May 2009 

NASA/TM-2009-215749 

NESC-05-57/04-027-I 

 

Support Provided to the External Tank (ET) 

Project on the Use of Statistical Analysis for ET 

Certification Consultation Position Paper 

Cynthia H. Null/NESC 

Ames Research Center, Moffett Field, California 
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May 2009 

NASA/TM-2009-215749 

NESC-05-57/04-027-I 

 

Support Provided to the External Tank (ET) 

Project on the Use of Statistical Analysis for ET 

Certification Consultation Position Paper 

Cynthia H. Null/NESC 

Ames Research Center, Moffett Field, California 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

The use of trademarks or names of manufacturers in the report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
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NESC Request No. 04-027-I 

Support Provided to the External Tank (ET) Project on the Use of 

Statistical Analysis for ET Certification 

Consultation Position Paper 

Prepared by: 

Cynthia Null 

NESC Statistics Consulting Team Lead 

May 26, 2005 
NASA Engineering and Safety Center 

(NESC) Technical Consultation Position 

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NESC Request No. 04-027-I 

VOLUME I: REPORT 

Table of Contents

1.0 EXECUTIVE SUMMARY...........................................................................................................................5

2.0 IDENTIFICATION.......................................................................................................................................6

 2.1 TEAM MEMBERS, CONSULTANTS, AND ADVISORS..........................................................................7

3.0 CONSULTATION PLAN.............................................................................................................................7

4.0 DESCRIPTION OF THE PROBLEM AND PROPOSED SOLUTIONS................................................8

 4.1 PROBLEM.......................................................................................................................................................8

 4.2 PROPOSED STATISTICAL METHODS FOR ET CERTIFICATION SUMMER 2004.......................9

 4.3 NEW STATISTICS APPROACH PROPOSED IN OCTOBER 2004......................................................10

5.0 EVALUATION OF USE OF STATISTICS FOR CERTIFICATION APPROACH ...........................12

 5.1 JOINT EVALUATION BY ET PROGRAM AND NESC .........................................................................12

 5.2 ADDITIONAL EVALUATION BY NESC TECHNICAL CONSULTATION TEAM ...........................14

6.0 FINDINGS AND RECOMMENDATIONS ..............................................................................................17

 6.1 THE COMBINED TEAM FINDING ..........................................................................................................17

 6.2 RECOMMENDATIONS TO THE PRCB BY THE COMBINED TEAM...............................................17

 6.3 NESC TECHNICAL CONSULTATION FINDINGS (THREE-ESTIMATE APPROACH).................18

 6.4 NESC TECHNICAL CONSULTATION FINDINGS (NEW STATISTICS APPROACH)...................18

 6.5 NESC TECHNICAL CONSULTATION CONCLUSION (THREE-ESTIMATE APPROACH) .........19

 6.6 NESC TECHNICAL CONSULTATION CONCLUSION (NEW STATISTICS APPROACH) ...........19

7.0 LESSONS LEARNED ................................................................................................................................19

8.0 REFERENCES............................................................................................................................................19

9.0 LIST OF ACRONYMS...............................................................................................................................19

10.0 DEFINITION OF TERMS .........................................................................................................................20

List of Figures

4.2-1 Three-Estimate Approach – Summer 2004....................................................................10 

4.3-1 New Statistics Approach – October 2004 .......................................................................11 

5.2-1 Fitting Distributions to a Sample of Dissection Data ....................................................16 
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List of Appendices

Appendix A. NESC Request Form PR-003-RM-01................................................................21 

Appendix B. Joint Presentation to PRCB................................................................................25 

Appendix C. Statistical Methodology.......................................................................................34 
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NESC Request No. 04-027-I 

Signature Page 

NESC Technical Evaluation Team 

 

Dr. Cynthia H. Null 

Dr. Jeffrey D. Scargle, ARC 

_________________________________ 

Dr. Bruce Conway 
NASA Engineering and Safety Center 

(NESC) Technical Consultation Position 

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1.0 Executive Summary

In June 2004, the June Space Flight Leadership Council (SFLC) assigned an action to the NASA 

Engineering and Safety Center (NESC) and External Tank (ET) project jointly to characterize 

the available dataset [of defect sizes from dissections of foam], identify resultant limitations to 

statistical treatment of ET as-built foam as part of the overall thermal protection system (TPS) 

certification, and report to the Program Requirements Change Board (PRCB) and SFLC in 

September 2004. The NESC statistics team was formed to assist the ET statistics group in 

August 2004. 

Based on previous flight history and early destructive analysis (dissections), decisions were 

made to remove manually sprayed foam from several closeout areas. These “remove and 

replace” areas have foam reapplied using enhanced processes and more rigorous controls. 

Approximately 95 percent of the foam is being left on the tanks, as it was originally sprayed, 

with no rework or repair. These areas consist mainly of “acreage foam” applied with automated 

processes, but a large number of manually sprayed areas will also be left “as is”. 

In its simplest terms, the certification approach taken by the ET project for the debris 

requirement (cohesive failure mode) is to determine, by testing, those combinations of defect 

size, shape, and depth within the foam which can cause a divot (foam debris). 

