platform Spill Volume Confidence Intervals 

Section 3.5.6 on pipeline spills presents alternative ways to develop confidence intervals.

explained in that section the recomme

thresholds is the one given in Table 3.9. Thus in this section it is the only approach applied. A

in the pipeline Section 3.5.6 the approach is given here only for the production exposur

variable. 

T

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ile the full set of volumes is used, this section focuses on applying that data only to the 199

variable. The 1990 – 2

Wh 0-

2005 production volume exposure 005 production spill rate is 3.420 

ills/Bbbl production as given in the earlier Table 3.13. To implement the confidence interval 

approach recommended the binomial confidence eed to be computed. Table 3.16 

does that below and then the results are used to get the desired Poisson based confidence 

intervals th

Tab act om terv ario o e

shol

Threshold P(≥ Threshold) Lower Binomial Upper Binomial 

sp

intervals first n

for higher resholds in Table 3.17.

le 3.16 Ex Bin ial Confidence In als for V us Platf rm Spill Volum

Thre ds

Confidence Level Confidence Level 

100 0.57 0.45 0.68 

500 0.19 0.11 0.30 

1000 0.11 0.05 0.19 

Table m te for us orm

V usin 0 – t

Threshold P(≥ T shold oisson

Bbbl ted

1 0 7 .53

3.17 Reco mend

olume

Rate Estimates and

Spill Thresholds (

Confidence In

g the 199

rvals

005 R

Vario

)

Platf

2 a e

hre ) Rate per

Adjusted P Adjus LCL Adjusted UCL

00 .5 1.94 1 2.31

500 0.19 0.64 0.38 1.02 

1000 0.11 0.37 0.16 0.66 

Threshold) is relatively well estimated. This is felt to be the case for 

utions developed. 

erspective. Inter-spill analyses used three different exposure variables: time, 

the declining rates between the two time intervals. 

Three parameter lognormal distributions fit the platform volume data very well. Using the larger 

≥ 50 bbl data set, it was shown how to estimate the likelihood of spills exceeding over 

The above Table 3.17 is useful for estimating spill volumes for the thresholds given above. It is 

based on the larger ≥ 50 bbl data set. Other thresholds of interest can easily be examined in the

same manner. In addition to providing rate estimates for the 100 bbl, 500 bbl, and 1,000 bbl

thresholds, this table bounds the rate with the recommended approach to establishing confidence

intervals when the P(≥

platform spills using the three parameter lognormal distrib

3.6.6 Summary and Conclusions 

Section 3.6 analyzed platform spills ≥ 50 bbl from both an inter-spill perspective as well as a 

volume p

production, and platform-years. This analysis showed that platform spill rates have significantly

dropped over time for all exposure variables. The data was divided into two fairly equal time

intervals 1972 – 1989 and 1990 – 2005. Exact Poisson rate ratio analysis provided confidence 

intervals for

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thresholds bound

ese rates. This methodology can be applied to any desired spill threshold. 

In summary, it is believed that th ger set such as used in this section can add 

considerable value. In addition t to e ate rates for other spill thresholds, this 

larger data set conclusively show rm spill rates have indeed fallen over time. This 

was not evident in earlier analyses based on data ≥ 00 bbl.

The following conclusions are dr e re in this section:

1. The use of the larger latf ≥ 50 bbl adds remarkable modeling 

flexibility and improv tion he conceptual underpinnings of the

statistical modeling. arg ta set, it is unlikely that the statistically 

significant drop in pla tes would have been detectable. 

2. Production and platfo use xposure variables to help understand and 

model not only the GOM but will be advantageous in the GOM to Arctic extension of 

Chapter 4. 

3. The application of ex onfi ce intervals for differing exposure variables 

provides a more firm foundation for uncertainty quantification and prediction. 

4. The application of ex at c ence intervals allows quantification 

of the uncertainty in t an p atform spill rates for the two time 

periods used. 

5. Table 3.13 provides p r r ee exposure variables for spill rates 

≥ 50 bbl for both the 1972 – 1989 and 1990 – 2005 time intervals. 

6. A three parameter log ib o form spill volumes ≥ 50 bbl provides 

ibutions for pipelines and 

latforms. 4

examine h The

data in these tw re lim po butio sis

shows that the Poisson distribution assumption e e ble t this

data. s fit the sp volumes for both pipelines and platforms. 

Section 3.5 expands the pipeline da o include spil 50 bbl. Three exposure variables are 

used: tim , production, and pipeline miles. The inter-spill data for line expo e 

variables are found to be adequately fit by exponential distributions. Therefore a Poisson 

distribution can be used to assess spill rates for these exposure variables as well as quantifying 

the associated uncertainty. This section also highlig the relation tween the onential

and Poisson and illustrates their relationship. Pipeline spill volum odeled w y a

Weibull distribution and ways to estimate rates for spills of varying thresholds are given along 

, e.g., 100 bbl, 500 bbl, and 1,000 bbl. Confidence intervals were developed to

th

e use of a lar data

o being able stim

ed that platfo

1,0

awn from th sults

data set for p orm spills 

es the valida of t

Without the l er da

tform spill ra

rm-years are ful e

act Poisson c den

act Poisson r e ratio onfid

he relative ch ge in l

latform spill ates fo all thr

normal distr ution f r plat

a more complete use of available data and reduces the width of spill rate confidence 

intervals. 

7. Table 3.17 presents the recommended production spill rate confidence intervals for 

thresholds ≥ 50 bbl. 

3.7 Chapter Summary 

Chapter 3 examines inter-spill distributions and spill volume distr

p Section 3.2 introduces exact Poisson confidence intervals. Sections 3.3 and 3.

t e Anderson and Labelle (2000) data and respectively.

o sections a

for pipelines

≥ 1,000 bbl. Ex

is vali for th

platforms,

nential distri

xposu e varia

ited to spills n analy

d r ime for

Weibull distribution ill

ta t ls ≥

e all pipe sur

hts ship be exp

es are m ell b

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with alternative confidence interval approaches. The recommendation approach is documented. 

pill rates from 1972 – 1989 versus 1990 – 

005. All techniques strongly showed that platform spill rates are significantly lower in the latter 

and confidence intervals a parately for the time 

eriods. Three parameter lognormal distributions fit the platform spill volume data and methods 

were pr to estimate spill thresholds from bl data.

There was no statistical evidence of a spill rate change over time for pipelines. 

Section 3.6 performs a similar analysis for platform spills ≥ 50 bbl, but complications arose in 

that the spill rates cannot be modeled by a single Poisson distribution for the full ≥ 50 bbl data 

set for any of the three platform exposure variables (time, production, and platform-years). 

Several statistical techniques were used to examine s

2

time period. Each of these two time periods separately is well modeled by Poisson distribution 

re provided for all three exposure variables se

p

esented rates for other the ≥ 50 b

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4 Extending to Alaska 

4.1 Introduction 

Rather than repeating discussions about the similarities and differences between the GOM and 

the Beaufort and Chukchi Seas, this section will simply describe the organization of this chapter 

and the methodology used to construct oil-spill probabilities for OCS areas north of Alaska. 

However, it is appropriate to begin with a description of the uncertainties that must be addressed 

so that the level of accuracy of the results can be placed in a realistic context. These 

uncertainties include: 

1. What is the best mix of drivers by which to measure oil spill probabilities?

2. What is the average rate of oil spills within the existing OCS infrastructure? 

3. What is the best way to deal with GOM oil spills with GOM specific causes, such as 

hurricanes and third party damage from fishing trawlers? 

4. What is the relationship between spill rates at the different spill thresholds of 50, 100, 

500, or 1000 bbl?

5. Since different values will be calculated depending on the exact data set and 

methodology, how should the uncertainty over which is best be reflected?

6. Is the average rate shifting over time, and if so what is it now and what is it projected to 

be?

7. How should this average rate be extended to new regions, such as Alaska?

8. What is the mix of infrastructure that will be used to produce oil in the OCS region of 

Alaska?

9. What spill probabilities are linked to Alaska specific spill causes and how do 

probabilities for existing causes such as human error change with increased cold and 

darkness?

10. What reductions in oil spill probabilities are possible through regulatory requirements for 

design and operations?

Many of these uncertainties are beyond the scope of this study, and some may in fact be 

unknowable. However, they collectively enforce the humble recognition that the uncertainties 

defined in this study are only the starting point for where other uncertainties begin. 

Oil spills in Alaskan waters can occur for reasons such as corrosion and human error that operate 

anywhere. The probabilities of these spills detailed in Section 4.3 are estimated using GOM 

data. The results are built upon, but distinct from the material of Chapter 3, as some spills 

included in the spill rates of Chapter 3, such as those from hurricanes and third party impacts, are 

extremely unlikely or impossible in the Arctic. 

One of the sets of spill rate estimates derived for the GOM is clearly unusable for extension to 

the Arctic. These are the spill rates based on time. For example, Table 3.13 includes platform

spill rate estimates for 1990 to 2005 of 1.375 or 1.504 spills per year, depending on approach. 

This is for an average of 3523 platforms, thus applying it to a development scenario with a 

maximum of 8 platforms would clearly be absurd. Thus, rates per year derived for the GOM 

should only be applied within the GOM. 

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The spill rates developed in this chapter, like the ones in Chapter 3, are stated as x pipeline spills 

per pipeline mile-year or y platform spills per platform-year. Thus, it is necessary to have a 

development scenario of how many pipeline miles and platforms in each year to produce what 

volume of production. Since any development is some time in the future, any scenario is in 

some sense speculative. However, for its own planning purposes and in conjunction with Bercha 

(2002 and 2006) MMS has constructed a Beaufort Sea development scenario. This is detailed in 

Section 4.2. While it is unlikely to match development if it occurs, it is certainly a realistic 

representation of one possibility. As such, it is a solid example of how the spill rates can be 

used, and a useful test case as to what methodologies are the most realistic. 

Sections 4.4 and 4.5 addresses what is known about Arctic specific causes that can be linked 

respectively with pipeline and with platform oil spills. Not surprisingly, some of this cannot 

currently be stated in statistical terms because not enough is known. 

Section 4.6 applies the spill rates to the Beaufort development scenario in order to calculate lifeof-field (LOF) probabilities where possible. This can be compared with results in Section 4.7 for 

the data in Bercha (2006). This is done in order to examine the level of agreement and 

disagreement between the two reports on oil spill occurrence estimators for the Beaufort/Chukchi 

Sea OCS. 

Section 4.8 summarizes this chapter. 

4.2 Development Scenario 

Table 4.1 summarizes a hypothetical development scenario for the Beaufort Sea. This is a 

simplification of data supplied by MMS for Bercha (2006, Table 3.2) and also directly for this 

study. As this study does not for example generally consider the water depth for pipelines or 

platforms, nor the diameter for pipelines; the scenario is simplified so that only the total rows 

and columns from the more detailed scenario are repeated in Table 4.1. While not part of the 

original scenario, the final row for total exposure has been created by simply counting the years 

or summing the platforms, pipelines, or production. 

One of the uncertainties described in Section 4.1 concerned the mix of infrastructure that will be 

used to produce oil in the OCS region of Alaska. This uncertainty includes both the details for 

each category, and the relationships between them. Obviously, the precise mix of miles of 

pipelines, numbers of platforms, and numbers of wells will not be known until and if they are 

built. This uncertainty means that probabilities derived from spill rates for each driver are 

combined in an uncertain way. Perhaps the most important of these uncertainties is how much 

production will come from the infrastructure, as fundamentally it is the level of production which 

produces the benefits and justifies all costs of development – economic, environmental, and 

social. This study can only recognize this uncertainty; this study cannot quantify it. 

The scale of the Beaufort development introduces another source of uncertainty. Unlike the 

GOM which has a large infrastructure that forms a sizeable statistical universe, the Beaufort 

development would be an example of small sample statistics – where greater variability in 

average outcomes is expected. While the GOM of Mexico has a platform spill rate for ≥ 50 bbls 

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of about 1.5 per year, it is not unexpected to have 5 spills in some years, but 15 spills in 1 year 

(or 10 times the average) would be extremely unlikely. On the other hand, if Alaska were to 

have a platform spill rate of 1 every 30 years; the year with a spill is 30 times the average. 

