U.S. Department of 

Transportation

Federal Railroad 

Administration

Analysis of the Relationship between Operator 

Effectiveness Measures and Economic Impacts 

of Rail Accidents 

Office of Railroad Policy and Development

Office of Safety

Washington, DC 20590

DOT/FRA/ORD-11/13 Final Report

May 2011
NOTICE 

This document is disseminated under the sponsorship of the 

Department of Transportation in the interest of information 

exchange. The United States Government assumes no liability for 

its contents or use thereof. 

NOTICE 

The United States Government does not endorse products or 

manufacturers. Trade or manufacturers’ names appear herein 

solely because they are considered essential to the objective of this 

report. 
i 

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson 

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

May 2011

3. REPORT TYPE AND DATES COVERED

Final Report

4. TITLE AND SUBTITLE

Analysis of the Relationship between Operator Effectiveness Measures and Economic 

Impacts of Rail Accidents 

5. FUNDING NUMBERS

6. AUTHOR(S)

Steven R. Hursh,

1

Joseph F. Fanzone,

1

and Thomas G. Raslear

2

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

1 Institutes for Behavior Resources

 2104 Maryland Avenue

 Baltimore, MD 21218

8. PERFORMING ORGANIZATION 

REPORT NUMBER

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

2 U.S. Department of Transportation 

 Federal Railroad Administration

 Office of Railroad Policy and Development

 1200 New Jersey Avenue, SE

 Washington, DC 20590

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

DOT/FRA/ORD-11/13

11. SUPPLEMENTARY NOTES

Program Manager: Thomas G. Raslear

12a. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available to the public through the FRA Web site at http://www.fra.dot.gov.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Data from 350 human factors (HFs)-related accident and 958 non-HFs-related U.S. rail accidents from January 1, 2003, through 

May 31, 2003, were analyzed for relationship between accident cost and crew performance effectiveness scores as estimated by 

the Sleep, Activity, Fatigue, and Task Effectiveness (SAFTE) biomathematical fatigue model. Property damage data was 

augmented by casualty cost using a combination of fatality costs and injury costs based on relationship between lost workdays and 

the Maximum Abbreviated Injury Scale. Preliminary analysis prompted grouping of accidents into groups based on crew 

effectiveness scores. Relative accident risk and relative economic risk were computed for each bin. Estimated relative economic 

risk (damage and casualty cost) of an HF was more than quadrupled for crew effectiveness scores at or below 70, increased by a 

factor of 5 when scores were at or below 77 and reduced by a factor of 4 when scores were above 90. Estimated relative accident

risk of an HF increased by 62 percent when effectiveness was at or below 70 and reduced by approximately 30 percent when 

effectiveness was above 90. Average total cost of accidents decreased exponentially as effectiveness increased from below 70 to 

above 90; average total cost when effectiveness was at or below 70 was more than triple the overall average cost and quadruple

the average cost when effectiveness was greater than 90. Results further validate the SAFTE for estimating work related fatigue 

risk.

14. SUBJECT TERMS

fatigue, railroad accidents, railroad accident cost, economics, fatigue modeling, effectiveness, 

relative risk, SAFTE, FAST

15. NUMBER OF PAGES

36

16. PRICE CODE

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

20. LIMITATION OF ABSTRACT

None

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std.239-18

298-102 
ii

METRIC/ENGLISH CONVERSION FACTORS

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE)

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in)

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in)

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft)

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd)

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE)

1 square inch (sq in, in2) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2)

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2)

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2)

1 square mile (sq mi, mi2) = 2.6 square kilometers (km2) 10,000 square meters (m2) = 1 hectare (ha) = 2.5 acres

1 acre = 0.4 hectare (he) = 4,000 square meters (m2)

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE)

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz)

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb)

1 short ton = 2,000 pounds 

(lb)

= 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg)

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE)

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz)

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt)

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt)

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal)

1 pint (pt) = 0.47 liter (l)

1 quart (qt) = 0.96 liter (l)

1 gallon (gal) = 3.8 liters (l)

1 cubic foot (cu ft, ft3) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3)

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT)

[(x-32)(5/9)] F = y C [(9/5) y + 32] C = x F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 3 4 5

Inches

Centimeters 0 1 2 3 4 5 6 7 8 9 10 11 12 13

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0 ° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and Measures. Price $2.50 

SD Catalog No. C13 10286 Updated 6/17/98
iii

Contents

Executive Summary........................................................................................................................ 1

1 Introduction............................................................................................................................ 3

1.1 Purpose............................................................................................................................. 3

1.2 Background...................................................................................................................... 3

1.3 Scope................................................................................................................................ 3

2 Concepts, Methods, and Sources........................................................................................... 4

2.1 Concepts........................................................................................................................... 4

2.1.1 Fatigue ......................................................................................................................... 4

2.1.2 Fatigue Modeling and SAFTE..................................................................................... 4

2.1.3 Effectiveness................................................................................................................ 4

2.1.4 Computation of Relative Risk ..................................................................................... 4

2.2 Methods............................................................................................................................ 5

2.2.1 Crew Effectiveness Scores.......................................................................................... 6

2.2.2 Sleep Estimates............................................................................................................ 6

2.3 Data .................................................................................................................................. 6

2.3.1 Recapitulation of Previous Study Results ................................................................... 7

3 Analysis of Economic Effects................................................................................................ 8

3.1 Measures.......................................................................................................................... 8

3.2 Grouping of Accidents by Effectiveness Score Intervals ................................................ 8

3.3 Evaluation of Accident Frequency and Damage Cost by Effectiveness Scores............ 10

3.4 Casualty Costs................................................................................................................ 12

3.5 Relative Risk of Accidents and Cost ............................................................................. 14

3.6 Total Accident Cost Relative to Effectiveness Scores................................................... 16

3.6.1 Accident Cost with Effectiveness Less than 70 ........................................................ 17

3.6.2 Statistical Test of Accident Cost Relative to Effectiveness of 70 or Below ............. 18

3.6.3 Relative Risk and Relative Economic Risk for Effectiveness of 70 or Below ......... 19

4 Conclusions.......................................................................................................................... 21

5 References............................................................................................................................ 22

Appendix A. Estimating the Cost of Casualties in Accidents Reported to the 

Federal Railroad Administration ............................................................................ 23

Abbreviations and Acronyms ....................................................................................................... 29
iv

Illustrations

Figure 1. Difference in Mean Accident Cost between HFs-Related Accidents at or below 

a Given Crew Effectiveness Score and Those above the Same Score with Cubic 

Polynomial Fit ................................................................................................................ 9

Figure 2. Total Cost of HFs-Related Accidents in Three Disjoint Crew Effectiveness Score 

Intervals by Accident Type .......................................................................................... 10

Figure 3. Number of Accidents in Three Disjoint Crew Effectiveness Score Intervals.............. 11

Figure 4. Average Accident Damage Cost in Three Disjoint Crew Effectiveness Score 

Intervals by Accident Cause Classification.................................................................. 12

Figure 5. Total Accident Cost ($) from Casualties (dark blue) and Property Damage 

(light blue) Associated with HFs-Related Accidents as a Function of Average 

Operator Effectiveness ................................................................................................. 13

Figure 6. Average Total Accident Cost ($) from Casualties (dark blue) and Property Damage 

(light blue) Associated with HFs-Related Accidents as a Function of Average 

Operator Effectiveness ................................................................................................. 14