The joint statistical team defined the data available, specified the assumptions that must be made 

to establish statistical descriptions of the dissection data, and defined limitations on using 

statistics for certification. Choosing a distribution to represent the observed dissection data is a 

critical step in the statistical analysis. There is currently no engineering rationale to choose one 

distribution over another. Several distributions may fit the data equally well, and provide very 

different estimates of the expected maximum defect size. 

In addition, the NESC technical consultation team concluded that: 

1. The largest characteristic defect size (CDS) value in the next sample is the quantity of interest, 

and should be estimated from the distribution of maximum values. 

2. Using the distribution of sample values in place of the distribution of the maximum values of a 

sample can raise the error probability by orders of magnitude. 

3. The critical information needed to predict maximum CDS for the next ET is the shape of the 

upper tail of the distribution of defect sizes. 
NASA Engineering and Safety Center 

(NESC) Technical Consultation Position 

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Adoption of a standard distribution cannot be justified, so this shape is unknown and cannot be 

effectively constrained by the existing dissection data. Based on these findings, the technical 

consultation team found that there is no firm basis for using statistical analysis of the dissected 

data from ET 94 to serve as a statistical distribution model for the certification of “as-built foam” 

for other tanks. 

2.0 Identification

A/I/C #: 04-027-I 

Initiator Name: 

Randy Galloway

Initiator Contact Info: 

Thomas.R.Galloway@nasa.gov

228-332-3281

Short Title: Technical Consultation of the Statistical Analysis Support Provided for the 

External Tank (ET) Project. Note: After the NRB presentation on May 26, 2005, it was 

recommended to change the title to Support Provided to the External Tank (ET) Project on 

the Use of Statistical Analysis for ET Certification

Description: The June 2004 Space Flight Leadership Council (SFLC) assigned an action to 

the NASA Engineering and Safety Center (NESC) and the External Tank (ET) project to 

characterize the available dataset, identify resultant limitations to statistical treatment of ET 

as-built foam as part of the overall Thermal Protection System (TPS) certification, and report 

to the PRCB and SFLC. 

Date Received: June 2004 Date A/I/C Initiated: June 2004 

Initial Evaluators Assigned: 

NA 

Initial Evaluators Contact Info: 

NA 

Lead Assigned: 

Cynthia H. Null

Lead Contact Info: 

Cynthia.H.Null@nasa.gov 

650-604-1260
NASA Engineering and Safety Center 

(NESC) Technical Consultation Position 

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2.1 Team Members, Consultants, and Advisors 

Last 

Name 

First 

Name 

Position/SPRT 

Affiliation 

Center/ 

Contractor 

Office 

Number Email 

Null Cynthia Lead LaRC 650-604-1260 Cynthia.H.Null@nasa.gov 

Conway Bruce Consultant, Statistical 

Evaluation of Shuttle 

External Tank 

Processing 

Swales 

Aerospace 

N/A baconway96@aol.com 

Scargle Jeffrey Space Science 

Planetary Branch, 

Statistical Data 

Analysis 

ARC 650-604-6330 Jeffrey.D.Scargle@nasa.gov 

McAlhaney Lisa Management & 

Technical Support 

Office (MTSO) 

LaRC 757-864-2139 Lisa.A.McAlhaney@nasa.gov 

Advisors: 

Ahumada Al Human Factors SPRT ARC 650-604-6257 Al.Ahumada@nasa.gov 

3.0 Consultation Plan 

The following are the major activities of the NESC consultation: 

Milestone Date 

Consultation Initiation June 2004 

Team Formation August 2004 

Technical Interchange Meeting 4-6 August, 2004 

Evaluation August – September 2004 

Stakeholder Out Briefing 26 September 2004 

Final Report Submission 16 May 2005 

The NESC consultation team met with the ET statistics group August 4-6, 2004 at the Michoud 

ET Assembly plant, for briefing and discussion of the dissection data. The NESC team was 

provided with the dissection data as well as already completed analyses of the dissection data. 

Through telecons and face-to-face meetings, the joint statistics team defined the data available, 

specified the assumptions that must be made to establish statistic descriptions of the dissection 

data, and defined limitations on using statistics for certification. Dr. Fayssal Safie presented the 

joint finding to the PRBC on September 30, 2004 (see Appendix B). 
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In addition, the NESC team did independent analyses of the dissection data to establish their 

conclusions. 

4.0 Description of the Problem and Proposed Solutions 

4.1 Problem 

Choosing a distribution to represent the observed data is a critical step in the statistical analysis. 

There currently is no engineering rationale to choose one distribution over another. Several 

distributions may fit the data equally well, and provide very different estimates of the expected 

maximum. The ET program has identified four foam failure modes. Understanding the 

frequency and size of internal defects has become important to understanding and predicting 

debris release. 

The ET has several different types of closed cells foam, various ablator materials, and ice /frost 

that form potential contributors to the debris environment around the Space Shuttle on ascent. 