Predicting the average spill rate is not significantly affected by this scale difference, but the 

uncertainty over the reasonable range of possible outcomes for an Alaskan scenario is heavily 

affected. Thus, it should be emphasized that it is average rates that are being estimated in this 

study. 

Table 4.1 Beaufort Sea Development Scenario 

Year 

Cumulative

Production 

Platforms 

Cumulative

Production 

Wells 

In-use 

Pipeline 

Length 

[miles] 

Production 

Mbbl 

2009 1 3 

2010 1 13 10 7.9 

2011 2 26 10 15.7 

2012 3 39 20 23.6 

2013 3 59 30 39.4 

2014 4 72 30 44.4 

2015 4 82 50 55.3 

2016 5 95 50 59.5 

2017 6 108 80 74.5 

2018 7 132 80 76.1 

2019 8 156 115 102.5 

2020 8 176 115 103.5 

2021 8 196 115 97.9 

2022 8 206 115 93.1 

2023 8 206 115 85.6 

2024 8 206 115 79.2 

2025 7 183 105 67.5 

2026 7 183 105 59.0 

2027 6 160 95 49.9 

2028 5 137 80 42.2 

2029 5 137 80 37.0 

2030 5 137 70 32.4 

2031 5 137 70 28.5 

2032 5 137 70 25.0 

2033 5 137 70 21.9 

2034 4 114 60 17.0 

2035 4 114 60 14.9 

2036 2 68 40 8.3 

2037 2 68 40 7.3 

2038 2 68 40 6.5 

Total exposure for variable 

30 148 3555 2035 1375.6 

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4.3 Extension of Non-GOM Specific Spills to the Arctic 

4.3.1 Methodology 

This section focuses on how the extension to the Arctic of GOM based models can be done. 

This allows the large data base of past experience to be used, but the results are expected to be 

less reliable predictors for the Arctic than they are the GOM. 

 

Two ways are envisioned to extend the GOM results to the Arctic: 

1. Use estimated spill rates from Chapter 3 for the GOM by exposure variable. To estimate 

rates for spills exceeding the threshold, use information from the spill size modeling 

sections of Chapter 3. Adjust these rates by using binomial probabilities for “applicable 

spills.” These binomial probabilities would be based on the best estimates as to which of 

the GOM spills above each spill threshold might be applicable to the Arctic. 

2. Discard GOM spill data that is thought to be not applicable to Arctic. Apply 

methodology similar to Chapter 3 to derive spill rates for the “applicable spills.” To 

calculate rates for spills exceeding the threshold, count the number spills exceeding 

threshold in the data. 

This section relies on the statistical foundation of Chapter 3, and some of the results are used 

here. There is a difference which affects the rates for pipeline spills with the production 

exposure variable. Chapter 3 analyses of pipeline spills used total OCS production, while 

chapter 3 analyses of platform spills used GOM production. In this chapter, GOM production 

has been used for both pipeline and platform spills. 

Method 1 is presented in Section 4.3.2.1 and 4.3.3.2, respectively for pipelines and platforms, for 

spills sizes ≥ 50 bbl. Since it starts with the full data set of spills ≥ 50 bbl, its statistical 

reliability is maximized. It is applied to spill rates exceeding size thresholds with three exposure 

variables – production, pipeline mile-years, and platform-years. Extensive work has gone into 

carefully analyzing the GOM data for each of the relevant exposure variables for pipelines and 

platforms. In addition, various approaches to defining confidence intervals for spill size 

thresholds were examined in detail with production as the exposure variable. 

There has not been detailed examination within the GOM data of spill size thresholds with 

pipeline mile-years and platform-years as the exposure variable. However, the basic work on 

what proportion lies within above each spill size threshold does not depend on the exposure 

variable. Thus, the authors believe that method 1 can be applied with the same validity to the 

exposure variables of production, pipeline mile-years, and platform-years. 

Method 1 allows the uncertainty in the selection of what is applicable or not applicable from the 

GOM to the Arctic to be directly folded into the analysis. Method 1 results in conservative 

estimates for the lower and upper confidence limits (LCL, UCL). Consider the LCL for method 

1. It is found by multiplying (1) the LCL for the Poisson rate times (2) the LCL for the binomial 

proportion of the ≥ 50 spills above each threshold times (3) the LCL for the binomial proportion 

of the spills within above each threshold that are applicable. Because it is relatively unlikely for 

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the Poisson rate, the threshold binomial proportion, and the applicable binomial proportion to be 

simultaneously at their respective LCLs, the resulting computation is conservative. That is, the 

confidence interval is wider than it needs to be to account for the combination of these three 

uncertainties. 

The results of method 2, which considers only data from applicable spills at each spill size 

threshold, are presented respectively in Sections 4.3.2.2 and 4.3.3.3 for pipeline and platform

spills. The calculation of Poisson rates and confidence intervals is relatively straight-forward 

given the number of spills and the exposure variable. Detailed testing of exponential inter-spill 

quantities for “applicable spills” has not been possible within the constraints of this study. Nor is 

it obvious that such testing (the equivalent of much of Chapter 3) is warranted, since the focus is 

on the predicted spill rate parameter. Under method 2, it is not possible to consider the two 

uncertainties in the fraction of spills to be included. Under this method, a spill is either dropped 

(GOM specific) or not dropped (applicable). There is no uncertainty about it. Similarly, there is 

no uncertainty in the proportion of spills exceeding any size threshold. The exact number is 

counted in the data. 

Before applying these methods, it is appropriate to look again at the scale issue briefly discussed 

in Section 4.1 for the extension of GOM results to the Arctic. The scale issue is an analog of the 

distribution of the sample mean. A particular time period (or quantity of other exposure 

variable) may be used to develop an estimate of the spill rate which is an average of the number 

of spills divided by the quantity of exposure variable (time, production, pipeline mile-years, or 

number of platforms). Fewer spills are expected for the Arctic than for GOM. Thus the interspill times will likely be more uncertain resulting in the exponential distribution taking longer to 

stabilize on a good estimate (assuming the system is time homogeneous). Thus, the numerator of 

the spill rate is more variable. For the denominator the number of pipeline-miles (platforms) 

may be as much 60 (400) times larger in the GOM than in the Arctic. In some sense these 

exposure variables may be thought of as volumes. In geostatistics (Clark and Harper, 2000, 

chapter 11) the volume variance relationship explains the phenomena. As volumes increase the 

resulting standard deviation decreases. With increased variability in the Arctic, the resulting 

confidence intervals should be wider for the Arctic than for GOM. 

Method 2, which uses only data for applicable spills to derive estimates, is equivalent to another 

intuitively appealing, but limited approach. If one simply used portion ρ of the GOM spills 

(pipeline or platform) for an Arctic analysis, one gets a simple but possibly misleading Poisson 

approach. While intuitively appealing, it underestimates the uncertainty in the Arctic rate. 

The difficulty is that for a Poisson process, the rate parameter λ is the mean and variance of the 

distribution. Hence a lower mean implies a lower variance and thus a lower standard deviation. 

This is not a justifiable procedure for extending the GOM results to the Arctic. While the rate 

for “applicable spills” is lower, the confidence intervals must recognize the uncertainties in the 

binomial proportions of “applicable spills” and of “spills above the threshold.” 

In addition to the work presented here, analysis has also been done for two other approaches. 

The first is similar to method 1, but it used a single binomial proportion applicable for all spills, 

instead of using a different proportion applicable for each spill size threshold. While 

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conservative, this approach ignored the apparent relationship between spill size and 

“applicability.” Its usefulness was clearly surpassed by the method 1 presented here. An ad hoc 

modification to method 2 is also not presented, as the improved method 1 made it less necessary 

and because its complexity made it difficult to explain and validate. 

Method 2 represents a lower bound on the uncertainty involved in the extension from the GOM 

data to the Arctic, while method 1 provides an upper bound for the sources of uncertainty 

consider. This analysis deals with the known statistical uncertainties as completely as possible 

and method 1 does so in conservative way that overestimates that statistical uncertainty. 

However, the results in Sections 4.3.2 and 4.3.3 do not address some of the different 

uncertainties summarized in Section 4.1 – in particular the uncertainties related to the Arctic. 

Thus, the confidence intervals for both methods are most likely still an underestimation of the 

overall uncertainty in any Arctic predictions. As more data and better methods of estimation 

become available, Arctic predictions can be improved. 

4.3.2 Pipeline Spills 

4.3.2.1 Pipeline Spills using Method 1 

Method 1 starts with the basic uncertainty in the Poisson rate which was detailed for GOM 

pipeline spills in Table 3.3. However, in Table 4.2 the value for the production exposure 

variable is based upon GOM rather than OCS production from 1972 to 2005. Since the exposure 

volume is lower, the spill rate is slightly higher than in Table 3.3. 

Table 4.2 Method 1 Arctic Pipeline Spill ≥ 50 bbl Poisson Based Rate and 95% Confidence 

Intervals 

Label # 

Spills Exposure Variable Sum Exposure Variable Rate LCL UCL 

Spills/Bbbl 36 Production Bbbl 12.445 2.8927 2.0260 4.0048 

Pipeline Spills 

/KMile-year 36 KMile-years 161.796 0.2225 0.1558 0.3080 

The second source of uncertainty that must be addressed by method 1 is the proportion of spills 

at each spill size threshold. Chapter 3 examined spill rates for varying spill thresholds using the 

rates per Bbbl of production for ≥ 50 bbl spills and the distribution of spill volumes. For 

pipelines a Weibull distribution fit the GOM spill volumes. Table 3.8 (relevant part reproduced 

below) describes the proportion and the exact binomial confidence intervals for the proportion of 

a spill data set above the thresholds of 100, 500, and 1000 bbl. Multiplying Table 3.8 times the 

Poisson rates and confidence limits was the conservative procedure in Chapter 3 to estimate 

pipeline spill rates at higher spill thresholds with production volume as the exposure variable. 

Exactly the same approach can be applied for pipeline mile-years using the last row of Table 4.2 

times the proportion and exact binomial confidence intervals for spill size thresholds shown in 

Table 3.8. 

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Table 3.8 Proportion of ≥ 50 bbl Pipeline Spills above Different Thresholds with 95%

Binomial Confidence Limits 

Threshold P(≥ Threshold) LCL UCL 

50 1 1 1 

100 0.7932 0.6398 0.9181

500 0.5440 0.3810 0.7206

1000 0.4293 0.2551 0.5924

The third source of uncertainty is the proportion of spills above each threshold that are applicable 

to the Arctic vs. those with a GOM-specific cause. Table 4.3 details that the spill sizes are on 

average larger for GOM-specific spill causes than the non-GOM or applicable spill causes. The 

number of GOM-specific pipeline spills is about the same for each threshold, while the number 

of applicable spills falls sharply as the threshold increases. 

Table 4.3 GOM and Applicable Pipeline Spills at Different Thresholds with 95% Binomial 

Confidence Limits (Based on Table 2.17) 

Spill 

Threshold 

GOM 

Specific 

Applicable 

or NonGOM Total 

Proportion 

Applicable LCL UCL 

≥ 50 bbl 15 21 36 .5833 0.4076 0.7449 

≥ 100 bbl 15 14 29 .4828 0.2945 0.6747 

≥ 500 bbl 13 6 19 .3158 0.1258 0.5655 

≥ 1000 bbl 11 5 16 .3125 0.1102 0.5866 

The estimated Arctic pipeline spill rate for each spill threshold is simply the Poisson rate times 

the size proportion times the applicable proportion for that size threshold. For conservative 

estimates of the lower and upper confidence limits, the three LCLs are multiplied, as are the 

three UCLs. As noted in Section 4.3.1, calculating a lower confidence limit by multiplying the 

LCLs for two or three variables is a conservative approach, as it is relatively unlikely that all 

variables will simultaneously be at their lower confidence limits. 