Figure 7. Relative Accident Risk (blue bars) and Relative Economic (damage and 

casualty cost) Risk (red bars) Associated with HFs-Related Accidents ...................... 15

Figure 8. Difference in Mean Accident Cost Including Casualty Cost between HFs-Related 

Accidents at or below a Given Crew Effectiveness Score and Those above the 

Same Score with Cubic Polynomial Fit (blue line)...................................................... 16

Figure 9. Average Total Accident Cost ($) from Casualties (dark blue) and Property Damage 

(light blue) Associated with HFs-Related Accidents as a Function of Average 

Operator Effectiveness ................................................................................................. 17

Figure 10. Average Total Accident Cost ($) from Casualties (dark blue) and Property Damage 

(light blue) Associated with HF Accidents as a Function of Average Operator 

Effectiveness ................................................................................................................ 18

Figure 11. Proportion of HF Accidents with Total Cost Greater than $80,000 Relative to 

Crew Effectiveness Scores........................................................................................... 19

Figure 12. Relative Accident Risk (light gray) and Relative Economic (damage and casualty 

cost) Risk (dark gray) Associated with HFs................................................................. 20

Figure 13. MAIS Level as a Function of LWDs.......................................................................... 27
v

Tables

Table 1. Example of Injury Data from the FRA Casualty Detail Reports................................... 23

Table 2. The MAIS of the U.S. Department of Transportation ................................................... 24

Table 3. Examples and Descriptions of Injuries for MAIS Levels.............................................. 24

Table 4. Nature of Injury Codes and Feasible MAIS Levels....................................................... 25

Table 5. LWDs, Number of Injuries, and Mean MAIS for FRA Injury Codes........................... 26

Table 6. Mean LWD and MAIS Level ........................................................................................ 27

Table 7. MAIS Level and LWDs................................................................................................. 28
1

Executive Summary

Data from the Federal Railroad Administration’s (FRA) database of railroad accidents,

augmented by work schedules for the train crew involved, was analyzed to investigate the 

existence and strength of a hypothetical relationship between the economic impact (cost) of an 

accident and the estimated performance effectiveness of the train crew at the time when the 

accident occurred. This report shows that high levels of fatigue increase the average cost of 

human factor (HF) accidents by 300 percent and increase the risk of a HF accident by 65 percent. 

By contrast, HF accidents without fatigue cost less than the average HF accident and have 

30 percent reduced accident risk.

Information for 1,308 railroad accidents involving the five Class I freight rail carriers that 

occurred between January 1, 2003, and May 31, 2005, was extracted from FRA databases. Of 

these, 350 were identified as having HF-related causes and 958 were caused by non-HFs (NHF). 

Data included date and time of the accident, property damage costs, number of injured, workdays 

lost by each injured person, and the number of fatalities. In a previous FRA study, the carriers 

had provided work histories for crewmembers on trains involved in these accidents. These data 

consisted of shift starting and ending times for 30 calendar days prior to and including the time 

of the accident and other information such as train movements relative to the crewmember’s 

home terminal.

Crewmembers’ work histories were used to estimate their performance effectiveness by applying 

the Sleep, Activity, Fatigue, and Task Effectiveness (SAFTE) fatigue model as implemented in 

the Fatigue Avoidance Scheduling Tool (FAST). The work histories were processed in FAST to 

compute ―AutoSleep,‖ an estimate of when each crewmember could reasonably be expected to 

be asleep between work shifts, and this was used to estimate crewmembers’ effectiveness scores 

during each work interval. The crew effectiveness at the time of the accident was estimated as 

the harmonic mean of the individual members’ estimated effectiveness scores at that time.

Property damage costs of accidents from the FRA accident database were augmented with the 

estimated cost of casualties. The cost equivalent for each fatality was set to $6 million, which is 

the value of a statistical life (VSL) used by U.S. Department of Transportation. A cost 

equivalent for each nonfatal casualty was computed by relating the number of lost workdays 

(LWDs) recorded in the FRA casualty detail database by a linear function to a score on the 

Department of Transportation’s Maximum Abbreviated Injury Scale (MAIS) and thence to the 

corresponding fraction of the VSL. Property damage cost, fatality costs, and injury costs were 

summed to provide a total cost associated with each accident.

Preliminary analysis searched for crew effectiveness score values that would serve as plausible 

cut points for collecting accident cost data into bins. The difference in average property damage 

costs for HFs-related accidents above and below a given crew effectiveness score was found to 

have extreme points near scores of 77 and 90, suggesting the classification of accidents by 

effectiveness score into three bins (x ≤ 77, 77 < x ≤ 90, and x > 90). When casualty costs were 

included, the lower extreme point shifted to near 70, prompting the grouping into three slightly 

different bins (x ≤ 70, 70 < x ≤ 90, and x > 90).

The relative accident risk of HFs-related accidents in bins defined by these values was then 

computed. The computation of relative risk first involved calculating a ratio of the proportion of 
2

accidents within an effectiveness bin (incident fraction) to the proportion of crewmembers duty 

time spent within that effectiveness bin (exposure fraction). That ratio was then divided by the 

same quantity computed for accident risk outside the bin. Relative economic risk was computed 

in the same fashion as relative accident risk, except that each accident was multiplied by its cost

to provide a relative measure of the consequences of each accident. The following results were 

noted:

 The estimated relative economic risk (damage and casualty cost) of an HF-related accident 

is more than quadrupled when crew effectiveness scores are at or below 70. 

 The estimated relative economic risk (damage and casualty cost) of an HF-related accident 

is increased by a factor of 5 when crew effectiveness scores are at or below 77 and 

reduced by a factor of 4 when crew effectiveness scores are above 90.

 The estimated relative accident risk of an HF-related accident is increased by 62 percent

when crew effectiveness scores are at or below 70 and reduced by approximately 

30 percent when crew effectiveness scores are above 90.

 The average total accident cost (damage and casualties) when crew average effectiveness is 

equal to or less than 70 (highly fatigued) is approximately $1.6 million, which is more 

than triple the overall average cost of accidents. In comparison to accidents without 

fatigue (when effectiveness is greater than 90), the average cost when crew average 

effectiveness is equal to or less than 70 is quadrupled. The average total cost of 

accidents decreases exponentially as effectiveness increases from below 70 to above 90.

These results further validate the utility of biomathematical fatigue models (here the SAFTE 

model and the FAST software) for estimating work related fatigue risk. They also calibrate the 

model to indicate that a score of 70 or below is associated with an elevated relative risk in the 

number and severity (cost) of accidents.
3

1. Introduction

1.1 Purpose

The Federal Railroad Administration (FRA) continues to develop tools for managing fatigue in 

railroad operations. A previous report established a statistically reliable relationship between 

train crew performance effectiveness (inverse of fatigue) and the risk of an HFs accident (Hursh

et al., 2006, 2008). The purpose of the current report was to use the data from the FRA database 

of railroad incidents, augmented by work schedules for the train crew involved, to investigate the 

relationship between the economic impact (cost) of an incident and the estimated fatigue of the 

train crew at the time when the incident occurred. 