For the return to flight (RTF) certification effort, the major focus has been on the areas of 

manually sprayed foam which were shown to be highly susceptible to having latent defects 

(voids) within the foam that could cause structural failure of the surrounding foam due either to 

entrapped gas pressure or liquid nitrogen /liquid air gasification within the voids on ascent. 

Based on previous flight history and early destructive analysis (dissection), decisions were made 

early in the RTF process to remove manually sprayed foam in the area of the bipod fitting and 

the intertank-to-liquid-hydrogen-tank flange. Since that time, other areas were added to the 

“remove and replace” category based on data acquired in the RTF process. These include the 

forward 10 feet of the Protuberance Airload (PAL) ramp on the liquid hydrogen tank and the 

longeron areas at the aft end of the tank. These “remove and replace” areas are having foam 

reapplied using enhanced processes and more rigorous process controls. The manually applied 

foams include BX-250 and BX-265. BX-265 replaced BX-250 due to environmental issues with 

the blowing agent in BX-250. Generally speaking, BX-250 is installed on tanks through ET-120, 

and BX-265 is installed on existing tanks subsequently processed (ET-121 and forward). BX265 is being applied in all redesign/rework areas. 

Approximately 95 percent of the foam is being left on the tanks as it was originally sprayed with 

no rework or repair. These areas consist mainly of “acreage foam” applied with automated 

processes, but a large number of manually sprayed areas will also be left “as is”. 

In its simplest terms, the certification approach taken by the ET project for the debris 

requirement (cohesive failure mode) is to determine, by test, those combinations of void (defect) 

size /shape and depth within the foam which can cause a divot. This test program is referred to 
NASA Engineering and Safety Center 

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as “critical defect testing.” Defects of “slot” and “cylindrical” shape are tested, based on 

principles of fracture mechanics. 

In order to determine whether an area of foam (referred to as a “closeout”) complies with the 

debris mass requirement, an analysis must be undertaken to determine the process yield of 

defects from that area. If the process yield defect size is less than the critical defect size (i.e., 

regardless of depth within the foam, no critical mass debris will be generated), then the area 

would be considered acceptable. If the process yield exceeds the critical defect size (i.e., at a 

certain range of depths, it would be possible to liberate debris exceeding the allowable limit) then 

further assessments that include local geometry, foam thicknesses, and thermal profiles during 

ascent (e.g., an area that stays cold throughout ascent can have a much larger critical defect size 

without producing a divot than other areas) may be required to determine if the situation is 

acceptable. 

A survey of the technical community would undoubtedly conclude that the most intractable 

issues for certification of the ET for debris lie in the area of “as-built” foams. Knowledge must 

be inferred, either by statistical or engineering methods, from destructive evaluation of one tank 

(ET-94), with a few areas from other tanks. 

4.2 Proposed Statistical Methods for ET Certification by ET Program 

Summer 2004.

The proposed statistical method during Summer 2004 is outlined in Figure 4.2-1 (provided by 

ET program). The 3-sigma estimates of ET foam defect size are all point estimates—distribution 

to be determined. All defects were divided into two types, slots and cylinders, depending on the 

ratio of the largest (L1) and second largest (L2) dimension of the defect. If L1/L2 > 2.5 a defect 

is called a slot, all others are called cylinders. In addition, the defects were labeled by process 

type (elongated cell, rollover, delamination, gunspit, void). This method assumed that datasets 

are primarily separated by the part that is sprayed (PAL ramp, Liquid Oxygen (LOX) intertank 

flange, bipod, longeron, etc.). 
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Figure 4.2-1. Three-Estimate Approach – Summer 2004

4.3 New Statistics Approach Proposed in October 2004

For this analysis two types of defects are defined: 

1. Defects inherent to the process = “Inherent”. (If a defect can be assumed to be in potentially 

any part, numerical treatments will be used to assess possible size and likelihood.) 

2. Defects unique to a particular configuration = “Configuration Dependent”. (Specific defect 

risks are determined by part geometry. 

Each part will be assessed for areas prone to defect generation.) Figure 4.3-1 outlines the new 

approach (provided by the ET program). 

Select Largest 

Estimate for 

Max Expected

Maximum Observed 

Estimate

Data 

Assessment 

•Outliers 

•Descriptive statistics & Data 

characterization 

•Statistical testing 

3-Sigma Estimate for 

Multiple Parts/Same 

Configuration

•Descriptive statistics & Data 

characterization 

•Statistical testing 

3-Sigma Estimate for 

Similar Complexities/ 

Geometries
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Figure 4.3-1. New Statistics Approach – October 2004 

Distributions were fitted to the data and 3-Sigma values were derived for the best-fit distribution 

and for the distribution with the biggest 3-Sigma (of distributions considered). These values are 

point estimates that control only the probability that a single defect chosen at random will not 

exceed that size. Frequency of the defects in flight is not considered. 

For each defect estimate for a part, the determination of an expected maximum begins with the 

3-Sigma from the grouped data. This estimated can be increased by information from partspecific geometry or reduced to accommodate any hardware/ foam thickness constraints. 
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5.0 Evaluation of Use of Statistics for Certification Approach 

5.1 Joint Evaluation by ET Program and NESC 

What dissection data is available? 