Tables 4.4 and 4.5 are the result. They specifically consider (1) the underlying uncertainty in 

estimating the Poisson rate using the full data set of 36 pipeline spills ≥ 50 bbl, (2) the 

uncertainty in estimating what fraction of spills ≥ 50 bbl exceed higher spill size thresholds, and 

(3) the uncertainty in the binomial proportion that is applicable to the Arctic. Since, for example, 

the LCL is formed by multiplying the LCL for each source of uncertainty, the result is a 

conservative one. 

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Table 4.4 Method 1 Conservative Procedure to Estimate Arctic Pipeline Spill Rates for 

Various bbl Thresholds with Exposure Variable = Production 

 Adjusted Poisson

x Rate per Bbbl LCL UCL 

50 1.6874 0.8257 2.9830 

100 1.1077 0.3817 2.4805 

500 0.4969 0.0971 1.6320 

1000 0.3881 0.0569 1.3918 

Table 4.5 Method 1 Conservative Procedure to Estimate Arctic Pipeline Spill Rates for 

Various bbl Thresholds with Exposure Variable = Pipeline Mile-Years 

 Adjusted Poisson

x Rate per KMile-yr LCL UCL 

50 0.1298 0.0635 0.2294 

100 0.0852 0.0294 0.1908 

500 0.0382 0.0075 0.1255 

1000 0.0299 0.0044 0.1071 

4.3.2.2 Pipeline Spills using Method 2 

Method 2 is using the actual data rather than a fitted distribution for the number of spills 

exceeding each size thresholds and for whether the spill cause is GOM-specific or applicable to 

the Arctic. Thus, for method 2 it is only the number of applicable spills for each spill size 

threshold (see Table 4.3) that is used in calculating the rates and Poisson confidence limits. 

Thus, for each spill size threshold the rate, LCL, and UCL depend only on the number of spills 

and the exposure variable. 

Tables 4.6 and 4.7, respectively, show the result of method 2 for production and pipeline mileyears. As detailed in Section 4.3.1, this method limits the data to spills above each threshold that 

are “applicable to the Arctic” or stated another way, spills that have a “non-GOM specific 

cause.” This approach assumes the lower rate for these spills lowers the variability and tightens 

the confidence interval values. This ignores the uncertainty in the proportion of spills that are 

applicable to the Arctic vs. GOM-specific causes and the uncertainty about the proportion of 

spills above each spill size threshold.

Methods 1 and 2 get slightly different results for the rate estimate for spills at thresholds of 100 

bbls or larger. Tables 4.6 and 4.7 are based on the number of spills found in each category, not 

on a distribution of spill sizes. 

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Table 4.6 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for Arctic 

Pipeline Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with Exposure 

Variable = Production 

Spill 

Threshold 

# 

Spills Exposure Variable

Sum Exposure 

Variable Rate LCL UCL 

≥ 50 bbl 21 Production Bbbl 12.445 1.6874 1.0445 2.5794

≥ 100 bbl 14 Production Bbbl 12.445 1.1249 0.6150 1.8875

≥ 500 bbl 6 Production Bbbl 12.445 0.4821 0.1769 1.0494

≥ 1000 bbl 5 Production Bbbl 12.445 0.4018 0.1305 0.9376

Table 4.7 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for Arctic 

Pipeline Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with Exposure 

Variable = Pipeline Mile-Years 

Spill 

Threshold 

# 

Spills Exposure Variable

Sum Exposure 

Variable Rate LCL UCL 

≥ 50 bbl 21 KMile-years 161.796 0.1298 0.0803 0.1984

≥ 100 bbl 14 KMile-years 161.796 0.0865 0.0473 0.1452

≥ 500 bbl 6 KMile-years 161.796 0.0371 0.0136 0.0807

≥ 1000 bbl 5 KMile-years 161.796 0.0309 0.0100 0.0721

4.3.3 Platform Spills 

The extension of GOM pipeline spill statistical results to the Arctic was done using method 1 in 

Section 4.3.2.1 and method 2 in Section 4.3.2.2. A parallel structure for platforms will be found 

in Sections 4.3.3.2 and .3. However, it is first necessary to deal with a complication found in the 

data for platform spills. 

4.3.3.1 Applicable vs. GOM-Specific Platform Spills 

Both methods for extending the GOM statistical results rely on data about applicable spills for 

each spill size threshold. Method 1 uses the proportion, LCL, and UCL; while method 2 uses the 

number of spills. While straightforward for pipeline spills, there are complications for platform

spills. 

Table 4.8 lists platform spills for the 1990 – 2005 period, which are then summarized in top half 

of Table 4.9, which lists the number of GOM-specific and “applicable” spills at each spill size 

threshold. 

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Table 4.8 GOM Platform Spills – Hurricane & Applicable (1990 – 2005) 

1991-10-13 280

1992-12-26 100

1994-11-23 148

1995-01-25 600

1995-07-06 75

1995-10-03 89

1995-12-15 435

1996-09-29 105

1996-12-31 62

1997-12-16 170

1998-04-29 100

1999-01-23 105

1999-09-09 125

2000-02-28 200

2000-08-09 60

2001-03-30 127

2002-10-03 1,588 Lili 

2003-05-09 264

2003-05-10 430

2004-09-15 1,053 Ivan 

2005-08-29 2,225 Katrina 

2005-09-24 7,371 Rita 

As shown in Table 4.9, the platform spills for 1990 – 2005 exhibit a problem that can occur with 

small samples. In this case all of the GOM specific platform spills exceed 1000 bbl and there are 

no “applicable” spills of that size in that time frame. This means that there is a relationship 

between spill size and spill cause measured at the GOM/applicable level. More importantly, this 

would also imply that all calculated values for extending to the Arctic for ≥ 1000 bbl would 

indicate a probability of zero. This is clearly not true, since there are 4 applicable spills of that 

magnitude in the earlier portion of the 1972 – 2005 period. 

Table 4.9 GOM and Applicable Platform Spills at Different Thresholds 

 Spill 

Threshold GOM 

Applicable or 

Non-GOM 

Proportion 

Applicable Total 

1990 – 2005 

≥ 50 bbl 4 18 81.8% 22 

≥ 100 bbl 4 14 77.8% 18 

≥ 500 bbl 4 1 20.0% 5 

≥ 1000 bbl 4 0 0.0% 4 

1972 – 2005 

≥ 50 bbl 7 71 91.0% 78 

≥ 100 bbl 5 44 89.8% 49 

≥ 500 bbl 4 7 63.6% 11 

≥ 1000 bbl 4 4 50.0% 8 

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A conservative solution is to use the larger data set from 1972 – 2005 to define the proportion of 

spills in the ≥ 1000 bbl category (50%) that are applicable. This increases the number of 

applicable spills above the top spill threshold to 2, and these two spills increase the number of 

applicable spills ≥ 500 bbl to 3. The lower two spill thresholds are left unchanged. Table 4.10 is 

the result with the changed numbers in italics. Table 4.10 also includes the exact binomial lower 

and upper confidence limits for these proportions. 

Table 4.10 Adjusted GOM and Applicable Platform Spills at Different Thresholds for N = 

22 Spills (Changed Values in Bold Italic) 

Spill 

Threshold GOM 

Applicable or 

Non-GOM Total 

Proportion 

Applicable LCL UCL 

≥ 50 bbl 4 18 22 .8182 0.5972 0.9481 

≥ 100 bbl 4 14 18 .7778 0.5236 0.9359 

≥ 500 bbl 2 3 5 .6000 0.1466 0.9473 

≥ 1000 bbl 2 2 4 .5000 0.0676 0.9324 

Because the number of spills ≥ 500 and 1000 bbl is small, the lower and upper confidence limits 

for the applicable proportions are very wide. 

4.3.3.2 Platform Spills using Method 1 

For method 1 the first factor in the confidence limits is the basic uncertainty in the Poisson rate 

which was detailed for GOM platform spills in Table 3.13. Table 4.11 is extracted from Table 

3.13 for ease of reference. 

Table 4.11 GOM Platform Spill ≥ 50 bbl Exact 95% Poisson Confidence Intervals for 1990 

– 2005 

GOM Platforms 1990-2005 

Label # 

Spills Exposure Variable Sum Exposure Variable Rate LCL UCL 

Spills/Bbbl 22 Production Bbbl 6.766 3.252 2.038 4.923 

Spill/(Number of Platforms) 22 KPlatforms-Years 56.37 0.3903 0.2446 0.5909

Chapter 3 examined spill rates for varying spill thresholds using the rates per Bbbl of production 

for ≥ 50 bbl spills and the distribution of spill volumes. However, the results of fitting a three 

parameter lognormal to the GOM platform spill volumes can be applied to all exposure 

variables. Table 3.15 for platform spills describes the proportion and the exact binomial 

confidence intervals for the proportion of a spill data set above the thresholds of 100, 500, and 

1000 bbl. 

The average platform spill size for 1990 and later cannot be shown to be statistically 

significantly higher than the average spill size for 1972 and later. However, the proportion ≥ 100 

bbl and ≥ 500 bbl is larger in the later time frame, which matches the break point used for the 

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lower spill rate. Thus, to ensure that the results are conservative a new 3-parameter lognormal fit 

was done for the 1990 to 2005 data. The parameters for that fitted distribution are location = 

5.047, scale = 1.606, and threshold = 49.9. Table 4.12 summarizes the binomial proportions and 

confidence limits for the number of spills exceeding the higher thresholds. This is the second 

source of uncertainty included in method 1. 

Table 4.12 Proportion of ≥ 50 bbl Platform Spills above Different Thresholds with 95%

Binomial Confidence Limits (1990-2005 Data) 

Threshold P(≥ Threshold) LCL UCL 

50 1 1 1 

100 0.7597 0.5463 0.9218

500 0.2541 0.1073 0.5022

1000 0.1299 0.0291 0.3491

The third source of uncertainty is the proportion applicable in each of the spill size categories. 

The proportions and lower and upper confidence limits were defined in Table 4.10 for each spill 

size threshold. 

The estimated Arctic platform spill rate for each spill threshold is simply the Poisson rate times 

the size proportion times the applicable proportion for that size threshold. For conservative 

estimates of the lower and upper confidence limits, the three LCLs are multiplied, as are the 

three UCLs. As noted in Section 4.3.1, calculating a lower confidence limit by multiplying the 

LCLs for two or three variables is a conservative approach, as it is relatively unlikely that all 

variables will simultaneously be at their lower confidence limits. 

Tables 4.13 and 4.14 are the result. They specifically consider (1) the underlying uncertainty in 

estimating the Poisson rate using the full data set of 22 pipeline spills ≥ 50 bbl for 1990 – 2005, 

(2) the uncertainty in estimating what fraction of spills ≥ 50 bbl exceed higher spill size 

thresholds, and (3) the uncertainty in the binomial proportion that is applicable to the Arctic. 

Since, for example, the LCL is formed by multiplying the LCL for each source of uncertainty, 

the result is a conservative one. 

Table 4.13 Method 1 Conservative Procedure to Estimate Arctic Platform Spill Rates for 

Various bbl Thresholds with Exposure Variable = Production 

Adjusted 

Poisson 

x Rate per Bbbl LCL UCL 

50 2.6606 1.2169 4.6679 

100 1.9215 0.5829 4.2474 

500 0.4958 0.0321 2.3421 

1000 0.2112 0.0040 1.6026 

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Table 4.14 Method 1 Conservative Procedure to Estimate Arctic Platform Spill Rates for 

Various bbl Thresholds with Exposure Variable = Platform-Years 

 Adjusted Poisson 

x Rate per Platform-Year LCL UCL 

50 0.3193 0.1461 0.5602 

100 0.2306 0.0700 0.5098 

500 0.0595 0.00385 0.2811 

1000 0.0254 0.00048 0.1923 

4.3.3.3 Platform Spills using Method 2 

Method 2 is using the actual data rather than a fitted distribution for the number of spills 

exceeding each size thresholds and for whether the spill cause is GOM-specific or applicable to 

the Arctic. Since this assumes the lower rate for “spills applicable” to the Arctic and for larger 

spill sizes also reduces the variability, this has tighter confidence intervals than the conservative 

approach. This ignores the uncertainty in the proportion of spills for each spill threshold and the 

proportion that is applicable to the Arctic vs. GOM-specific causes. 