1.2 Background

In 2006, the FRA completed the third phase of a research program to demonstrate a method to 

validate and calibrate fatigue models for use in predicting and managing fatigue in railroad 

workers. A fatigue model offers the possibility of objectively assessing and forecasting fatigue so

that employees and employers can schedule work and rest to avoid fatigue. A useful fatigue 

model needs to be calibrated to the demands of a particular job so that the measures from the 

model can be related to the risk of meaningful failures of human performance. One important 

part of calibration of a fatigue model for use as a fatigue management tool is an assessment of 

whether the tool can predict an increased risk of an HFs error or risk of having an HF-caused 

accident. As part of this assessment, FRA sponsored a project, in partnership with the five Class 

I freight rail carriers, to examine 2.5 years of data on accidents. 

1.3 Scope

This report describes an extension of analyses performed for the FRA that investigated the 

relationship between accident cost and estimated crew impaired effectiveness from fatigue. The 

original effort developed estimates of train crew performance effectiveness using the Sleep, 

Activity, Fatigue, and Task Effectiveness (SAFTE) fatigue model implemented in the Fatigue 

Avoidance Scheduling Tool (FAST).1 These estimates were then used to estimate accident risk 

based on crew member estimated effectiveness at the time of accidents, and to compare risk 

between accidents with HFs-related causes and those whose causes were not HFs-related. The 

work described herein extends that analysis to investigate the relationship of HFs-related 

accident (HF-related accidents) cost to estimated train crew effectiveness.

 

1 Note that SAFTE is the quantitative model itself (i.e., the algorithm that defines how fatigue is estimated and 

effectiveness measures computed from the required inputs), whereas FAST is the implementation of the model in 

software. Since FAST is used for the actual computations, it is referred to as ―the model‖ hereinafter, but the 

distinction should be kept in mind. The SAFTE model and the FAST software are both patented; rights to SAFTE 

are owned by the U.S. Army and licensed to Fatigue Science, Inc., owner of the rights to FAST and other software 

implementations of the SAFTE model (www.fatiguescience.com).
4

2. Concepts, Methods, and Sources

2.1 Concepts

2.1.1 Fatigue

Fatigue is more than simple sleepiness. It is a complex state characterized by a lack of alertness 

and reduced mental and physical performance, often accompanied by drowsiness. Fatigue is 

associated with symptoms including measurable changes in performance, lapses in attention and 

vigilance delayed reactions, impaired logical reasoning and decisionmaking, reduced ―situational 

awareness,‖ low motivation to perform ―optional‖ activities, poor assessment of risk (or failure 

to appreciate the consequences of actions), and operator inefficiencies. Clearly the appearance 

of any of these symptoms in a railroad operations crew could potentially lead to incidents.

2.1.2 Fatigue Modeling and SAFTE

Although fatigue is one potential root cause for these symptoms, no direct measure or 

physiological marker for fatigue has ever been identified. However, the conditions leading to 

fatigue are well understood, and sufficiently quantifiable that the degree to which an individual is 

fatigued can be estimated by means of biomathematical models such as the SAFTE fatigue 

model. A fatigue model offers the possibility of objectively assessing and forecasting fatigue so 

that employees and employers can schedule work and rest to avoid fatigue.

2.1.3 Effectiveness

The SAFTE Model predicts effectiveness based on opportunities to sleep and time of day. 

Effectiveness is a metric that ranges from 0 to 100 and tracks speed of performance on a simple 

reaction time test. It is strongly related to overall cognitive speed, vigilance, and the probability 

of attention lapses or ―micro-sleep‖ (Hursh et al., 2004; Van Dongen, 2004). Cognitive 

effectiveness can be interpreted as the inverse of fatigue.

In terms of cognitive impairment, an effectiveness value of 70 is roughly equivalent to a blood 

alcohol level of 0.08 percent, or having remained awake for 21 h following an 8-hour sleep 

period the previous night (Arnedt et al., 2001; Dawson and Reid, 1997). Major quantifiable 

factors that produce or exacerbate fatigue include a time of day between midnight and 6 a.m., 

insufficient sleep in the last 24 h, long intervals since the last major sleep period, accumulation 

of ―sleep debt‖ since last full night of sleep, work intensity, and duration. 

2.1.4 Computation of Relative Risk

In a previous report on fatigue modeling and accident risk (Hursh et al., 2006, 2008), the authors 

examined the proportion of accidents at a particular level of fatigue (effectiveness) relative to the 

proportion of work time at that level of fatigue. That analysis tested whether a fatigue model 

could predict an elevation of the chances of an accident relative to the chance exposure to a 

particular level of predicted fatigue.2 Here we are interested in quantifying that risk relative to 

 

2

In Hursh et al. (2006, 2008), relative risk was computed as the ratio of events (E) in the given category to exposure 

to that category (C). Here the definition follows the epidemiological usage, where relative risk is expressed as a 
5

the alternative of not being in that state of fatigue, which is the standard epidemiological 

definition of relative risk (Armitage and Berry, 1994). Relative risk quantifies risk relative to 

other alternative conditions: it is the expected loss under a given set of conditionsrelative to the 

expected loss when those conditions are not present.3For an event E and a condition4 C, 

Relative risk of E given C= Prob (E|C)/Prob (E|not C)

where (E|C) denotes the event that E occurs when condition C is present, and (E|not C) the 

event that E occurs when condition C is not present.5 

Relative risk can have any non-negative value. A relative risk of 1 means that the probability of 

E is the same whether or not condition C obtains; in other words, E is statistically independent of 

C. A relative risk greater than 1 means that event E is more likely to occur under condition C

than when it is absent, and a relative risk less than 1 means that event E is less likely to occur 

under conditions C than when that condition is absent. 

Suppose condition C occurs 20 percent of the time in the data set; then if 20 percent of all 

occurrences of event E occur when C obtains and 80 percent occur when C does not, the event E

is independent of C [relative risk = 1 = (0.2/0.2)/(0.8/0.8)]. Suppose instead that 30 percent of all 

occurrences of event E occur when condition C is present; then the relative risk is computed as 

(0.3)/0.2/(0.7/0.8) = 0.24/0.14 ≈ 1.71, which means the relative risk of event E occurring is 

increased by 71 percent if condition C is present. If on the other hand only 10 percent of all 

occurrences of event E occur when condition C is present, the relative risk is (0.1/0.2)/(0.9/0.8) = 

0.08/0.18 ≈ 0.44, so that the relative risk of event E occurring is reduced by 56 percent if 

condition C is present.6

In the current instance, it is natural to ask what relative risk is associated with an accident when 

crewmembers are in various states of fatigue relative to when they are in other states, specifically 

to what extent the relative risk might be magnified (or reduced) for a crew at a higher (or lower) 

state of fatigue. The following analysis examines both relative accident risk and relative 

economic risk resulting from an accident.

2.2 Methods

The SAFTE model as implemented in FAST estimates an individual’s effectiveness in 

performing cognitive tasks as a function of the amount and timing of the individual’s prior sleep 

and the time of day or ―circadian rhythm‖ of cognitive functioning.

 

ratio of risk of an event within a category to the risk for all events excluding that category (Armitage & Berry, 

p. 508).

3 Note that the ―loss‖ in question may be the occurrence of an event, as well as the magnitude of an adverse outcome 

associated with an event. In the current instance, the loss could be the occurrence of a railway accident, or the cost 

incurred by such an occurrence.

4

For simplicity, the subsequent discussion assumes a single (pre)condition.

5 This is analogous to the definition of risk in epidemiology, with the occurrence of an accident corresponding to 

contracting a disease and the crew effectiveness score falling into a given interval corresponding to the putative risk 

factor (e.g., see Armitage & Berry, pp. 508–522).