The ET program goal is to make inferences about defects on the next tank to be flown—to 

support the certification of as-built foam—from the dissection data that has been collected from 

tank 94, and selected areas from tanks 120, 121, and 123. 

Each defect is measured in three dimensions – length, width and thickness. These are sorted by 

largest (L1), 2nd largest (L2) and smallest (L3). Based on fracture mechanics principles, all 

defects were divided into two types, slots and cylinders, depending on the ratio of the largest 

(L1) and second largest (L2) dimension of the defect. If L1/L2 > 2.5 a defect is called a slot, all 

others are called cylinders. If the defect is categorized as a slot, the CDS of the slot is defined to 

be the smaller dimension, L2; if the defect is a cylinder, the CDS is equal to the largest 

dimension, L1. 

There are several types of void defects – elongated cells, voids, rollovers, delaminations, 

gunspits, etc. Void defects are further classified by the type of foam used – BX or PDL. 

Elongated cells typically are small voids that were judged to be primarily a function of foam 

chemistry, whereas the other defects are primarily a function of the spray process. In order to 

concentrate the analysis on defects due to the spray process, most elongated cells were purged 

from the database by removing defects with L1< 0.5” and L2 < 0.3” (i.e., defects with any one 

dimension ≥ 0.5” or any two dimensions ≥ 0.3” were kept). Also, void defects from the repair of 

production acceptance test areas were not included. 

The available data were “conveniently”, not randomly sampled, based upon tanks that were 

available for dissection. Since the data were not randomly selected and are available from only a 

few tanks, derived statistics are valid only for the sampled population and not the fleet, unless the 

dissected tanks are found to be typical of the fleet. 

Available dissection data (as of September 2004)

PALRamps: 94LH2, 94LO2,123LO2, 120LH2(10’), 121LH2(10’), 94SRB 

I/T Flanges: 94LO2, 94LH2, 120LH2, 121LH2

Flange Thrust Panel 94LH2, 120LH2

LO2 feedline fairing: 94LO2, 120LH2, 121LH2

Feedline Yoke: 94 (incomplete) 

Ice Frost Ramps: 94LO2, 128LO2, 94I/T, 94LH2, 120LH2
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Dog Leg C/T cover: 121LH2

Longeron: 94LH2

Nosecone: 94 

What are the limitations? 

The major assumptions that must be made to use statistical analysis of dissection data for 

certification include: 

• The defects found in ET-94 are representative of all defects that are produced during the 

manually-sprayed processes for all in-stock tanks. 

• The distributions of defects, for both slots and cylinders, are homogeneous (stable) and 

the samples are statistically independent. 

The combined team recognized that there are major limitations to generalizing from ET-94 

to other tanks with “use-as-is” foam. These include: 

• Data for some parts are available from only one tank. 

• Data in some cases are a mixture of BX-250 and BX-265 material. 

• Data on some parts have very small sample size (e.g., N=3). 

• Samples are not random—tank 94 plus certain parts of other tanks removed in support of 

redesign. 

• Sprayer-to-sprayer differences are not well understood. 

The combined team recognized several major limitations to fitting statistical distributions 

to the dissection data, including: 

• There is no a priori knowledge of the shape of distribution of CDS. 

• There is no engineering rationale to pick a specific distribution. 

• The natural variation of the process is not well understood. 

• There is a lack of random samples (historical) of sufficient size to empirically select a 

distribution. 

• Process controls related to manually-sprayed foam were related to environmental 

parameters and overlap time. Distributions of these process variables have been studied. 

However, the relationship between process control variables and defects is not known. 

• The critical part for predicting the maximum CDS distribution is the upper tail, where we 

have the least information. 
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5.2 Additional Evaluation by NESC Technical Consultation Team 

What is the critical statistic? 

There are two random variables that can be treated statistically: 

1) The measurement of a single foam defect, selected at random. 

2) The measurement of N foam defects, and then selecting the maximum of the N values. 

These variables are not the same, and in particular the equivalent 3-Sigma point in the 

distribution of (1) is not the same as that of (2). The latter is what is relevant to the basic 

questions posed here. The distribution of the maximum value of a set of random variables can be 

derived from their individual distributions. The single foam defect statistic is an underestimate 

of the maximum expected defect. The single foam defect statistic misleads by underestimating 

the probability of a large defect. See Appendix C for a description. 

What assumptions must be made to perform statistical analysis on the foam dissections

from ET-94? 

A key assumption that must be made is that the defects found in ET-94 are representative of all 

defects that are produced during the manually-sprayed processes for all in-stock tanks. 

Process control was applied to very few variables, and internal defects were not considered a 

process failure when the as-built tanks were produced. Among the variables controlled (and 

documented) are room temperature and humidity, substrate temperature at the beginning of a part 

spray, and component temperatures and proportions. The rise-time between layers and overlap 

time between layers of foam were well-understood by sprayers and quality personnel, though a 

method for timing was not provided and records were not made. Measurements made on witness 

panels and from plug pulls include tensile strength, density, and pull strength. The relationship 

between these control variables and measurements and defect production has not been 

determined. In addition, sprayer to sprayer differences and how they influence defect production 

are not well understood. 