The number of applicable spills from Table 4.10 is then used to generate Table 4.15 and 4.16, 

which show the results for different spill sizes when production and platform-years are used as 

the exposure variables. 

Table 4.15 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for 

Arctic Platform Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with

Exposure Variable = Production 

Spill Threshold 

# 

Spills Exposure Variable

Sum Exposure 

Variable Rate LCL UCL 

≥ 50 bbl 18 Production 6.766 2.6606 1.5768 4.2048

≥ 100 bbl 14 Production 6.766 2.0693 1.1313 3.4720

≥ 500 bbl 3 Production 6.766 0.4434 0.0914 1.2959

≥ 1000 bbl 2 Production 6.766 0.2956 0.0358 1.0679

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Table 4.16 Method 2 Results (Ignores Uncertainty in Applicability and Spill Size) for 

Arctic Platform Spill ≥ 50 bbl Poisson Based Rate 95% Confidence Intervals with

Exposure Variable = Platform-Years 

Spill Threshold 

# 

Spills Exposure Variable

Sum Exposure 

Variable Rate LCL UCL 

≥ 50 bbl 18 KPlatforms-yrs 56.37 0.3193 0.1892 0.5047

≥ 100 bbl 14 KPlatforms-yrs 56.37 0.2484 0.1358 0.4167

≥ 500 bbl 3 KPlatforms-yrs 56.37 0.0532 0.0110 0.1555

≥ 1000 bbl 2 KPlatforms-yrs 56.37 0.0355 0.0043 0.1282

4.4 Arctic Specific Hazards for Pipeline Oil Spills 

Section 2.6 which discusses the data on Arctic specific hazards is the introduction to this section. 

While these Arctic specific hazards are a key part of defining oil spill risk in the Arctic, this 

study’s focus has been on the extension of statistical results from the GOM to the Arctic. Thus, 

these results are much less comprehensive than other sections of the report. The statistically 

based results within this section are relatively limited, but where possible they are presented. 

4.4.1 Ice Keel Gouging 

Weeks, et al. (1983, 1984) included modeling of required burial depths for one ice impact during 

a 100-year period. Lacking detailed engineering analysis, and to demonstrate the estimation 

methodology, this study will rely on the Weeks model. This requires an assumption as to the 

burial depth of the pipeline. For consistency, this study will use the same 2.5 m that is assumed 

in Bercha (2006), which is nearly identical with the 8’ that was assumed for the Liberty pipeline 

in Blanchet et al. (2000). 

While the burial depth of 2.5 m is assumed to be critical, which matches Weeks, detailed 

engineering analysis is appropriate to determine whether the critical incision depth is shallower 

or deeper than the burial depth. It is possible that shallower incisions may be an issue, if the 

region of soil deformation which extends below the incision is an issue for pipeline integrity. In 

Paulin et al. (2001) this appeared to be the design approach used for Northstar. On the other 

hand, if the pipeline can resist, break-off, or be safely displaced by ice ridges that have some

scale of contact, then the key incision depth is deeper than the burial depth. This latter 

possibility can be modeled using HS, the conditional failure probability for the pipeline given an 

ice gouge impact (Bercha, 2002 & 2006). For descriptions of the pipeline’s strength and testing 

at Northstar see Lanan and Ennis (2001). 

Equation 17 from Weeks et al. (1983, p. 30) can be simplified as equation 4.1 to calculate the 

number of km-years for a single ice keel (gouge) to pipeline contact. Note that 0.2 m is 

subtracted from the burial depth to match this calculation to the probability distribution derived 

from the censored data (no gouges shallower than 0.2 m were measured). The flux or gouge 

density measured by Weeks et al. was 5.2 gouges/km-yr for deeper water gouges. 

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1 contact/km-yr = e–λ(x – 0.2) g sinθ (4.1) 

Where λ = parameter for probabilistic distribution of incision depth 

x = burial depth (2.5 m assumed) 

g = average number of gouges/km-year along pipeline route (5.2 gouges/km-yr) 

θ = angle between the route and the trend of the gouges (90o

 assumed) 

For this study θ, angle between the route and the trend of the gouges, is assumed to be 90o

. As 

detailed in Chapter 2, this value was chosen because the bulk of the ice movement is roughly 

parallel to the shore and the pipeline is assumed to be largely perpendicular to the shore. This is 

also a conservative assumption. It is worth noting that Bercha (2002 & 2006) uses 45o

 for an 

average orientation. The impact of this assumption on the results can be estimated by the ratio 

between 1 and the sin(45o

) = 0.707. 

Table 4.17 summarizes the key inputs and outputs for the probabilistic model developed by 

Weeks et al. There are two pairs of columns λ and for the corresponding gouge rate. The first 

pair is based on calculating λ from Equation 2.1, and the second pair is based on subtracting 1 

from the value of λ to adjust for the difference between all gouges (used to derive λ) and new 

gouges (Weeks et al., 1983, p. 30). Note: that adjustment accounts for the fact that if all gouges 

are used to build the depth distribution, infilling over time has reduced the average incision 

depth. 

Table 4.17 Gouge rate for a burial depth of 2.5 m 

Water

depth 

(m) λ

Gouge 

/km-yr 

Gouge 

/mi-yr λ - 1 

Gouge 

/km-yr 

Gouge 

/mi-yr 

5 8.16 3.65E-08 5.88E-08 7.16 3.64E-07 5.86E-07

10 6.68 1.10E-06 1.77E-06 5.68 1.09E-05 1.76E-05

15 5.47 1.78E-05 2.87E-05 4.47 1.78E-04 2.86E-04

20 4.48 1.74E-04 2.80E-04 3.48 1.74E-03 2.80E-03

25 3.67 1.13E-03 1.82E-03 2.67 1.13E-02 1.81E-02

30 3.00 5.21E-03 8.38E-03 2.00 5.19E-02 8.36E-02

35 2.46 1.82E-02 2.93E-02 1.46 1.82E-01 2.92E-01

Table 4.17 makes it clear that each 5 m increase in depth from 10 m to 25 m makes about an 

order of magnitude increase in the probability of a keel to pipeline contact. Thus, if the burial 

depth is constant, the probability of an oil spill is dominated by how much of the pipeline is in 

deeper water beyond the barrier islands. There is also an order of magnitude difference at all 

water depths depending on whether the adjustment for new versus all gouges is made. 

If these values are compared with the 5.23 x 10 – 6spills/km-yr reported in Bercha (2006), they 

are roughly comparable at a water depth of 10 m. However, they differ radically from Bercha 

for deeper water depths where Bercha reduces the rate, and Table 4.17 indicates an order of 

magnitude increase for each 5 m of water depth. 

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In the future, it should be possible to apply the results of Table 4.17 or the underlying equation, 

but it will require information on how much pipeline would be in each water depth class, and 

how much cover or what burial depth should be assumed for each water depth class. In addition 

it would seem appropriate to consider the presence of barrier islands or other geological shields 

from the moving ice. 

Finally, there is the question of whether keel contact with the pipeline is required (Î decrease 

the effective burial depth of pipe in above calculations, because the pressure of displaced soil is a 

problem) or can say 0.5m of a keel impact the pipe without damage (Î increase the effective 

burial depth of pipe in above calculations)? Note: because there is an order of magnitude change 

for each 5m of depth, it is suggested that changing the effective burial depth is a superior 

modeling choice to using a conditional probability for pipeline spill given keel to pipeline 

contact. That conditional probability might be better used to account for a pipeline that is 

damaged (bent and needing replacement) versus one that is broken and spilling oil. 

4.4.2 Strudel Scour 

Section 2.6.2 on strudel scour concluded with the calculated probabilities for a free span greater 

than 0’ of 3.8x10-4 and for a free span ≥ 100’ of 5.2x10-5 (Blanchet et al., 2000, p. ix). As this 

was for 1.8 miles of pipe vulnerable to strudel scours for a year, the latter probability can be 

converted to a value of 2.9x10-5 per mile-yr or 0.029 per KMile-yr for comparison with rates for 

non-GOM specific spill causes. Note: that the further off-shore a platform is; the more 

opportunity there is to select landfall locations that are as remote as possible from major river 

outlets, which will minimize the probability of strudel scours.

There are 2035 mile-years for pipelines within the Beaufort development scenario. This can be 

split between 985 miles in 10 m to 20 m water depth and 1035 mile-years in less than 10 m

depth. Without more detailed information, it is not possible to calculate how many mile-years of 

strudel scour exposure there is over the life of the field. 

However, at this level of detail a first-order approximation would place about 30% of the shallow 

water pipeline-years in 2 to 5 m water depth (30% of the shallow water range) where strudel 

scour is most likely to be a problem. This assumes that some platforms are in say 6 m of water 

depth so that pipeline would have a larger fraction in the critical range and other platforms are in 

say 9 m of water depth – and connected to the platform in 6 m – so that none of that pipeline 

would be in the critical range of water depths. 

Thus, an estimate for the Beaufort Development Scenario for the number of pipeline spills due to 

strudel scour is 0.009 (= 2.9x10-5 per mile-yr * 1035 mile-years * 30%) over the life of the field. 

4.4.3 Upheaval Buckling 

As the engineering expertise and assumptions to model upheaval buckling are not within the 

scope of this study, it is assumed that the critical length defined for the probability of a strudel 

scour has appropriately considered the probability of upheaval buckling. Thus, the probability of 

upheaval buckling is assumed to equal the probability of a strudel scour. 

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4.4.4 Thaw Settlement 

As there is no statistical basis for estimating the probability of an oil spill due to thaw settlement, 

this study will not attempt to do so. However, it is worth noting that thaw settlement is a much 

more gradual phenomenon than the impact of an ice keel. Thus, an appropriate schedule for an 

appropriate pig can identify any thaw settlement before pipeline integrity is compromised. 

While it is outside the scope of this study, it is worth noting that if a clear design standard will be

applied to this phenomenon, then the design standard is potentially another way to establish a 

spill probability. For example, suppose that the design standard is for 1 spill every 100 or every 

1000 years. Such values can be converted into the probability of a spill. 

4.5 Arctic Specific Oil Spill Causes for Platforms 

The focus of this study has been on MMS data for the GOM and OCS total, and on data focused 

on Alaska specific natural hazards for pipelines. While Arctic effects on platform spills are 

clearly potentially important, this study does not address these beyond the following discussion. 

Bercha (2006) included values for ice forces, low temperature, and a category for other. Ice 

forces that can move or damage a platform must clearly be considered, and the low temperatures

of the Arctic are a hazard. However, this is based on spill cause classifications that do not 

include the second most common cause of platform oil spills – human error (see Table 2.21). 

The authors of this study suggest that the significant share of spills caused by human error could 

quite possibly increase in the Arctic environment. There is absolutely no question that human 

errors increase in the dark and in the cold, as well as in other forms of more challenging 

environments. Thus, there is the potential that platform spills due to human error could increase 

beyond the level experienced in the GOM. 

4.6 Application of Spill Rates to Development Scenario 

The exposures summarized at the bottom of Table 4.1 can be combined with the spill rates and 

limits calculated in Section 4.3. If method 1 rates are used, then the rates include the uncertainty 

in the rate and the uncertainty in the fraction of the spills that are “applicable” to the Arctic. For 

spill sizes exceeding 100, 500, and 1000 bbl then the uncertainty in the size variable is included. 

The results are predicted numbers of spills for the life of the field (LOF) represented by the 

development scenario. Method 2 considers only the uncertainty in the Poisson rate of spills. 