6

In prior reports (Hursh et al., 2006, 2008), risk was defined as the proportion of events E given condition C, or 1.50 

or a 50 percent increase, in this example. 
6

2.2.1 Crew Effectiveness Scores 

Effectiveness scores at the time of the incident were averaged among all on-duty crewmembers 

of the train involved. Because these scores are effectively rates for accomplishing a fixed set of 

cognitive tasks, the appropriate average is the harmonic mean.7

2.2.2 Sleep Estimates 

This analysis was undertaken well after the incidents’ times of occurrence. It was, therefore, 

impossible to collect accurate information on subjects’ actual sleep patterns. Available data were 

limited to the start and end times of subjects’ work shifts from the railroads’ records, which were 

obtained for each subject for 30 calendar days prior to the incident time. This information, 

which captures all time spent by the subject on site during the interval, was augmented with 

railroad- and terminal-specific call and commute times. Call time represents the amount of 

advance notice a worker must be given (usually by telephone) by the railroad before the start of a 

work shift. Commute time is the railroad’s estimate of the time required by a subject leaving the 

site at the end of a work shift to return to lodgings and make ready for sleep. These times are 

added to the times of the beginning and end of the work shifts to generate intervals during which 

the subject would be excluded from sleeping. 

With the remaining time as time available for sleep, FAST was applied to compute ―AutoSleep,‖ 

an estimate of when the subject could reasonably be expected to be asleep between work shifts. 

This recursive estimate is based on reasonable assumptions about how crewmembers allocate 

off-duty time between sleep and other activities and has been validated against measures of sleep 

in other studies of railroad engineers. At any time of interest, whether the subject is modeled to 

go to sleep (or remain asleep) depends upon the time of day (which affects sleep quality) and the 

interval available for sleeping (FRA, 2011). 

Once FAST has been run to generate AutoSleep for an individual, the tool is rerun using the 

estimated sleep intervals to generate average effectiveness scores averaged over half-hour 

intervals beginning at 00:01. An instantaneous effectiveness score at the time of the incident is 

also computed. 

2.3 Data 

Incident data were derived from the publicly available FRA database of railroad incidents. 

These data were augmented by information provided by the study railroads about work schedules 

for each train crewmember involved in incidents and used to validate and calibrate fatigue 

modeling (Hursh et al., 2006, 2008). Work schedule data consisted of on-duty and off-duty dates 

and times for each individual involved in an incident during the 30 calendar days prior to that 

 

7

 The rationale for this choice can be understood by analogy with actual speed: The average speed of a train that 

travels 30 miles at 40 miles per hour (mph) and then 40 miles at 80 mph is most easily computed by dividing the 

total distance traveled (30+40=70 miles) by the total amount of time taken (for the first stretch, 30 miles/40 mph = 

3/4 h; for the second stretch, 40 miles/80 mph = 1/2 h; in all, 3/4 h + 1/2 h = 1 1/4 h) to obtain 70 miles/1 1/4 h = 56 

mph. This is the same as 

80

40

40

30

30 40





HM  . 
7

incident. The railroads also provided call and commute times for originating and destination 

stations. The resultant data set was recently purged for data inconsistencies and now covers 

1,308 accidents from the study railroads during the period from January 1, 2003, through May 

31, 2005. At least one HFs cause code was associated with 350 of these accidents, whereas the 

remaining 958 had no HFs (NHFs) cause code associated with the accident. Of the 350 HFrelated accidents, 63 were associated with cause codes that were most frequent when fatigue was 

high or effectiveness was low (less than 70; see Hursh et al., 2006, 2008), such as passing a red 

signal, excessive speed, violating train orders, or poor train handling. 

Accident data used in the prior study were limited to the date and time of the accident along with 

primary and secondary cause codes. These FRA-defined codes indicate the factors that were 

identified as having caused the accident, such as passing a stop signal or exceeding authorized 

speed. The current study augments this information with economic impact data, also drawn from 

the FRA incident database. Data available from the database includes the dollar cost of damage 

to equipment and track. The dollar cost of equipment and track damage combined was used as 

the measure of economic impact. Later, in this report, we discuss the added cost of death and 

injury associated with these same accidents, based on data from the FRA database. 

2.3.1 Recapitulation of Previous Study Results 

The previous study was directed at investigating whether a fatigue model (specifically, SAFTE 

as implemented in FAST) could predict an increased risk of HFs-related accidents under certain 

conditions that cause fatigue. Incidents were separated into those with a primary and/or 

secondary HF cause code (i.e., a code indicating that HFs were involved) and those lacking such 

cause codes. 

There was a reliable inverse linear relationship between crew effectiveness score and the risk of 

an HF accident (r = -0.93). No such relationship was found for NHF accidents. These results 

satisfied the criteria for model validation. 
8

3. Analysis of Economic Effects 

3.1 Measures 

This study investigated the relationship between the cost of a rail incident and train crew fatigue. 

The measure used for cost was total accident damage as recorded in the FRA accident database 

(field ACCDMG). The measure representing crew fatigue was the combined effectiveness score 

(the harmonic mean of crew members’ effectiveness scores) computed by FAST at the time of 

the accident, based on crew work schedules and the AutoSleep estimates of crew sleep patterns. 

Initial inspection of the HFs cost data indicated that higher average HF-related accident costs 

tend to be found at somewhat lower crew effectiveness scores than is true for NHF-related 

accidents, particularly below 75. Moreover, lower average HF-related accident costs, 

particularly in comparison with average costs for NHF-related accidents, tend to be found at 

scores above 85. This suggested that reduced effectiveness results in relatively more expensive 

accidents but the exact form of that relationship was unclear from the raw data. 

3.2 Grouping of Accidents by Effectiveness Score Intervals 

One possible form of a relationship between the damage cost of a railway accident and the 

estimated fatigue of the crew members involved is for the accident cost data to behave 

differently in different ranges of effectiveness score values. For example, it is plausible to 

expect HFs-related accidents to be generally less costly when the crew effectiveness score is 

above 90, which value is typical of an individual working a 40-hour week who gets 8 h of quality 

sleep per night (see Hursh et al., 2006, 2008). The salient questions are whether effectiveness 

score intervals may be defined that collect accidents into distinct and distinguishable subsets on 

the basis of their cost, and how such intervals can be determined. Preliminary analysis indicated 

that HF-related accident costs may be behaving somewhat differently in the regions below 75, 

between 75 and 90, and above 90. To investigate this pattern further, the average cost of HFrelated accidents associated with crew effectiveness scores at or below a given value and the 

average for accidents with scores above that value was computed. Figure 1 plots the differences 

between these averages for effectiveness scores of 65 and higher (above which value the average 

cost at or below is always greater than the average above). The difference increases with 

effectiveness score to a local maximum of nearly $180,000 at a score of about 77, then falls 

gradually to a local minimum just under $140,000 at a score of about 91, and begins to rise again 

to a maximum of $228,413 at a score of 100. 
9

y = 30.347x3- 7667.8x2 + 641566x - 2E+07

R2 = 0.7102

$0

$50,000

$100,000

$150,000

$200,000

$250,000

60 65 70 75 80 85 90 95 100 105

Difference in average cost (above - below)

Crew effectiveness score

Difference in average damage cost by crew effectiveness scores at time of incident

Human factors incidents (crew effectiveness > 65)

HF Difference in avg damage cost above & below Poly. (HF Difference in avg damage cost above & below)

Figure 1. Difference in Mean Accident Cost between HFs-Related Accidents at or below a 

Given Crew Effectiveness Score and Those above the Same Score with Cubic Polynomial 

Fit 

As the value of the effectiveness score ―cut point‖ rises, accidents migrate from the right-hand 

side (―above‖) to the left (―at or below‖). This pattern suggests that below 77 and above 91, the 

accidents that are being shifted to the left are costly relative to those remaining on the right, 

increasing the average at or below and/or decreasing the average above; between these values, 

the accidents shifted from right to left are relatively close to the (lower) average above that 

value. 