The manually sprayed foam on test tank 94 and as-built tank 120 is predominately BX-250. The 

manually sprayed foam on the rest of the as-built tanks is BX-265. Whether the defects that 

appear in BX-250 and BX-265 are similar in frequency and size is not known. The chemical 

formulas for BX-250 and BX-265 vary in not only propellant, but the BX-265 formula was 

modified in hopes that the handling of the foam, in terms of rise-time and overlap time would 

remain about the same. 
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Although this is described as a small change, the data about the effect of this change is only 

understood in terms of tensile strength, compression, and density. Whether the chemical change 

affects any defect production variables (number, size, defect type, defect category, location, 

distribution, maximum characteristic defect) has not been investigated. Since BX-250 is not 

available for controlled testing, this is unanswerable. 

BX-265 is sprayed at a much higher temperature (BX-250 was sprayed at about 110 °F, while 

BX-265 is sprayed at about 155 °F). Whether the higher temperature affects defect frequency or 

maximum defect size is unknown. The sprayers were forced to change their arm/hand 

position(s) to avoid hot component feedlines resting on their hands. Whether this awkward body 

position changed defect production is not known. Assuming that defect frequency and size from 

a BX-250 tank is representative of a BX-265 tank is unjustified. 

What statistical distribution represents the defect dissection data? 

Traditional statistical methods address the problem of characterizing the distribution of a variable 

from one or more samples. In some cases one has considerable a priori knowledge of the 

distribution. For example, a standard formula with a few parameters may be known to be valid. 

And, often the goal is to predict features of the main core of the distribution—such as its median. 

The problem here is to estimate properties of the distribution of the maximum CDS, but there is 

no useful a priori knowledge about the distribution family and the key properties are features of 

the upper tail of the distribution –so little knowledge is gained per sample about the features. 

Process control variables for manually-sprayed foam were related to environmental parameters, 

component temperatures, and overlap time. Distributions of these process variables have been 

studied. However, knowledge of the process control does not provide the requisite information, 

since the relationship between process control variables and defects is unknown. 

Additionally, witness panels, and plug pulls from sprayed foam were analyzed—density, 

compressions, adhesion, and so forth. Again, the relationship between these foam characteristics 

and defects is unknown. 

For two reasons, fitting of any of the dozens of standard distributions in the statistics literature to 

the dissection data provides no useful information (Note: with small samples, data in the tails of 

the distribution are not expected.): 

1. A superior fit of one of these distributions to the core of the data provides little or no 

information on whether that distribution provides a more accurate description of the upper 

tail—the critical aspect. Standard goodness-of-fit tests are not sensitive to shape of the tail of 

the distribution. 
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2. Various distributions with quite different tails can provide equally acceptable fits to the 

available datasets. 

Figure 5.2-1 has three fits to one set of data of slots. Each fit is statistically acceptable (Note: the 

estimated 3-Sigma values are as low as .6766 and as high as 1.255). The first might be 

considered too small to cause a significant divot, and the latter could be above engineering 

limits. At this point there is no reason to pick one distribution over another. 

Figure 5.2-1. Fitting Distributions to a Sample of Dissection Data 

Is the 3-step largest defect approach conservative? 

In this 3-step approach, the max expected void is defined as the worst of three estimates: 3-

Sigma estimate for multiple parts/same configuration, 3-Sigma estimate for similar complexities 

or geometries, and maximum observed estimate (See Figure 4.2-1). 

This process does not assure that the estimate will always be wrong in the too large direction—

despite the claims. Each of the 3-Sigma estimates is contingent on the selection of a distribution 

type by a goodness-of-fit test. The selection of a distribution can be erroneous (a low tail 

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

-3.s +3.s

0

2

4

6

8

10

12

14

16

18

Fre que ncy

Beta

Extrem e Value

Log Norm al 1.255

0.823

0.6766

Log

Normal

Extreme

Value

Beta

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

-3.s +3.s

0

2

4

6

8

10

12

14

16

18

Fre que ncy

Beta

Extrem e Value

Log Norm al 1.255

0.823

0.6766

Log

Normal

Extreme

Value

Beta
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distribution may fit best when a high tail distribution is appropriate). With a choice of 

distribution varying from part to part, a statistical description of this three-step process, such as 

its distribution, is as yet undetermined. 

Is the new largest defect approach an improvement? 

The same problems experienced with the old approach continue with the new approach (See 

Figure 4.3-1). In addition, partitioning the data into meaningful sets for analysis after the data 

has been collected and examined raises the concern of statistical bias. Keeping the data separate 

by part can be easily justified, but yields very small samples of defects. The present new 

partitioning of the defects into chemistry, process, and geometry or part-specific categories may 

be useful. However, setting the criterion for this division in an unbiased manner is difficult after 

the data has been examined (and does not change the fact that tank-to-tank differences are not 

well understood). 