Table 4.18 is the expected number of spills over the LOF for the Beaufort development scenario 

using the conservative approach of method 1. This is only for the “applicable” spills and it does 

not include factors for increasing or reducing the impact of specific spill causes in the Arctic. It 

does adjust the exposures so measured in thousands of pipeline mile-years, thousands of 

platform-years, and billions of barrels of oil. This is required so that exposures are measured in 

the same units as the spill rates derived from the GOM with its much larger values. 

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Table 4.18 Application of Conservative (Method 1) Extended “Applicable” GOM Spill 

Rates (Spills ≥ 50 bbl) to Beaufort Development Scenario 

Pipeline Spills Platform Spills 

 In-use 

Pipeline 

Length 

[KMiles] 

Production 

Bbbl 

PlatformsYears 

[KPlatforms]

Production 

Bbbl 

Exposure 2.035 1.3756 0.148 1.3756 

rate 0.1298 1.6874 0.3193 2.661 

95% LCL 0.0635 0.8257 0.1461 1.217 

95% UCL 0.2294 2.9830 0.5602 4.668 

LOF # spills 0.2641 2.3212 0.0473 3.6605 

95% LCL 0.1292 1.1359 0.0216 1.6741 

UC 0 4.1034 9 213

One of the most important conclusions from examining Table 4.20, is that selecting the right 

driver to determine the spill rate is enormously important. For pipeline spills using spills per 

Bbbl oil produced versus spills per pipeline KMile-years makes about an order of magnitude 

difference in the predicted spill number and confidence limits. For platforms, it makes nearly 

two orders of magnitude difference. 

Consider the more extreme case of platform spills. The difficulty is that in the GOM from 1990 – 

2005 an average of 3523 platforms averaged 0.12 Mbbl of production per year each, while in the 

Beaufort development scenario an average of 5.1 platforms averaged 8.6 Mbbl of production per 

year for each. The authors believe that the probability of an oil spill is much more closely linked 

to the activities associated with each platform, than it is to the volume of oil produced by each 

platform. 

The authors suggest that using spills per volume of oil produced is not a reliable approach for 

estimating oil spills in the Arctic. Thus, further analysis in this section will be done only with 

the exposure variables of pipeline mile-years and platform-years. 

In contrast with these spill rates, the expected number of strudel scour caused oil spills is an 

addition of 0.009 expected pipeline spills over LOF is much, much smaller than 0.264 number of 

pipeline spills expected over LOF, and much smaller than the level of uncertainty associated 

with other causes. Thus, while strudel scour must be a design and planning issue, it is not the 

key uncertainty or source of potential oil spills. 

On the other hand, ice keel gouging can possibly have much larger values, but there is not yet a 

scenario against which those rates can be applied. 

Table 4.19 for applicable pipeline spills in the Arctic combines the information from Tables 4.5 

and 4.7 to make it easy to compare the conservative confidence limits (method 1) and minimum 

(method 2) confidence limits at different spill thresholds. These are the values that should be 

multiplied by the exposure variables for the Arctic to produce life of field probabilities of 

95% L .4668 0.082 6.4

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applicable pipeline oil spills at each spill threshold. This is only for “applicable” spills with 

causes similar to those that occur in the GOM, and it does not include Arctic-specific causes. 

One significant difference between the GOM and the development scenario is the average length 

of the pipelines. As noted in the list of cautions and caveats in Chapter 5, this seems likely to 

overstate the spill rates for the pipelines in the Arctic. 

Table 4.19 Arctic Pipeline Spills for Applicable Causes – Rates and 95% Confidence 

Limits (Spills/KMile-Years) 

Method 1 Conservative Method 2 

Spill Threshold Rate LCL UCL Rate LCL UCL 

50 0.1298 0.0635 0.2294 0.1298 0.0803 0.1984 

100 0.0852 0.0294 0.1908 0.0865 0.0473 0.1452 

500 0.0382 0.0075 0.1255 0.0371 0.0136 0.0807 

1000 0.0299 0.0044 0.1071 0.0309 0.0100 0.0721 

Table 4.20 for applicable platform spills in the Arctic combines the information from Tables 4.14 

and 4.16 to make it easy to compare the conservative confidence limits (method 1) and minimum 

(method 2) confidence limits at different spill thresholds. These are the values that should be 

multiplied by the exposure variables for the Arctic to produce life of field probabilities of 

applicable platform oil spills at each spill threshold. This is only for “applicable” spills with 

causes similar to those that occur in the GOM, and it does not include Arctic-specific causes. 

Table 4.20 Arctic Platform Spills for Applicable Causes – Rates and 95% Confidence 

Limits (Spills/KPlatforms-Years) 

Method 1 Conservative Method 2 

Spill Threshold Rate LCL UCL Rate LCL UCL 

50 0.3193 0.1461 0.5602 0.3193 0.1892 0.5047 

100 0.2306 0.0700 0.5098 0.2484 0.1358 0.4167 

500 0.0595 0.00385 0.2811 0.0532 0.0110 0.1555 

1000 0.0254 0.00048 0.1923 0.0355 0.0043 0.1282 

Tables 4.19 and 4.20 have been left as spill rates, rather than being multiplied by the exposure 

variables for the Beaufort development scenario, because it only requires a multiplication to 

convert to LOF spill probabilities. Also the Beaufort development scenario is itself subject to 

considerable uncertainty.

The many uncertainties listed at the start of this chapter may increase or lower the spill rate, but 

they certainly widen the confidence intervals. 

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4.7 Sensitivity Analysis of Platform Spill Rates to Data Adjustment 

In Section 4.3.3.1 the number of applicable spills ≥ 1000 bbl was adjusted from 0 to 2. This was 

done because there were 4 such spills in the 1972 – 1989 time frame, but none in 1990 – 2005. 

This is a conservative choice, as it increases the number of large spills with an applicable cause. 

While it may be unreasonable to use 0 for the number of such spills, it is certainly possible that a 

better adjustment might have been a single spill. 

Table 4.21 summarizes the rates and confidence limits for assuming 2 (as before) large 

applicable spills and for assuming 1 large spill. Not surprisingly, all rates and confidence limits 

are lower if the spill data adjustment is 1 spill rather than 2 spills. 

Table 4.21 Sensitivity Analysis for Arctic Platform Spills for Applicable Causes – Rates 

and 95% Confidence Limits (Spills/KPlatforms-Years) 

Method 1 Conservative Method 2 

Spill Threshold Rate LCL UCL Rate LCL UCL 

1000 (2 appl.) 0.0254 0.00048 0.1923 0.0355 0.00430 0.1282 

1000 (1 appl.) 0.0104 0.00002 0.1389 0.0177 0.00045 0.0988 

While the lower level assumption may be appropriate, given the limited data it is the original 

assumption of a 2-spill adjustment that is recommended. 

4.8 Comparison with Bercha (2006) 

To facilitate comparison of this methodology with the results of the probabilistic risk assessment 

done in Bercha (2002 and 2006), Poisson spill rates and confidence intervals are calculated for 

that data. Since the relevant data is reproduced in this report, all references in this section are to 

this report. This analysis is done only at the aggregated level for all spills ≥ 50 bbls and over the 

entire 1972 – 1999 time frame used in Bercha. 

There are 31 pipeline spills listed in Table 2.4 and 21 platform spills listed in Table 2.7. There 

are 117,705 pipeline mile-years listed in Table 2.13 and 119, 714 well-years listed in Table 2.15. 

These values can be used to compute exact confidence limits for the spill rates for ≥ 50 bbl spills. 

The results are shown in Table 4.22. 

Table 4.22 Poisson Rates for Bercha (2006) Data for 1972-1999 

 n 

exposure 

variable 

Sum

Exposure 

variable rate LCL UCL 

Platforms 21 KWell-yr 119.714 0.1754 0.1086 0.2681 

Pipelines 31 KMile-yr 115.385 0.2687 0.1825 0.3813 

The uncertainty reported in Table 4.22 can most easily be put into context by considering the 

ratio between the upper and lower confidence limits for the 95% confidence interval. That ratio 

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for platforms is about 2.5 and about 2 for pipelines. This is the uncertainty for rates based in the 

GOM assuming time stationarity. It does not consider any of the many sources of uncertainty in 

moving to applications in the Arctic. This is a lower bound on the uncertainty from this data, as 

this uncertainty applies to every pipeline and well and it is not reduced through an averaging 

process. 

It also does not consider the increase in uncertainty that results if the data sets of 21 and 31 spills 

are subdivided by pipe size, water depth, spill size, or spill cause. Nor does it consider any of the 

data refinements that MMS has been able to provide or that have been developed in this study. 

Table 4.23 illustrates this by deriving the Poisson rates for pipeline spills due to corrosion (4 of 

31) pipeline spills and for platform spills due to storage tank releases (3 of 21) platform spills. In 

this case the ratio of the upper and lower confidence levels is about a factor of 10 or an order of 

magnitude. 

Table 4.23 Poisson Rates for Specific Spill Causes for Bercha (2006) Data for 1972-1999 

 n 

exposure 

variable 

Sum

Exposure 

variable rate LCL UCL 

Platforms: storage 

tank release 3 KWell-yr 119.714 0.0251 0.0052 0.0732

Pipelines: 

corrosion 4 KMile-yr 115.385 0.0347 0.0094 0.0888

Thus the uncertainty of a factor of 2 or 2.5 is the absolute minimum range, and realistic estimates 

of the uncertainty in extrapolation to the Arctic are larger by some unknown amount, which in 

some cases is at least an order of magnitude. 

4.9 Summary and Conclusions 

It is suggested that Tables 4.19 and 4.20 represent a valid way to estimate with rates and 

confidence limits the probabilities of “applicable” pipeline and platform spills in the Arctic. 

Method 1 in a conservative way considers the statistical uncertainties in spill size and the 

applicability of the spill cause to the Arctic. Method 2 provides a lower bound on the amount of 

uncertainty that is unavoidable. 

Because these tables do not include adjustments for Arctic-specific spill causes, the spill rates 

can only go up. However, preliminary analysis indicates that strudel scour is less significant 

than the applicable causes. No conclusions can be reached for ice keel gouging. 

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5 Recommendations and Conclusions 

In order to maximize ease of use and clarity of references, this chapter is structured and written 

as “bullet points.” In addition, using the detailed results from and methods of this study is best 

done within the context provided by the discussions in this chapter. For example, there is about 

an 8.7% adjustment required for pipeline spill rates applied to the GOM based on volume of oil 

production. Fundamentally, the authors are concerned that abstracting key numbers may lead to 

their use out of context. 

Sections 5.1 to 5.3 are based on the body of this report. Section 5.4 presents a promising 

alternative approach to modeling pipeline spill risks that was first conceptualized and developed 

while this report was in the final review stage. 

5.1 Major Conclusions 

The Poisson distribution for pipeline and platform spill rates is satisfactory. Other distributions

could be chosen, but the Poisson 

1. Fits with historical practice 

2. Has a theoretical foundation – it is not just an empirical curve fit 

3. Is “not rejected” at reasonable levels of statistical confidence 

4. Even though the fit of any distribution may be imperfect, the key question when 

estimating rates, is “how much do these imperfections change the estimated rate? 

Generally, the answer is very little.” 

For the GOM, any of the exposure variables can be used to model the rate of oil spills, due to the 

high level of correlation between them. Furthermore, with production as the exposure variable, 

the results are generally consistent with MMS published results. 

The best exposure variables for extension to the Arctic are pipeline mile-years and platformyears. Using production volumes as the exposure variable seems to significantly overstate the 

risk. Time cannot be used as the exposure variable. 

The level of uncertainty for Arctic extension is very high due to the many uncertainties. 

However, it is possible to make reasonable, justifiable extensions from the GOM data to the 

Arctic. 

5.2 Cautions in Using and Interpreting the Results 

Platform spills for this study have included spills of refined petroleum products such as diesel, 

while other studies such as Bercha (2002 & 2006) focus on crude and condensate. 