The pattern of one local maximum and one local minimum is suggestive of a cubic polynomial, 

and in fact such a function fitted by least squares accounts for over 70 percent of the variation in 

2

accident costs in terms of the effectiveness score of the crew involved (R = 0.71). The fitted 

polynomial (superimposed blue line on the accident data in Figure 1) has a local maximum at a 

score of 77 and a local minimum at a score of 90. 

Taken together, the observations above strongly suggest that accident costs behave differently 

among three intervals: at or below 77, between 77 and 90, and above 90. These three intervals 

are used in all subsequent analyses. Note that the value of 77 is not to be taken as a discrete 

threshold for judging safe from unsafe schedules; it is merely a statistical method for segregating 

the more expensive accidents from less expensive accidents in this sample. 
10

3.3 Evaluation of Accident Frequency and Damage Cost by Effectiveness 

Scores 

The three intervals defined immediately above were used to subdivide the accident damage cost 

data for further investigation and define the horizontal axis in Figure 2 through Figure 5 below. 

Figure 2 shows the total accident damage costs for HF-related accidents in the given intervals, 

breaking out from this category a subcategory labeled ―Fatigue Type Cause Codes.‖ These 

codes were identified in the previous report as the 10 HF-related cause codes that were more 

often reported when crew effectiveness scores were at or below 70. In the lowest interval, these 

cause codes account for over half of all costs resulting from HF-related accidents, but only onesixth of the costs above an effectiveness score of 77. 

$24,937,742

$3,301,446 $4,287,684

$22,487,165

$16,955,505

$11,576,416

$47,424,907

$20,256,951

$15,864,100

$0

$5,000,000

$10,000,000

$15,000,000

$20,000,000

$25,000,000

$30,000,000

$35,000,000

$40,000,000

$45,000,000

$50,000,000

Less than or equal to 77 77 to 90 Greater than 90

Total damage cost of accidents

Effectiveness scores

Other Human Factors Type Cause Codes

Fatigue Type Cause Codes

Total Damage Cost, All Human Factors

High Fatigue Low Fatigue

Figure 2. Total Cost of HFs-Related Accidents in Three Disjoint Crew Effectiveness Score 

Intervals by Accident Type 
11

Figure 3 presents the number of accidents in each interval, and, together with Figure 2, suggests 

that these particular types of accidents are especially costly: The 13 percent of HF-related 

accidents with fatigue type cause codes at scores above 77 account for 21 percent of all HFrelated accident costs, whereas at 77 or below, the 26 percent of HF-related accidents that are 

attributable to these cause codes account for 53 percent of all HF-related accident costs. 

34

14 15

131

102

117

356

288

314

0

50

100

150

200

250

300

350

400

Less than or equal to 77 77 to 90 Greater than 90 Number of accidents

Effectiveness scores

Fatigue Type Cause Codes All Human Factors Non-Human Factors

Figure 3. Number of Accidents in Three Disjoint Crew Effectiveness Score Intervals 

Figure 4 (on the next page) dramatically highlights the situation: Although average NHF-related 

accident costs (light gray bars) are roughly equivalent among the intervals, HF-related accidents 

(blue checked bars) taken together show an increase in average accident damage cost of 

approximately 2.7 times between the highest effectiveness category (low fatigue) and the lowest 

effectiveness category (high fatigue). The average damage cost of accidents at or below 77 

bearing fatigue-type cause codes (solid blue bars) are more than 2.5 times the cost of those of 

fatigue-type accidents in the highest intervals (low fatigue) and cost five times the average cost 

of all HF-related accidents above a score of 90. 
12

$733,463

$235,818

$285,846

$362,022

$198,598

$135,591

$289,836

$316,311

$269,482

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

Less than or equal to 77 77 to 90 Greater than 90

Average damage cost of accidents 

Effectiveness scores

Fatigue Type Cause Codes

All Human Factors Accidents

All Non-Human Factors Accidents

High Fatigue Low Fatigue

Average damage cost for 

all accidents = $277,097 

Figure 4. Average Accident Damage Cost in Three Disjoint Crew Effectiveness Score 

Intervals by Accident Cause Classification 

3.4 Casualty Costs 

Figure 2 and Figure 4 are based on accident costs that were limited to the financial impact of 

property damage as reported by the railroads to the FRA. A railroad accident can also incur 

costs in terms of casualties. Human injuries and/or death were reported to the FRA in 82 of the 

accidents analyzed in this study, including 15 fatalities and 408 cases of nonfatal human injury. 

Including casualties in the total cost of an accident necessitated assigning a dollar cost to each 

instance of injury or death. Costs were assigned to each casualty on the basis of the MAIS, 

which runs from 1 (minor injury) through 6 (death) and associates each level with a cost as a 

fraction of the value of a statistical life (VSL),8 which is estimated as $6 million in accordance 

with current DOT practice (see U.S. Department of Transportation, 2008). 

Fatalities were set to an MAIS level of 6. The MAIS level for each nonfatal injury was 

estimated using the number of LWDs by the injured, reported in the FRA accident databases, 

using equation (1), rounded to the nearest whole number, with a minimum value of 1 and a 

maximum value of 5.9

 

8

 A description of MAIS levels with corresponding injuries and the associated VSL fraction are included as 

Appendix A, Table 2.

9

 See Appendix A for the derivation of the equation relating LWD to MAIS level.
13

MAIS level = 0.031 × (LWD) – 0.37. (1)

Finally, for each accident, the estimated costs for all casualties were summed and added to the 

accident damage cost, yielding an estimated total cost for the accident. We added these casualty 

costs to the damage costs shown in Figure 2 and obtained the total accident cost values shown in 

Figure 5. The casualty costs of accidents (dark blue bars) decreased with increases in 

effectiveness and reductions in fatigue. For accidents with average operator effectiveness at or 

below 77, casualty costs are more than triple the property damage costs. Total cost of accidents 

in that range was over $200 million compared with total cost of $46 million for accidents above 

an effectiveness score of 90.

$160,554,000

$29,301,000 $30,384,000

$47,424,907

$20,256,951 $15,864,100

$207,978,907

$49,557,951 $46,248,100

$0

$50,000,000

$100,000,000

$150,000,000

$200,000,000

$250,000,000

Less than or equal to 77 77 to 90 Greater than 90 Total cost of accidents

Effectiveness scores

Damage costs -HF

Casualty costs -HF

Total Costs, All Human Factors

High Fatigue Low Fatigue

Figure 5. Total Accident Cost ($) from Casualties (dark blue) and Property Damage (light 

blue) Associated with HFs-Related Accidents as a Function of Average Operator 

Effectiveness

As one might expect, then, average accident cost decreases with increasing effectiveness, shown 

in Figure 6. Average accident cost, including casualty costs, was approximately $1.6 million 

when average operator effectiveness was at or below 77, compared with about one-quarter of 

that value (approximately $400,000) when average effectiveness was above 90. The average 

cost of HF accidents between 77 and 90 was very nearly equal to the overall average cost of HF 

accidents, or approximately $485,000. 
14

$1,587,625

$485,862

$395,283

$1,225,603

$287,265 $259,692

$0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

$1,600,000

$1,800,000

Less than or equal to 77 77 to 90 Greater than 90 Average Accident Cost ($)

Human Factors Average Cost - Damage and Casualties

Human Factors Average Casualty Cost

Average cost of all 

accidents = $488,681

Figure 6. Average Total Accident Cost ($) from Casualties (dark blue) and Property 

Damage (light blue) Associated with HFs-Related Accidents as a Function of Average 

Operator Effectiveness*

*Overall mean accident cost is shown as the horizontal dashed line.