Although there are some defects that are unique to a part (such as a gap behind a bolt), the 

argument, in many cases, that a particular defect can only happen in an exact location or at a 

specific depth must be viewed with skepticism unless accompanied by solid data and analysis. 

6.0 Findings and Recommendations 

6.1 The Combined Team Finding 

Dissection data statistics have severe limitations and significant uncertainty in predicting the size 

of the largest defect CDS on the next tank. 

6.2 Recommendations to the PRCB by the Combined Team

1. Any statistical results should be subject to an engineering evaluation for consistency with 

experience, engineering analysis, and hardware limitations. 

2. Statistical analysis results/estimates should be used in a support role and as information to 

engineering in ET certification. 

3. Data limitations need to be addressed and minimized to improve the credibility of the 

statistical analysis to support RTF decisions (data must address tank-to-tank or part-to-part 

variation). 

4. The ET Program needs to pursue methods beside statistics to predict the largest possible 

defect CDS. 
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6.3 NESC Technical Consultation Team Findings (Three-Estimate 

Approach)

1. The largest CDS value in the next sample is the quantity of interest, and should be estimated 

from the distribution of maximum values. Using the distribution of sample values in place of 

the distribution of the maximum of a sample can raise the error probability by orders of 

magnitude. 

2. The assumption that Tank 94 will have the same type, number, and distribution of defects 

sizes as any as-built tanks is unfounded. The assumption that BX-250 and BX-265 foam will 

have the same type, number and distribution of defect size is unfounded. 

3. To predict maximum CDS for the next tank, the critical information needed is the shape of 

the upper tail of the distribution of defect sizes. Adoption of a standard distribution cannot 

be justified, so this shape is unknown and cannot be effectively constrained by the existing 

dissection data. 

4. The Three-Estimate Largest Defect Approach has not been statistically justified nor assured 

to be conservative. 

6.4 NESC Technical Consultation Team Findings (New Statistics 

Approach)

1. The largest defect in the next sample is the quantity of interest, and should be estimated from 

the distribution of maximum values. Using the distribution of sample values in place of the 

distribution of the maximum of a sample can raise the error probability by orders of 

magnitude. 

2. The assumption that Tank 94 will have the same type, number, and distribution of defects 

sizes as any as-built tanks is unfounded. The assumption that BX-250 and BX-265 foam will 

have the same type, number and distribution of defect size is unfounded. 

3. To predict maximum defect size for the next tank, the critical information needed is the shape 

of the upper tail of the distribution of defect sizes. Although the amount of data has 

increased by combining all defects in a category, different distributions will still provide very 

different 3-sigma estimates and choosing a distribution is still tenuous. 

4. The probabilities associated with statistical analyses are only considered defensible if the 

analysis methods have been described prior to the collection of the data. If the analysis has 

been done after the data has been examined, the analysis is considered to be suggestive. New 

data would be required to draw valid conclusions. 
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6.5 NESC Technical Consultation Team Conclusion (Three-Estimate 

Approach)

Based on the findings above, there is no firm basis for using statistical analysis of the dissected 

data from ET-94 to serve as a statistical distribution model for the certification of as-built foam 

for other tanks. 

6.6 NESC Technical Consultation Team Conclusion (New Statistics 

Approach)

The “new” approach suffers from the same issues as the “old” approach—wrong statistic (based 

on the distribution of defects instead of the distribution of maximums), unfounded assumptions 

of tank-to-tank and foam-to-foam similarity, and unfounded choice of distribution to represent 

the data. Therefore, there is no basis for using statistical analysis of the dissected data from ET94 to serve as a statistical distribution model for the certification of as-built foam for other tanks. 

7.0 Lessons Learned 

N/A

8.0 References 

N/A 

9.0 List of Acronyms 

°F Degrees Fahrenheit 

CDF Cumulative Distribution Functions 

CDS Characteristic Defect Size 

ET External Tank 

LOX Liquid Oxygen 

NESC NASA Engineering and Safety Center 

PAL Protuberance Airload 

PDF Probability Distribution Function 

PRCB Program Requirements Change Board 

RTF Return to Flight 

SFLC Space Flight Leadership Council 

TPS Thermal Protection System 
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10.0 Definition of Terms 

Corrective Actions Changes to design processes, work instructions, workmanship practices, 

training, inspections, tests, procedures, specifications, drawings, tools, 

equipment, facilities, resources, or material that result in preventing, 

minimizing, or limiting the potential for recurrence of a problem. 

Finding A conclusion based on facts established during the assessment/inspection 

by the investigating authority. 

Lessons Learned Knowledge or understanding gained by experience. The experience may 

be positive, as in a successful test or mission, or negative, as in a mishap 

or failure. A lesson must be significant in that it has real or assumed 

impact on operations; valid in that it is factually and technically correct; 

and applicable in that it identifies a specific design, process, or decision 

that reduces or limits the potential for failures and mishaps, or reinforces a 

positive result. 

Observation A factor, event, or circumstance identified during the 

assessment/inspection that did not contribute to the problem, but if left 

uncorrected has the potential to cause a mishap, injury, or increase the 

severity should a mishap occur. 