For GOM use for pipeline spills if production is the exposure variable. It is suggested that the 

spill rate and confidence limits be adjusted upwards by dividing by 0.92. This is the ratio 

between GOM production from 1972 – 2005 to total OCS production. This would closely 

approximate the results that would have been obtained if the GOM spills had been measured 

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against GOM production. (No similar adjustment is required for platforms or for the extensions 

to the Arctic, as GOM production was used.) 

Many users of statistics are accustomed to the idea that variability averages out by having many 

years, many pipelines, and many platforms. Variations of this principle have been part of several 

discussions in this report, however, the principal uncertainty addressed in this report is the basic 

uncertainty about what is the average spill rate. This affects every pipeline and platform equally, 

and it is NOT averaged out by independent, identically distributed random selections. 

The more recent aggressive data collection effort for platform spills linked to hurricanes suggests 

that recent reported spill volumes are relatively higher, so that true spill rate declines for 

platforms are probably somewhat larger than reported here. 

Using a constant or average spill rate per pipeline mile-year will overestimate the rate for 

pipeline runs longer than average and underestimate the rate for pipeline runs shorter than 

average. In particular, rates developed for average length pipeline runs in the GOM are likely to 

overstate the spill rate per pipeline mile-year for the longer Arctic pipelines. This is addressed in 

much more detail in Section 5.4. 

The rates and confidence intervals for spills exceeding the thresholds of 100, 500, and 1000 bbl 

are less reliable than the results for the 50 bbl threshold. There are more uncertainties in which 

statistical approach is better, and there are fewer spills so that small sample variability is more of

an issue. 

5.3 Suggestions for Future Work 

The very preliminary work in Section 5.4 on platforms as an exposure variable for pipeline spills 

should be extended. Other potential “termination” exposure variables such as number of 

segments should also be explored. A very significant fraction of pipeline spills happen because 

of a connection to a platform. The connection may be severed when a platform is moved or 

destroyed by a hurricane, a work boat may collide with a riser, or an anchor may damage the 

pipeline during operations around a platform. Accurately representing the oil spill probabilities 

associated with this should support better estimates and better extensions to different operating 

environments. Using a constant or average spill rate per pipeline mile-year will overestimate the 

rate for pipeline runs longer than average and underestimate the rate for pipeline runs shorter 

than average. In particular, rates developed for average length pipeline runs in the GOM are 

likely to overstate the spill rate per pipeline mile-year for the longer Arctic pipelines. 

The influence of the scale of development in the Arctic on the predictability of the spill history 

that will be experienced has not yet been explored. To avoid future surprises, it should be. 

Given the robustness of using spill models for volume of oil produced based on the larger data 

sets available for spills ≥ 50 bbl; these models should be applied to the spill rates used in the 

extension of GOM spill experience to the Arctic, which are based on pipeline spills per thousand 

mile-years and platform spills per thousand platform-years. This will support the production of 

more reliable estimates for the spill rates for larger spills, such as exceeding 1000 bbl. 

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Two different methods for extending the GOM data to the Arctic with confidence intervals were 

explored. Additional approaches should be explored. For example, simulation might be an 

appropriate tool for estimating how conservative an LCL is produced by multiplying the LCL’s 

for three different variables. Clearly, verifying whether the confidence limits are realistic, 

optimistic, or overly conservative would greatly increase their value. 

It should be possible to construct confidence intervals for the Arctic specific risks as the 

scenarios are better defined. 

5.4 Potential New Pipeline Spill Model 

This section describes a different approach for modeling pipeline spills that is based on the fact 

that each pipeline spill occurs either in conjunction with a platform termination or elsewhere 

along its length. This appears to produce a model that more accurately reflects pipeline spill 

risks. 

As described in Section 5.3 and detailed in Tables 5.1 and 5.2, many pipeline spills have a 

platform-related cause. For this preliminary work, it is assumed that all pipelines, short or long, 

have about the same risk of pipeline spills at a platform termination. (There have not been 

enough spills to differentiate spill rates by pipe diameter, water depth, etc. in this report. Thus, 

we do not believe it will be possible to initially differentiate between risks linked to floating vs. 

fixed platforms, water depth, etc.) 

This work is at an early stage, and it has not yet received the detailed analysis and review that the 

other models presented in this report have received. It is also incomplete, as it only presents one 

approach for developing confidence intervals; and some points are illustrated but not fully 

developed. Nevertheless, the authors suggest that it is an approach that merits further review, as 

it does appear to more realistically model the risk of a pipeline spill, and it is much more robust 

for pipeline lengths different from “average.” 

The model is first explained by analogy in Section 5.4.1. Since each pipeline has a termination 

at each end, the spill rate at the terminations is like a fixed cost, which is incurred by every single 

pipeline no matter how long. The spill rate along the length of a pipeline is like a variable cost

that depends on how long each pipeline is. Then spill rates for different spill sizes are developed 

in Section 5.4.2. Then in Section 5.4.3 the rates are applied to the Beaufort development 

scenario for comparison with the results developed earlier in this report. 

This class of model is useful both for extrapolating from the GOM to the Arctic and for 

estimating spill rates for new GOM developments that are at significantly higher distances from

shore than the statistical average for the GOM. The specific model presented here uses pipeline 

mile-years and platform-years as variables. While future models may use different variables, the 

intent is to show the value of a new approach. 

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5.4.1 Analogy to Fixed and Variable Cost Model vs. Average Cost Model 

The clearest way to introduce this model is by analogy with another model that most readers will 

have previously used. There are many circumstances where a choice must be made between two 

cost models, which are summarized in Figure 5.1. 

The constant rate model uses an average cost, such as cost per mile, cost per square foot, or cost 

per call. For any volume, the estimated cost equals the average cost multiplied by the expected 

volume. This model is analogous to the models presented previously in this report, which 

present average spill rates per pipeline mile-year, per platform-year, per billion barrels of 

production, or per year. 

The other model defines a fixed cost that must be incurred for any non-zero volume, and a 

variable cost for each unit of that volume. The new approach presented here is analogous to the 

fixed/variable cost model (henceforth called fixed cost model for linguistic convenience). This 

approach recognizes that whether a pipeline is short or long, it typically has at least one 

termination at a platform. And that the spill rate for those terminations depends on the number 

of terminations, and not on the length of each pipeline. This is analogous to the fixed cost. The 

spill rate along the pipeline’s length is analogous to the variable cost. 

For those who are unfamiliar with these models, Figure 5.1 was developed using the following 

data. There is a fixed cost of $800 for any volume, and then there is a variable cost of $50 per 

unit. Thus, if the average volume is 20, the total cost is $1800 (= 800 + 50*20). The average 

cost per unit is the total cost divided by the average volume or $90 (= 1800/20). 

0

1000

2000

3000

4000

0 5 10 15 20 25 30 35 40

Volume

Total C

ost

Average Fixed & Variable

Figure 5.1 Average Cost versus Fixed and Variable Cost Models 

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This familiar context of fixed/variable cost versus average cost can be used to illustrate why each 

type of model is used for situations where there is a significant fixed cost. The average cost is 

easiest to determine or to statistically estimate. And for volumes close to the average volume 

(which is the point where the two lines cross) it provides a realistic estimate. In many situations 

this is enough for good results. For the example data the average cost model works pretty well 

for volumes between 15 and 25. 

However, for volumes that are significantly different than the average volume, the estimated 

value for the average cost model is considerably less accurate than the inherently more accurate 

fixed cost model. For the example in Figure 5.1 consider the estimated cost for volumes of 5 or 

40. The average cost model performs poorly. The average rate is too low for low volumes and 

too high for high volumes. 

Thus, if it is possible to estimate the fixed and variable costs, this model is more accurate. Note: 

the fixed cost model can use a fixed cost of zero, thus the average cost model is a special case of 

the fixed cost model, and non-zero fixed costs are only used when they provide a more accurate 

model. 

There are at least two situations where the average model for spill rates is likely to be inferior. 

First, a fixed cost class of model is useful for extrapolating from the GOM to different 

environments, such as the Arctic. Second, the fixed cost class of model is useful for estimating 

spill rates for new GOM developments that are at significantly higher distances from shore than 

the statistical average for the GOM. 

5.4.2 Determining Pipeline Spill Rates for Fixed and Variable Probability Model 

5.4.2.1 Platform-Related Pipeline Spills vs. “Pipeline” Spills 

Table 5.1 details the authors’ categorization of pipeline spills between platform-linked spills and 

those “pipeline” spills without such a link. This was done using the same database that was used 

for Table 2.17. The added information is in the new fourth and fifth columns. The last three 

hurricane-caused spills were listed as having both pipeline and platform-linked causes because 

the spills are actually the accumulation of multiple spills with a common cause. 

In many cases the categorization was clear and unambiguous. For example, if a platform is 

destroyed and the pipeline severed, then the platform cause is clear. For another example, if the 

anchor from a platform service vessel damaged the pipeline, it is reasonable to classify this as 

platform related as both the vessel and the pipeline are being brought together at the platform. In 

others, the lead author’s judgment was used, as the distance from the platform was longer or the 

connection to platform operations was weaker. 

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Table 5.1 Modified Table 2.17 Platform Related Primary Cause of GOM Pipeline Oil 

Spills 

Spill Date 

Spill 

Size 

GOM 

Specific 

Pipeline Platform Cause 

1972-06-13 100 Y Corrosion 

1973-05-12 5,000 Y Corrosion 

1974-04-17 19,833 GOM Y Anchor drag 

1974-05-21 65 Y Operational: anchor from derrick barge 

1974-09-11 3,500 GOM Y Hurricane Carmen 

1976-02-29 414 Y Corrosion: after pipeline kinked by anchor 

1976-12-18 4,000 GOM Y Shrimp trawl damaged valve 

1977-03-29 250 Y Natural: mud slide 

1977-06-05 50 Y Operational: lay barge anchor 

1977-10-18 300 GOM Y Anchor drag 

1978-04-08 135 Y Mechanical/operational 

1978-07-17 900 Y Operational: anchor drag 600’ from platform

1979-07-15 50 Y Operational: workboat searching for rig anchor 

1980-01-29 100 GOM Y Trawler drag broke valve 

1981-08-05 80 Y Corrosion: external or metal fatigue 

1981-12-11 5,100 Y Operational: service vessel anchor 

1983-01-20 80 Y Natural: mud slide 

1985-02-16 323 

Y Operational: pipeline dented, cracked during 

construction 

1985-11-09 50 Y Operational: spud barge anchor 

1986-02-03 119 

Y Mechanical/operational: pinhole leak during 

abandonment 

1986-12-30 210 

Y Mechanical/operational: anchor or original 

construction 

1988-02-07 15,576 GOM Y Ship illegally dropped and dragged anchor 

1990-01-24 14,423 GOM Y Fishing net or anchor 

1990-05-06 4,569 GOM Y Trawler net drag 

1992-01-03 190 Y Unknown 

1992-08-31 2,000 GOM Y Rig broke loose during Hurricane Andrew 

1993-06-17 50 Y Operational: workboat anchor 

1994-11-16 4,533 GOM Y Trawl net damaged valve 

1998-01-22 800 GOM Y Mechanical damage: probably anchor 

1998-01-26 1,211 Y Operational: anchor during overboard rescue 

1998-09-29 8,212 GOM Y Hurricane Georges 

1999-07-23 3,200 Y Operational: jackup rig set down on pipeline 

2000-01-21 2,240 Y Operational: anchor drag from drill rig 

2004-09-15 3,445 GOM Y Y Hurricane Ivan 

2005-08-29 553 GOM Y Y Hurricane Katrina 

2005-09-24 8162 GOM Y Y Hurricane Rita 

Table 5.2 summarizes the N = 36 spill data in Table 5.1 by spill size for the spill causes that are 

applicable to the Arctic, and in total for GOM-specific causes. The spills with GOM-specific 

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causes are not analyzed further for four reasons. First, this analysis is intended to explore and 

demonstrate the value of a new approach, not to provide definitive well-supported results. 

Second, results for the GOM are complicated by the hurricane spills. Third, the number of 

platform related spills is much smaller for GOM-specific causes. Fourth, the focus of this study 

is the Arctic not the GOM.