3.5 Relative Risk of Accidents and Cost

Figure 7 presents the results of applying the discussion of relative risk in Section 2.1.4 to HFrelated accident cost data in these intervals. Estimates of the relative risk of accident occurrence 

and of damage cost began with the work histories for 30 calendar days prior to an accident 

provided by the participating railroads for each crew member on duty aboard the train involved 

at the time of the accident. Processing these work histories with the FAST Batch software 

generated estimates of each crew member’s sleep patterns and an estimated effectiveness score 

for each half-hour time slice of each work shift, including an estimate of individual effectiveness 

at the time of the accident. The half-hour intervals were allocated to the effectiveness score 

intervals where the estimate fell.

Crew harmonic mean effectiveness scores at the time of the accident were computed from 

individual crew members’ estimated effectiveness, as described in Section 2.2.1 above, and the 

accidents were allocated among the three effectiveness score intervals by the resulting scores. 

Risk of an HF-related accident in each of the three effectiveness score intervals was estimated as 

the ratio of the fraction of such accidents with crew effectiveness scores in that interval divided 

by the fraction of half-hour intervals across all crew members with estimated effectiveness 

scores in the same interval. This is the risk value computed in the prior report (Hursh et al.,

2006, 2008).

The relative accident risk was then computed as the ratio of this value divided by the risk of an 

accident with a crew effectiveness score that was found in either of the other intervals. The 
15

relative economic risk was computed in the same fashion, except that each accident was 

weighted (multiplied) by its cost. In the subsequent graphs, we convert the fractional value to a 

percent; 100 percent is an unchanged relative risk, a value of 200 percent represents a doubling 

of relative risk, and a value of 70 percent represents a 30 percent reduction in relative risk.

Figure 7 shows the results of this effort. The risk of an HF-related accident is estimated to 

increase by 42 percent for crew effectiveness scores of 77 or below, relative to the risk when 

crew effectiveness scores are above 77. That is, the frequency of HF-related accidents is 

42 percent greater when the crew effectiveness scores are 77 or lower versus when they are 

higher. In contrast, relative accident risk is reduced by 30 percent when crew effectiveness 

scores are above 90, and virtually unchanged (+3 percent) in the intermediate range.

516%

49%

25%

142%

103%

70%

0

1

2

3

4

5

6

Less than or equal to 77 77 to 90 Greater than 90 Relative Risk

Crew Effectiveness Score

Economic Risk - Damage & Casualty Cost

Accident Risk

$

$ # $ #

#

1 = Unchanged relative risk 

-30%

-75%

-51%

Figure 7. Relative Accident Risk (blue bars) and Relative Economic (damage and casualty 

cost) Risk (red bars) Associated with HFs-Related Accidents*

*For relative risk values less than 100 percent, we also show the change in risk by subtracting 1 (i.e., risk reduction).

More drastically, the relative economic risk—relative accident risk multiplied by the 

corresponding average cost of an HF-related accident (damage cost and casualty cost 

combined)—is estimated to be more than five times higher (516 percent) when crew 

effectiveness scores are at or below 77 compared with when crew effectiveness is above 77. At 

the other end of the continuum, relative economic risk is reduced by a factor of 4 (–75 percent)

when crew effectiveness is above 90, relative to when crew effectiveness is below 90. In the 

middle of the effectiveness range, between 77 and 90, relative economic risk is reduced by 

51 percent.
16

3.6 Total Accident Cost Relative to Effectiveness Scores

The analysis that was conducted for Figure 1 was repeated with the costs of casualties included 

to see if these added costs altered the threshold for maximal difference in cost between fatigue 

associated and non-fatigue-associated accidents. Figure 8 is the same analysis as shown in 

Figure 1 but with casualty costs included.

y = 86.379x3- 21148x2+ 2E+06x - 4E+07

R2 = 0.7721

y = 30.347x3- 7667.8x2+ 641566x - 2E+07

R2 = 0.7102

$0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

60 65 70 75 80 85 90 95 100 105

Difference in average cost (above - below)

Crew effectiveness score

Difference in average damage cost and average total cost (damage + casualties)

by crew effectiveness scores at time of incident

Human factors incidents (crew effectiveness > 65)

HF difference in average total cost above & below HF Difference in avg damage cost above & below

Poly. (HF difference in average total cost above & below) Poly. (HF Difference in avg damage cost above & below)

Figure 8. Difference in Mean Accident Cost Including Casualty Cost between HFs-Related 

Accidents at or below a Given Crew Effectiveness Score and Those above the Same Score

with Cubic Polynomial Fit (blue line)

The upper line of the graph includes casualty costs and the lower data graph does not include

casualty costs (as in Figure 1). Now it is clear that the point of maximal difference in accident 

cost shifts closer to 70 and the point of minimal difference remains close to 90. Of course, the 

new graph also shows the increase in total cost difference, reaching a maximum of 

approximately $1.1 million for accidents near 70. We, therefore, repeated the main cost analysis 

with these boundaries since FRA is considering a level of 70 as a threshold for examining fatigue 

under proposed new hours of service regulations.
17

3.6.1 Accident Cost with Effectiveness Less than 70

The effectiveness categories used in the preceding figures were chosen to maximize the 

differentiation between costly and less costly accidents based on the analysis shown in Figure 1. 

The cutoff score chosen to differentiate high fatigue from lower fatigue was 77. However, for 

regulatory purposes, a score of 70 would represent a hazard that creates a sufficiently high risk 

that it should be mitigated, based on the fatigue model calibration study reported previously 

(Hursh et al., 2006, 2008). It is, therefore, important to understand the economic benefit of 

reducing such extreme cases of fatigue using appropriate fatigue mitigation methods. The prior 

analysis was repeated with a lowest category set with an upper bound of 70. Figure 9 shows the 

average cost of HFs accidents (property damage and casualties) when average operator 

effectiveness was at or below 70. The average of total cost of accidents at or below 70 is nearly 

identical to the average cost of accidents at or below 77. However, the average cost of accidents 

in the large category from 70 to 90 now includes some higher valued accidents and increases to 

approximately $770,000. Overall, the trend line indicates that the total cost of accidents 

decreases exponentially as effectiveness increases from below 70 to above 90.

$1,589,938

$771,686

$395,283

$1,266,853

$503,652

$259,692

y = 3E+06e-0.696x

R2 = 0.9995

$0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

$1,600,000

$1,800,000

Less than or equal to 70 70 to 90 Greater than 90 Average Accident Cost ($)

Human Factors Average Cost - Damage and Casualties

Human Factors Average Casualty Cost

Average cost of all 

accidents = $488,681

(N=95)

(N=138)

(N=117)

Figure 9. Average Total Accident Cost ($) from Casualties (dark blue) and Property 

Damage (light blue) Associated with HFs-Related Accidents as a Function of Average 

Operator Effectiveness*

*Overall mean accident cost is shown as the black horizontal dashed line. The number of accidents (N) in each category is 

indicated in each panel.