Problem The subject of the independent technical assessment/inspection. 

Recommendation An action identified by the assessment/inspection team to correct a root 

cause or deficiency identified during the investigation. The 

recommendations may be used by the responsible C/P/P/O in the 

preparation of a corrective action plan. 

Root Cause Along a chain of events leading to a mishap or close call, the first causal 

action or failure to act that could have been controlled systemically either 

by policy/practice/procedure or individual adherence to 

policy/practice/procedure. 
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VOLUME II: APPENDICES 

 

Appendix A. NESC Request Form PR-003-FM-01 
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NESC Request No. 04-027-I 

Appendix B. Joint Presentation to PRCB 
NESC Request No. 04-027-I 

Statistical Treatment and Limitations for t

As-built TPS Foam 

September 24, 2004

The information contained in this briefing should be considered “preliminary” and is subject to ITAR control 
NESC Request No. 04-027-I 

• June Space Flight Leadership Council assigned 

action to NESC and ET project jointly to: 

1) Characterize available dataset 2) Identify resultant limitations to statistical tr

 of External Tank as-built foam as part of ove certification and 

3) Report to PRCB and SFLC. 

The information contained in this briefing should be considered “preliminary” and is subject to ITAR control 
NESC Request No. 04-027-I 

• Goal

– Assess the risk that somewhere on the "nex

 there will be a defect large enough to divot 

• Statistical treatment 

– Defect data Characterization 

• Descriptive statistics • Fitting distribution to data 

– Extrapolation

• Estimation of the Max void size - upper sta

 limit on defect size for a specified  probability/confidence 

• Estimation of risk of as-built foam divoting

Statistical Treatment/Analysis

The information contained in this briefing should be considered “preliminary” and is subject to ITAR control
NESC Request No. 04-027-I 

What is being measured? 

• Foam Defects 

– Defects due to foam chemistry (e.g. elongated cells) – Defects due to foam spray process (e.g. voids, rollovers) 

• Focus of the analysis is characteristic defect size (CDS) 

– Defects are measured in three dimensions: L1 >L2>L3 

– Slots are defined by L1 /L2>2.5, CDS = L2 – Cylinders are defined by L1 /L2<2.5, CDS = L1 

Available dissection data 

PALRamps: 94LH2, 94LO2,123LO2, 120LH2(10’), 121LH2(10’), 94SRB 

I/T Flanges: 94LO2, 94LH2, 120LH2, 121LH2

Flange Thrust Panel 94LH2, 120LH2

LO2 feedline fairing: 94LO2, 120LH2, 121LH2Feedline Yoke: 94 (incomplete) Ice Frost Ramps: 94LO2, 128LO2, 94I/T, 

94LH2, 120LH2

Dog Leg C/T cover: 121LH2

Longeron: 94LH2

TPS foam dissection database

Being upd

Nosecone: 94 
NESC Request No. 04-027-I 

Major Assumptions 

• The defects found in ET-94 are representative of all defects 

produced during the manually-sprayed processes for all in-s

• The distributions of defects, for both slots and cylinders, are 

homogeneous (stable) and the samples are independent. 

Major Limitations to Generalization From ET-9

• Data for some parts are available from only one tank (tank 

 variability needs to be expressed in the data) 

• Data in some cases are a mixture of BX-250 and BX-265 m

• Data on some parts have very small sample size (e.g., N=3• Samples are not random —Tank 94 plus certain parts of ot

 removed in support of redesign 

• Sprayer to sprayer differences are not well understood. 

Assumptions and Limitations

The information contained in this briefing should be considered “preliminary” and is subject to ITAR control
NESC Request No. 04-027-I 

Major Limitations of Fitting Distribution Shapes To De

• It is not unusual to fit distribution shapes to data, under condit

 uncertainty. However, the level of uncertainty related to distrib

 high for defect CDS. 

• Distribution related limitations for manually-sprayed foam diss

– There is no a priori knowledge of the shape of distribution of 

– There is no engineering rationale to pick a specific distributio– The natural variation of the process is not well understood. – There is a lack of random samples (historical) of sufficient si

empirically select a distribution 

– Process controls related to manually-sprayed foam were rel

environmental parameters and overlap time. Distributions of process variables have been studied. However, the relationsprocess control variables and defects is not known. 

– Process controls for manually-sprayed foam were related to 

environmental parameters and overlap time, but other technvariables were not controlled. 

The information contained in this briefing should be considered “preliminary” and is subject to ITAR control 
NESC Request No. 04-027-I 

 • It is common practice to pick the 

 However, picking a distribution, 

 the “3-sigma” value. 

 • A distribution that does not statist

 of data could be the distribution th

• For the CDS datasets 

provided, most datasets 

can be fit well by several distributions having very different tail properties —

different “3-sigma” 

values. 

Log

Normal

Extreme

Value

Beta

 represents the shape of the tail 
NESC Request No. 04-027-I 

1. Dissection data statistics have severe limitations and 

uncertainty in predicting the size of the largest defect the next tank. 