Table 5.2 Summary of Platform vs. Pipeline Related GOM Pipeline Oil Spills 

Applicable or GOM 

Specific 

Pipeline 

Related 

Platform

Related 

Applicable 

≥ 50 bbl 14 7 

≥ 100 bbl 9 5 

≥ 500 bbl 2 4 

≥ 1000 bbl 2 3 

GOM Specific 15 11 + 3 1 + 3 

The fraction of the pipeline spills linked to a platform ranges from 66.7% for spills over 500 bbl 

down to 33.3% for spills over 50 bbl. These percentages are clearly a significant portion of the 

pipeline spills, which is the reason this model was analyzed. 

5.4.2.2 Spill Rates for Platform-Related Pipeline Spills vs. “Pipeline” Spills 

In developing spill rates for platform-related pipeline spills, the data summarized earlier offers 

two potential exposure variables – segments of pipeline and number of platforms. Further work 

may identify better exposure variables. 

The number of pipeline segments over time was detailed for the GOM in Table 2.12, however, 

similar information was not available for the Beaufort development scenario. Thus, even if rates 

were developed they could not yet be applied. In addition, the connection between pipeline 

segments and potential exposure variables is not yet well defined. Previous MMS work suggests 

that it could be. If each segment has a termination at each end, then this would be a very logical 

exposure variable, which would be preferred unless the data quality is poor. (Note that 

underwater terminations represent somewhat different spill probabilities than do platform

terminations.) However, if a pipeline with a termination at each end may have many logical 

segments to help identify where leaks, repairs, or other actions take place, then this would not be 

a good exposure variable. It is unclear how many pipeline segments fit either of these two 

possibilities.

Thus in the preliminary analysis reported here, the exposure variable for platform-related 

pipeline spills is platform-years. The span of time for this exposure variable is 1972 to 2005, 

since pipeline spills were not shown to have a significant time dependence (unlike platformspills which were split into 1972 – 1989 and 1990 – 2005). This initial work did not include an 

analysis of whether either the “pipeline” or “platform-related” pipeline spill rates are time

dependent. 

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Thus, the “fixed cost” model for oil spills uses platform-years as the exposure variable for 

platform-related pipeline spills and pipeline mile-years for “pipeline” spills. 

Table 5.3 applies method 2 with the data in Table 5.2 for applicable spills. With this approach 

exact Poisson confidence intervals can be derived with only the number of spills and the 

exposure variable. This initial work has not included testing of exponential inter-spill intervals 

for these two subsets of the data. 

Table 5.3 Spill Rates for Platform vs. Pipeline Related Applicable Pipeline Oil Spills 

Threshold

bbl N 

Exposure 

Variable 

Sum

Exposure 

Variable rate LCL UCL 

Pipeline-Related Pipeline Spill Rates

≥ 50 14 Kmile-yr 161.796 0.0865 0.0473 0.1374 

≥ 100 9 Kmile-yr 161.796 0.0556 0.0254 0.0974 

≥ 500 2 Kmile-yr 161.796 0.0124 0.0015 0.0344 

≥ 1000 2 Kmile-yr 161.796 0.0124 0.0015 0.0344 

Platform-Related Pipeline Spill Rates

≥ 50 7 Kplatform-yr 100.087 0.0699 0.0281 0.1305 

≥ 100 5 Kplatform-yr 100.087 0.0500 0.0162 0.1023 

≥ 500 4 Kplatform-yr 100.087 0.0400 0.0109 0.0876 

≥ 1000 3 Kplatform-yr 100.087 0.0300 0.0062 0.0722 

These spill rates cannot be compared directly with previous spill rates. That comparison is 

summarized in Section 5.4.2.3, and then these rates are applied to the Beaufort development 

scenario in Section 5.4.3. 

5.4.2.3 Consistency of Spill Rates for “Fixed/Variable” Rate and Average Rate Models 

While straight-forward, it is a first test of validity to show that the two models give consistent 

results for the GOM. This is done for the 21 spills ≥ 50 bbl, but it true for all spill size

thresholds. The rates cannot be directly compared, rather they must be applied to the exposure 

variables to compute the number of spills of each type. 

For each of these Poisson models, the spill rate was computed as the number of spills divided by

the exposure variable. Thus, the number of predicted spills of each spill type is simply the spill 

rate multiplied by the exposure variable. 

 Number of Applicable Oil Spills (from Table 4.7) 

21 = (161.796 Kmile-yr) * 0.1298 

 Number of Applicable Pipeline-Related Oil Spills (from Table 5.3) 

14 = (161.796 Kmile-yr) * 0.0865 

Number of Applicable Platform-Related Oil Spills (from Table 5.3) 

7 = (100.087 Kplatform-yr) * 0.0699 

And of course 21 = 14 + 7 

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Thus, the new approach that uses platform-years as the exposure variable for the “fixed cost” of 

spills at terminations and pipeline mile-years as the exposure variable for the “variable cost” of 

spills along a pipeline’s length has results that are consistent with those from the previous model 

that uses the average spill rate per pipeline mile-year. 

5.4.3 Applying Spill Rates for “Fixed/Variable” Rate Model 

As shown above, the numbers of spills for the two models are equivalent when applied to the 

total exposure within the GOM from 1972 to 2005. However, if these spill rates are applied to 

data with a different mix between platforms and pipeline lengths, then the results are different as 

well. 

One measure of the difference between the GOM data and the Beaufort development scenario is 

the number of pipeline miles per platform. For the GOM dividing the 161,796 pipeline mileyears by the 100,087 platform-years gives a result of 1.62 pipeline miles per platform. For the 

Beaufort development scenario dividing the 2035 pipeline mile-years by the 148 platform-years 

gives a result of 13.8 pipeline miles per platform. Thus, there is about an order of magnitude 

difference in the number of pipeline miles per platform for the Beaufort development scenario. 

Thus, there will be a large difference in results between the fixed/variable rate model and the 

average rate model. 

The reasons for this difference include: 

• Most of the thousands of platforms in the GOM are close to shore 

• GOM mileage does not include the 3 nautical miles or 3 leagues (prior to years of 

shoreline retreat) between shore and the boundary of OCS waters 

• Beaufort Sea pipeline mileage does include the 3 nautical miles from OCS waters to land 

The GOM has numerous platforms far offshore, yet there are only 1.62 pipeline miles per 

platform. Thus, it is reasonable to conclude that there must be very substantial variability in the 

length of GOM pipelines. Thus, the predicted spill rates for different GOM facilities will differ 

substantially between the potentially more accurate fixed/variable model versus the average spill 

rate model. In particular the average spill rate model may dramatically overestimate the spill rate 

for long pipelines. 

To apply the spill rates shown in Table 5.3 to the Beaufort development scenario, the “pipeline” 

values are multiplied by the exposure variable of 2.035 thousands of pipeline mile-years. 

Similarly, the “platform-related” values are multiplied by the exposure variable of 0.148 

thousands of platform-years. The resulting values for expected number of life-of-field spills are 

shown in the top two sections of Table 5.4. The total expected number of life-of-field spills is 

the sum of the two spill types, and the results are shown in the bottom section of Table 5.4. 

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Table 5.4 Expected Life-of-Field Spill Numbers for Beaufort Development Scenario for 

Pipeline Oil Spills 

Threshold 

bbl 

Exposure 

Variable 

Sum

Exposure 

Variable 

LOF 

E(#) LCL UCL 

Pipeline-Related Expected Pipeline Spill Numbers 

≥ 50 Kmile-yr 2.035 0.176 0.096 0.280 

≥ 100 Kmile-yr 2.035 0.113 0.052 0.198 

≥ 500 Kmile-yr 2.035 0.025 0.003 0.070 

≥ 1000 Kmile-yr 2.035 0.025 0.003 0.070 

Platform-Related Expected Pipeline Spill Numbers 

≥ 50 Kplatform-yr 0.148 0.010 0.004 0.019 

≥ 100 Kplatform-yr 0.148 0.007 0.002 0.015 

≥ 500 Kplatform-yr 0.148 0.006 0.002 0.013 

≥ 1000 Kplatform-yr 0.148 0.004 0.001 0.011 

Total Expected Pipeline Spill Numbers 

≥ 50 0.186 0.100 0.299 

≥ 100 0.121 0.054 0.213 

≥ 500 0.031 0.005 0.083 

≥ 1000 0.030 0.004 0.081 

Table 5.5 provides the results for method 2 using the average rates summarized in Table 4.19 

times the 2.035 thousands of pipeline mile-years for the Beaufort development scenario. For 

ease of comparison the values from Table 5.4 are repeated. 

Table 5.5 Comparing Expected Life-of-Field Spill Numbers for Beaufort Development 

Scenario for Pipeline Oil Spills for Fixed/Variable and Average Models 

Fixed/Variable Model Average Model 

Threshold

bbl

LOF 

E(#) LCL UCL 

LOF 

E(#) LCL UCL 

≥ 50 0.186 0.100 0.299 0.2641 0.1635 0.4037

≥ 100 0.121 0.054 0.213 0.1761 0.0963 0.2954

≥ 500 0.031 0.005 0.083 0.0755 0.0277 0.1643

≥ 1000 0.030 0.004 0.081 0.0629 0.0204 0.1468

Because the number of pipeline miles per platform is much higher for the Beaufort development 

scenario than for the GOM data, the expected number of spills is much lower with the new 

model. To use the analogy with the fixed/variable cost model of Figure 5.1, pipelines that have 

more length have more “volume” and are better estimated with the new model; and have lower 

estimated values. 

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5.4.4 Summary and Conclusions for Fixed and Variable Cost Model 

The model that is introduced here inherently has the potential to improve the accuracy of 

extrapolated results. The flexibility of separating spill rates into a fixed portion linked to 

pipeline terminations and a variable portion linked to the pipeline’s length greatly extends the 

accuracy of projections to environments and projects with lengths different from the average in 

the GOM data base. 

While promising, this approach has not yet received the level of review and validation that 

underlie the average spill rate models that are presented earlier in this report. In particular, the 

following issues merit attention: 

• After review and discussion how much does the classification of pipeline spills as 

platform- or pipeline-related change? 

• Is there a better exposure variable for the pipeline terminations than platform-years?

• Does the analysis of exponential inter-spill intervals support the use of the Poisson model 

for platform-related pipeline spills and for “pipeline” pipeline spills?

• Is there an analogous method 1 approach for defining the confidence limits that is more 

conservative than this method 2 approach?

• What are the results for use in the GOM? 

• How to handle hurricane spills when applying this approach to potential GOM 

developments?

The following observations may also be useful in examining this approach further. 

• In extrapolating from the GOM data to the Arctic, one of the key variables was the 

proportion of the oil spills at each spill size threshold that was “applicable or non-GOM 

specific.” The uncertainty in this binomial proportion was a key part of the method 1 

approach to the confidence limits for the spills per pipeline mile-year models. While 

there is uncertainty in the proportional split between “platform-related” and “pipeline” 

spills, these are complementary binomial proportions that must sum to 1. Thus, 

examination of this uncertainty is better done through sensitivity analysis than by 

expanding the confidence limits as method 1 does. 

• The spill cause classification as platform- or pipeline-related has less impact on the 

results than the GOM/applicable classification. This is true because the as the weight on 

platform-related spills (and the estimated number of such spills) goes up; the weight on 

pipeline-related spills (and the estimated number of such spills) goes down. So the total 

of the two moves up or down more slowly with the difference between the two parts. On 

the other hand the GOM/applicable classification excludes or includes spills which 

directly decreases or increases the estimated spill rates and numbers of spills. 

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Appendix A. Pipeline Spills ≥ 50 bbl through 1999 

Appendix A parallels the pipeline analysis in Section 3.5 of the main body of the report. In 

Section 3.5, analyses for pipeline spills ≥ 50 bbl are documented for data through 2005. Since 

the earlier draft report submitted in the fall of 2005 analyzed data only through 1999, it was felt 

important to provide the reader an opportunity to see what has changed by adding six additional 

years of pipeline spill data. While much of the data in this appendix is the same as given in the 

earlier draft report, the data in Appendix A are an update of the pipeline data through 1999 used 

in the draft. This was done to address re-interpretations of the earlier data based on dialogue 

with the MMS. We would like to thank Cheryl Anderson for her guidance on these efforts. 