Dividing the effectiveness dimension into two categories, accidents at or below 70 and accidents 

above 70, indicates that accidents at or below 70 when fatigue is likely to be high are 

approximately 2.65 times more costly (damage plus casualties) than accidents above 70 when 

fatigue is not high, shown in Figure 10. Most of this difference can be attributed to the greater 

cost of casualties when fatigue is high (effectiveness is at or below 70). 
18

$1,266,853

$391,718

$323,085

$207,266

$1,589,938

$598,984

$0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

$1,600,000

$1,800,000

Less than or equal to 70 Greater than 70 Average Accident Cost ($)

Human Factors Average Cost - Property and Casualties

Human Factors Average Casualty Cost

Total Cost, All Human Factors

Average cost of all 

accidents = $488,661

Figure 10. Average Total Accident Cost ($) from Casualties (dark blue) and Property 

Damage (light blue) Associated with HF Accidents as a Function of Average Operator 

Effectiveness*

*Overall mean HF accident cost is shown as the black horizontal dashed line.

3.6.2 Statistical Test of Accident Cost Relative to Effectiveness of 70 or Below

It is reasonable to ask if the differences in average accident cost shown in Figure 10 are 

statistically significant. However, subjecting the average accident cost to standard parametric 

tests based on an underlying normal distribution is not justified, since the observed distribution 

of accident costs in distinctly nonnormal; a relatively small number of costly accidents 

disproportionately affects the mean.

Instead, we investigated whether the proportion of costly HF accidents when the crew 

effectiveness score was equal to or less than 70 was significantly different from the proportion 

when crew effectiveness was over 70. We defined high cost accidents as ones with a total value 

greater than $80,000, which is approximately twice the overall median cost of all HF accidents 

of $39,913. We classified all HF accidents by costliness and crew effectiveness into a 2x2 

contingency table, see Figure 11, finding 84 high-cost accidents among 255 accidents with crew 

effectiveness scores above 70 (33 percent) and 42 high-cost accidents among the 95 accidents 

with crew effectiveness scores equal to or below 70 (44 percent). We analyzed the relationship 

between costliness and crew effectiveness scores using Fisher’s exact test for association.

This test found that if there were no association between cost and crew effectiveness, the 

probability of seeing purely by chance at least this large a difference in the fraction of high-cost 

accidents was 0.015. In other words, the proportion of high-cost accidents for crew effectiveness 

scores above 70 was significantly lower than that for crew effectiveness scores equal to or below 

70 at the 98.5 percent level. In addition, just considering the proportion of high-cost accidents 

association with effectiveness less than or equal to 70, the probability was 0.035. Therefore, the 

relationship between low effectiveness (less than or equal to 70) and the disproportionate number 

of high cost accidents (greater than $80,000) was statistically significant (p < 0.04). These 

findings are summarized in Figure 11.
19 44%

33%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

70 or Less Greater than 70

Percent HF Accidents Total Cost > $80,000

Crew Effectiveness Score

High-Cost Accidents Relative to Effectiveness

42 of 95 total

84 of 255 total 

P = 0.015 (Fisher's exact test)

Figure 11. Proportion of HF Accidents with Total Cost Greater than $80,000 Relative to 

Crew Effectiveness Scores

3.6.3 Relative Risk and Relative Economic Risk for Effectiveness of 70 or Below

Recomputing relative risk values, Figure 12, with the lowest category starting at 70, indicates 

that accident risk is elevated 62 percent relative to being above 70, and relative risk of costs from 

damage and casualties is more than quadrupled when effectiveness is at or below 70 

(430 percent). Relative risk of accidents between 70 and 90 is virtually identical to the risk at 

any other level of effectiveness and relative economic risk is 17 percent below the risk at other 

levels.

70 or Less Greater than 70

Greater $80K 42 84 

Less or Equal $80K 53 171 

% Greater than $80K 44% 33%

P = 0.015 (Fisher’s exact test)

For 70 or less, Prob >= 42: 0.035
20

430%

83%

25%

162%

100%

70%

0

1

2

3

4

5

Less than or equal to 70 70 to 90 Greater than 90 Relative Risk

Crew Effectiveness Score

Economic Risk - Damage & Casualty Cost

Accident Risk

$ $ # $ # #

1 = Unchanged relative risk 

-17%

-75%

-30%

Figure 12. Relative Accident Risk (light gray) and Relative Economic (damage and 

casualty cost) Risk (dark gray) Associated with HFs
21

4. Conclusions

This report summarizes an economic analysis of 350 HF accidents and 958 NHF accidents 

reported by the five U.S. Class I freight railroads between 2003 and the first half of 2005. The 

cost of accidents in relation to model-estimated crew average effectiveness indicated that 

accident damage and casualty costs increased with reductions in predicted performance or 

increased fatigue. The pattern of results may be summarized as follows:

 The estimated relative economic risk (damage and casualty cost) of an HF-related accident 

is more than quadrupled when crew effectiveness scores are below 70. 

 The estimated relative economic risk (damage and casualty cost) of an HF-related accident 

is increased by a factor of five when crew effectiveness scores are at or below 77 and 

reduced by a factor of four when crew effectiveness scores are above 90.

 The estimated relative accident risk of an HF-related accident is increased by 62 percent

when crew effectiveness scores are at or below 70 and reduced by approximately 

30 percent when crew effectiveness scores are above 90.

 The average total accident cost (damage and casualties) when crew average effectiveness is 

equal to or less than 70 (highly fatigued) is approximately $1.6 million, which is more than 

triple the overall average cost of accidents. In comparison to accidents without fatigue 

(when effectiveness is greater than 90), the average cost when crew average effectiveness 

is equal to or less than 70 is quadrupled. The average total cost of accidents decreases 

exponentially as effectiveness increases from below 70 to above 90. 

 There was a statistically significant disproportionate number of high cost accidents (total 

value greater than $80,000) when crew effectiveness was equal to or less than 70.

 Taken as a whole, these results further validate the utility of using biomathematical fatigue 

models (here the SAFTE model and the FAST software) to estimate work related fatigue 

risk. Furthermore, the results calibrate the model to indicate that a score of 70 or below is 

associated with both an elevated relative risk and severity (cost) of accidents.
22

5. References

Arnedt, J. T., Wilde, G. J., Munt, P. W., and MacLean, A. W. (2001). How do prolonged 

wakefulness and alcohol compare in the decrements they produce on a simulated driving 

task? Accident Analysis and Prevention, 33(3), 337–344.

Armitage, P., and Berry, G. (1994). Statistical Methods in Medical Research, Third Edition. 

Oxford, UK: Blackwell Science Ltd.

Dawson, D., and Reid, K. (1997). Fatigue, alcohol and performance impairment.

Nature, 388, 235.

Federal Railroad Administration. (2003). The FRA Guide for Preparing Accident/Incident 

Reports. Retrieved data from http://safetydata.fra.dot.gov/officeofsafety/

Federal Railroad Administration. (2011). Measurement and Estimation of Sleep in Railroad 

Worker Employees, Research Results, RR11-02 

http://www.fra.dot.gov/rpd/downloads/RR_Measurement_and_estimation_of_Sleep_final

_1102.pdf

Hursh, S. R., Redmond, D. P., Johnson, M. L., Thorne, D. R., Belenky, G., Balkin, T. J., Storm, 

W. F., Miller, J. C., and Eddy, D. R. (2004). Fatigue models for applied research in 

warfighting. Aviation, Space, and Environmental Medicine, 75(Suppl. 3), A44–A53; 

discussion A54–A60.