2. Any statistical results should be subject to an enginee

evaluation for consistency with experience, engineerinanalysis, and hardware limitations 

3. Statistical analysis results/estimates should be used i

support role and as information to engineering in ET certification 

4. Data limitations need to be addressed and minimized 

the credibility of the statistical analysis to support RTF (data must address tank to tank or part to part variatio

5. The ET Program needs to pursue methods beside 

statistics to predict the largest possible defect CDS. 

The information contained in this briefing should be considered “preliminary” and is subject to ITAR control
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Appendix C. Statistical Methodology

Consider these two random variables: 

1)The measurement of a single foam defect, selected at random. 

2)The measurement of N foam defects, and the selection of the maximum of the N values. 

If N>1, these variables are not the same, in particular, the equivalent 3-sigma point in the 

distribution of (1) can be much less than that of (2). If one is trying to ensure that none of the 

foam defects exceed a critical size, probability statements about variable (2) are needed to 

characterize the risk. 

Predicting the maximum Characteristic Defect Size for the next tank. 

The largest CDS value in the next sample is the quantity of interest. The distribution of the 

maximum value of a set of random variables can be derived from their individual distributions. 

The result is most easily described in terms of Cumulative Distribution Functions (CDF). If the 

Probability Distribution Function (PDF) of X is P(x), the CDF is defined to be the probability 

that the measured value is ≤ to x: 

 CDF(x) = ∫0

x

 P(x') dx'r 

Given a set of N independent variables, say X = { X1, X2, ... XN }, the CDF of their maximum is 

the product of their CDFs: 

 CDF( max(X) ) = CDF( X1 ) CDF( X2 ) ... CDF( XN ) 

so if the X's are N random “draws” from the same distribution, this equation becomes 

 CDF( max(X) ) = CDF( X )N 

The figure on the following page shows PDFs (derivatives of the CDFs) for the maximum of N 

variables, normally distributed – with zero mean and unit variance. The normal distribution fit to 

the logs of the defect sizes is one of the candidate distributions. Distributions of maximums can 

be derived for any candidate distribution. 
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The curve for N=1 is just the normal distribution itself. For increasing Ns, the peak of the curve 

(the most likely value of the maximum of N draws) sifts to larger values as one would expect, 

because, with more tries, the relatively rare values on the high-end of the distribution are more 

likely to be obtained. So, the distribution of the maximum values of a set of samples increases 

with the numbers of measurements in a sample. The variance of distribution of maximums 

decreases with N. 

The equation of interest is: 

P(nextmax > critical value) = Pcrit = 1- CDF( X )N

Either we set a Pcrit , for example to a probability equivalent 3-sigma for the normal (1-.9987) 

and solve for a critical value; or we can determine the probability that the nextmax is greater than 

some critical value—in this case a value set by engineering. 
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The population equivalent 3-Sigma point of a single defect CDS provides an estimate such that 

99.87% of the time a randomly chosen defect from the next tank will be less than this value. 

This estimate does not change with the expected number of defects in a specific part. Using the 

relationship between a single sample distribution and the distribution of maximums, the 

probability that the maximum of the next sample is greater then the single defect CDS equivalent 

3-Sigma point conditional on sample size can be determined. That is, the .13% chance of seeing 

a larger maximum defect could actually be a 12% chance if 100 defects were expected. 

Expected N 

P(observed max > 3 sigma 

single point estimate) 

1 0.0013 

2 0.002598 

5 0.006483 

10 0.012924 

20 0.025681 

30 0.038274 

40 0.050703 

50 0.062972 

60 0.075083 

70 0.087036 

80 0.098836 

90 0.110483 

100 0.121979 

200 .33907883 

400 .40568054 

600 .54182654 
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NESC Request No. 04-027-I 

Approval and Document Revision History 

Approved: Original signed on file 11/7/05 

 NESC Director Date 

Version Description of Revision Office of Primary 

Responsibility 

Effective 

Date 

1.0 Initial Release NESC Principal 

Engineer’s Office 

11/7/05 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Support Provided to the External Tank (ET) Project on the Use of 

Statistical Analysis for ET Certification Consultation Position Paper

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Null, Cynthia H.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-19684 NESC-05-57/04-027-I

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 15-Launch Vehicles and Launch Operations

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

In June 2004, the June Space Flight Leadership Council (SFLC) assigned an action to the NASA Engineering and Safety 

Center (NESC) and External Tank (ET) project jointly to characterize the available dataset [of defect sizes from dissections of

foam], identify resultant limitations to statistical treatment of ET as-built foam as part of the overall thermal protection system 

(TPS) certification, and report to the Program Requirements Change Board (PRCB) and SFLC in September 2004. The NESC 

statistics team was formed to assist the ET statistics group in August 2004. The NESC's conclusions are presented in this 

report.

15. SUBJECT TERMS

CDF; CDS; ET; NESC; TPS

18. NUMBER

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 PAGES

42

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

a. REPORT

U

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3. DATES COVERED (From - To)

March 2004-May 2005

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5f. WORK UNIT NUMBER

869021.07.07.01.99

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NASA/TM-2009-215749

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