The remainder of this section show analogous Figures and Tables to the pipeline information in 

Section 3.5 using a numbering scheme to make the matching of the through 1999 analysis 

figure/table to the through 2005 figure/table seen in the main body of the report obvious. For 

example Figure A3.10 is this appendix may be compared to Figure 3.10 in the main report. 

There may be minor differences in the titles to some Figures and Tables, as some revision has 

taken place.

Days InterSpill through 1999

Perc

ent

1 10 100 1000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Mean 319.4

N 31

AD 0.808

P-Value 0.195

Probability Plot of Days InterSpill

Exponential - 95% CI

Figure A3.10 Exponential Probability Plot of Pipeline Inter-Spill (spills ≥ 50 bbl) Times 

Using n = 32 through 1999 Data Set 

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Days InterSpill through 1999

Perc

ent

0 200 400 600 800 1000 1200 1400 1600

100

80

60

40

20

0

Mean 319.4

N 31

Empirical CDF of Days InterSpill

Exponential

Figure A3.11 Exponential Empirical CDF Plot of Pipeline Inter-Spill (spills ≥ 50 bbl) Times 

Using n = 32 through 1999 Data Set 

Prod Interspill Bbbl through 1999

Perc

ent 0.001 0.010 0.100 1.000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Mean 0.3137

N 3

AD 0.732

P-Value 0.243

Probability Plot of Prod Interspill Bbbl

Exponential - 95% CI

1

Figure A3.12 Exponential Probability Plot of Pipeline Inter-Spill Production Volumes 

(Bbbl) Using n = 32 though 1999 Data Set (spills ≥ 50 bbl) 

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Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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Prod Interspill Bbbl through 1999

Percent

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

100

80

60

40

20

0

Mean 0.3137

N 31

Empirical CDF of Prod Interspill Bbbl

Exponential 

Figure A3.13 Exponential Empirical CDF Plot of Pipeline Inter-Spill Production Volumes 

Using n = 32 through 1999 Data Set (spills ≥ 50 bbl) 

KMiles Interspill through 1999

Percent

0.01 0.10 1.00 10.00

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Mean 3.577

N 31

AD 0.198

P-Value 0.955

Probability Plot of KMiles Interspill

Exponential - 95% CI

Figure A3.14 Exponential Probability Plot of Pipeline Inter-Spill Pipeline Mile-Years 

(KMiles) Using n = 32 through 1999 Data Set (spills ≥ 50 bbl) 
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KMiles Interspill through 1999

Percent

0 5 10 15 20

100

80

60

40

20

0

Mean 3.577

N 31

Empirical CDF of KMiles Interspill

Exponential 

Figure A3.15 Exponential Empirical CDF Plot of Pipeline Inter-Spill Pipeline Mile-Years 

(KMiles) Using n = 32 through 1999 Data Set (spills ≥ 50 bbl) 

Table A3.3 

Spill Rates for ≥ 50 bbl Spills through 1999

Label # 

Spills 

Exposure 

Variable 

Sum 

Exposure 

Variable 

Rate LCL UCL 

Pipeline Spills/Kmile-year 32 Kmile-years 114.7 0.2790 0.1908 0.3938

Pipeline Spills/Bbbl 32 Bbbl Production 10.13 3.158 2.160 4.459

Pipeline Spills/year 32 Time, whole years 28 1.143 0.7817 1.613

Table A3.4 

Rate estimates using Exponential Distribution through 1999

Exposure Variable Exponential 

Mean Rate 

Pipeline Spills/Kmile-year 3.577 0.2796

Pipeline Spills/Bbbl 0.3137 3.188 

Pipeline Spills/year 319.4 Days, not years 1.143 
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Table A3.5 

Poisson Rates based on Inter-Spill Data through 1999

Label # 

Spills 

Exposure 

Variable 

Sum 

Exposure 

Variable 

Rate LCL UCL 

Pipeline Spills/Kmile-year 31 Kmile-years 110.9 0.2796 0.1899 0.3968

Pipeline Spills/Bbbl 31 Bbbl Production 9.724 3.188 2.166 4.525 

Pipeline Spills/year 31 Time, years 27.13 1.143 0.7765 1.622 

Spill >= 50_1

Percent

1.0000E+06

100000.000

10000.000

1000.000

100.000

10.000

1.000

0.100

0.010

0.001

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape 0.4124

Scale 1170

Thresh 50.00

N 32

AD 0.338

P-Value >0.500

3-Parameter Weibull - 95% CI

Probability Plot of Spill >= 50_1

Figure A3.16 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 50 bbl through 

1999 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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Spill >= 50_1

Percent

0 10000 20000 30000 40000 50000

100

80

60

40

20

0

Shape 0.4124

Scale 1170

Thresh 50.00

N 32

3-Parameter Weibull 

Empirical CDF of Spill >= 50_1

Figure A3.17 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 50 bbl 

through 1999 

Spill >= 100_1

Percent

1000000.00

100000.00

10000.00

1000.00

100.00

10.00

1.00

0.10

0.01

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape 0.4740

Scale 2021

Thresh 99.99

N 25

AD 0.394

P-Value 0.401

3-Parameter Weibull - 95% CI

Probability Plot of Spill >= 100_1

Figure A3.18 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 100 bbl 

through 1999 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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Spill >= 100_1

Percent

0 10000 20000 30000 40000 50000

100

80

60

40

20

0

Shape 0.4740

Scale 2021

Thresh 99.99

N 25

3-Parameter Weibull 

Empirical CDF of Spill >= 100_1

Figure A3.19 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 100 bbl 

through 1999 

Spill >= 500_1

Percent

100 1000 10000 100000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape 0.9933

Scale 5674

Thresh 500

N 15

AD 0.344

P-Value >0.250

3-Parameter Weibull - 95% CI

Probability Plot of Spill >= 500_1

Figure A3.20 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 500 bbl 

through 1999 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

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Spill >= 500_1

Percent

0 5000 10000 15000 20000 25000 30000

100

80

60

40

20

0

Shape 0.9933

Scale 5674

Thresh 500

N 15

3-Parameter Weibull 

Empirical CDF of Spill >= 500_1

Figure A3.21 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 500 bbl 

through 1999 

Spill >= 1000_1

Percent

100 1000 10000 100000

99

90

80

70

60

50

40

30

20

10

5

3

2

1

Shape 1.069

Scale 6173

Thresh 1000

N 13

AD 0.420

P-Value >0.250

3-Parameter Weibull - 95% CI

Probability Plot of Spill >= 1000_1

Figure A3.22 Weibull Probability Plot of Pipeline Spill Volumes for Spills ≥ 1000 bbl 

through 1999 
Oil Spill Occurrence Estimators for Beaufort and Chukchi Sea OCS (Statistical Approach) 

MMS 155 TGE Consulting

Spill >= 1000_1

Percent

0 5000 10000 15000 20000 25000 30000

100

80

60

40

20

0

Shape 1.069

Scale 6173

Thresh 1000

N 13

3-Parameter Weibull 

Empirical CDF of Spill >= 1000_1

Figure A3.23 Weibull Empirical CDF Plot of Pipeline Spill Volumes for Spills ≥ 1000 bbl 

through 1999 

Table A3.6 

Odds Ratios for the Four Different Threshold Weibull Distributions

U>U 50 bbl U>U 100 bbl U>U 500 bbl U>U 1,000 bbl 

50 vs. 100 1.303 

100 vs. 500 1.495 1.586 

500 vs. 1000 1.276 1.243 1.094 

1000 vs. 2000 1.373 1.336 1.194 1.154 

2000 vs. 15000 5.079 4.986 9.706 9.553 
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CDF Comparison through 1999

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2000 4000 6000 8000 10000 12000 14000 16000

Barrels Oil Spilled through 1999

F(x)

>= 50bbl

>= 100bbl

>= 500bbl

>= 1000bbl

Figure A3.24 Overlay of Weibull Empirical CDFs 

Table A3.7 

Exact Poisson Confidence Intervals for Different Pipeline Spill Thresholds through 1999

Threshold N Poisson Rate 

for Bbbl 

Exact Poisson CI 

Lower 

Exact Poisson CI 

Upper 

50 32 3.702 2.251 4.646 

100 25 2.982 1.664 3.795 

500 15 1.954 0.863 2.544 

1000 13 1.645 0.712 2.286 

Table A3.8 

Confidence Intervals for the Proportion of the ≥ 50 bbl Model 

Spills Exceeding the Larger Threshold 

Threshold P(> Threshold) 

Adjusted 

Poisson Rate 

per Bbbl 

Adjusted LCL 

100 0.7615 0.5660 0.8854 

500 0.5095 0.3189 0.6811 

1000 0.3994 0.2370 0.5936 
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Table A3.9 

Spill Rate Estimates and Confidence Intervals through 1999 using 3.70 Spill 

Rate for ≥ 50 bbl Times Values in Table A3.8

Threshold P(> Threshold) Adjusted Poisson 

Rate per Bbbl Adjusted LCL Adjusted UCL 

100 0.7615 2.819 2.095 3.278 

500 0.5095 1.886 1.181 2.522 

1000 0.3994 1.479 0.8774 2.197 

Table A3.10 

Confidence Intervals for “Worst Case” Approach through 1999 Using (2.25, 

4.65) Table A3.7 Poisson Confidence Intervals from ≥ 50 bbl Model and 

Confidence Interval Proportions from Table A3.8 

Threshold 

Adjusted LCL 

based on both 

CI 

Adjusted UCL 

based on both CI

100 1.274 4.113 

500 0.7178 3.164 

1000 0.5334 2.758 

Table A3.11 

Confidence Intervals Using (2.25, 4.65) Poisson Confidence Intervals from ≥

50 bbl Model and P(≥ threshold) 

Threshold P(≥ threshold) 

Adjusted 

LCL 

Adjusted 

UCL 

50 1.000 2.251 4.646 

100 0.7615 1.714 3.538 

500 0.5095 1.147 2.367 

1000 0.3994 0.8991 1.856 
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The Department of the Interior Mission 

As the Nation's principal conservation agency, the Department of the Interior has 

responsibility for most of our nationally owned public lands and natural resources. This 

includes fostering sound use of our land and water resources; protecting our fish, 

wildlife, and biological diversity; preserving the environmental and cultural values of 

our national parks and historical places; and providing for the enjoyment of life through 

outdoor recreation. The Department assesses our energy and mineral resources and 

works to ensure that their development is in the best interests of all our people by 

encouraging stewardship and citizen participation in their care. The Department also has 

a major responsibility for American Indian reservation communities and for people who 

live in island territories under U.S. administration. 

The Minerals Management Service Mission 

As a bureau of the Department of the Interior, the Minerals Management Service's 

(MMS) primary responsibilities are to manage the mineral resources located on the 

Nation's Outer Continental Shelf (OCS), collect revenue from the Federal OCS and 

onshore Federal and Indian lands, and distribute those revenues. Moreover, in working 

to meet its responsibilities, the Offshore Minerals Management Program administers 

the OCS competitive leasing program and oversees the safe and environmentally sound 

exploration and production of our Nation's offshore natural gas, oil and other mineral 

resources. The MMS Royalty Management Program meets its responsibilities by 

ensuring the efficient, timely and accurate collection and disbursement of revenue from 

mineral leasing and production due to Indian tribes and allottees, States and the U.S. 

Treasury. The MMS strives to fulfill its responsibilities through the general guiding 

principles of: (1) being responsive to the public's concerns and interests by maintaining a 

dialogue with all potentially affected parties and (2) carrying out its programs with an 

emphasis on working to enhance the quality of life for all Americans by lending MMS 

assistance and expertise to economic development and environmental protection. 
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