Hursh, S. R., Raslear, T. G., Kaye, A. S., and Fanzone, J. F. (2006). Validation and calibration 

of a fatigue assessment tool for railroad work schedules, summary report (Report No. 

DOT/FRA/ORD-06/21). Washington, DC: U.S. Department of Transportation. 

http://www.fra.dot.gov/downloads/Research/ord0621.pdf

Hursh, S. R., Raslear, T. G., Kaye, A. S., and Fanzone, J. F. (2008). Validation and calibration 

of a fatigue assessment tool for railroad work schedules, final report (Report No. 

DOT/FRA/ORD-08/04). Washington, DC: U.S. Department of Transportation. 

http://www.fra.dot.gov/downloads/Research/ord0804.pdf

Reinach, S., and Gertler, J. (2001). An Examination of Railroad Yard Worker Safety (Report 

No. DOT/FRA/ORD-01/20). Washington, DC: U.S. Department of Transportation. 

http://www.fra.dot.gov/downloads/Research/ord0120.pdf

U.S. Department of Transportation. (5 Feb 2008). Memorandum: Treatment of the Economic 

Value of a Statistical Life in Departmental Analyses. Retrieved data from 

http://ostpxweb.dot.gov/policy/reports/080205.htm

Van Dongen, H. P. A. (2004). Comparison of mathematical model predictions to experimental 

data of fatigue and performance. Aviation, Space, and Environmental Medicine, 75, 

A15–A36.
23

Appendix A. Estimating the Cost of Casualties in Accidents Reported 

to the Federal Railroad Administration

Accidents that are required to be reported to the Federal Railroad Administration (FRA) include 

the cost of damage in dollars to infrastructure (track and permanent structures such as buildings 

or bridges) and equipment (railcars, locomotives, etc.), but do not provide a cost for casualties 

with the exception of fatalities. Fatalities have a defined cost of $6,000,000, often called the 

value of a statistical life (VSL). As a concrete example, consider a derailment that occurred on 

the Union Pacific Railroad on August 4, 2010. On the FRA Office of Safety Analysis Web Site 

(http://safetydata.fra.dot.gov/officeofsafety/) the cost of damage to infrastructure, number of 

deaths and injuries for this accident (UP20100810DV003) can be found in the Accident Detail 

Reports. The detail report indicates that there was $295,812 in equipment damage, $205,503 in 

track damage, 0 deaths and 3 injuries. The same accident can be queried in the Casualty Detail 

Reports, where the following detail about the three injuries is provided (Table 1):

Table 1. Example of injury data from the FRA Casualty Detail Reports

Example 

Casualty # Age Job Injury Days Absent

1 57 Brakeman/Flagman Multiple 

Bruises/contusions

2

2 36 Brakeman/Flagman Multiple 

Bruises/contusions

0

3 44 Engineer Multiple 

Bruises/contusions

0

Consequently, it is not possible to calculate the total cost of this accident or the vast majority of 

other accidents reported to FRA. 

Currently, economic impact analyses that are required to document the benefits associated with 

the enactment of new regulations estimate the cost of casualties by reference to the MAIS (U.S. 

Department of Transportation Memorandum, February 5, 2008), which is shown in Table 2. 

Table 3 shows examples and descriptions of injuries for each of the MAIS levels. However, 

almost every injury can have more than one MAIS level. For example, concussions could be 

MAIS level 2 through MAIS level 5. In most accident reports there is little information for 

assigning a particular MAIS level to an injury. The difference between a concussion at MAIS 

level 2 and 5 is $4,482,000. 
24

Table 2. The MAIS of the U.S. Department of Transportation

MAIS Level Injury Severity Fraction of VSL Dollar Value

1 Minor 0.0020 $12,000

2 Moderate 0.0155 $93,000

3 Serious 0.0575 $345,000

4 Severe 0.1875 $1,125,000

5 Critical 0.7625 $4,575,000

6 Fatal 1.0000 $6,000,000

Table 3. Examples and Descriptions of Injuries for MAIS Levels

MAIS Level Examples and Descriptions of Injuries

1 Superficial abrasion or laceration of skin, digit sprain, first-degree burn, 

head trauma with headache or dizziness (no other neurological signs).

An AIS 1 injury is simple, and may not require professional medical 

treatment. Recovery is usually rapid and complete.

2 Major abrasion or laceration of skin, cerebral concussion (unconscious 

less than 15 min), finger or toe crush/amputation, closed pelvic fracture 

with or without dislocation.

An AIS 2 injury almost always requires treatment but is not ordinarily 

life-threatening or permanently disabling.

3 Major nerve laceration; multiple rib fracture (without a flail chest); 

abdominal organ contusion; hand, foot, or arm crush/amputation.

An AIS 3 injury has the potential for major hospitalization and long-term 

disability but is not generally life-threatening.

4 Spleen ruptures, leg crushes, chest wall perforations, and cerebral 

concussions with other neurological signs (unconscious less than 24 h). 

An AIS 4 injury is often permanently disabling, but survival is probable.

5 Spinal cord injury, extensive/deep laceration of kidney or liver, extensive 

second- or third-degree burns, cerebral concussions with severe 

neurological signs.

An AIS 5 injury usually requires intensive medical care. Survival is 

uncertain.

6 One that will probably eventually lead to death, massive destruction of 

the cranium, skull, and brain.
25

The FRA Guide for Preparing Accident/Incident Reports (FRA, 2003) lists the injury and illness 

codes that are used in accident reports. This is shown in Table 4. Note that the codes are used in 

conjunction with body part location codes which are not in Table 4. The FRA Guide does not 

code severity of the injury. Table 4, however, shows the feasible range of MAIS levels that each 

injury might have, based on the examples and descriptions of injuries in Table 3. There are six 

injury codes (highlighted) that could reasonably have MAIS levels 1–5. These six codes 

epitomize the problem of assigning dollar values to injuries in the FRA accident reports. 

Table 4. Nature of Injury Codes and Feasible MAIS Levels

MAIS Level

Minor Moderate Serious Severe Critical Fatal

NATURE OF INJURY Code 1 2 3 4 5 6

Bruise or contusion 10 1

Crushing Injury 13 1 2 3 4

Sprain or strain 20 1 2

Cut/laceration or abrasion 30 1 2

Puncture wound (other than needle stick) 35 1 2

Needle stick 36 1 2 3 4

Electric shock or burn 40 1 2 3 4 5

Other burns 50 1 2 3 4 5

Dislocation 60 2

Fracture (broken bone) 70 2 3

Rupture/tear (tendon, cartilage) 71 2 3

Gunshot, knife wounds 72 2 3 4 5

Animal/snake/insect bite 74 1 2 3

Dental related 75 1 2

Amputation 80 2 3

Fatatilly injured 90 6

Foreign object in eye 91 1 2

Hernia 92 2

Concussion/closed head injury 93 1 2 3 4 5

Nervous shock (injury related) 94 1 2

Internal injury 95 3 4 5

Loss of eye 96 4

Reaction from one-time external 

 exposure to chemicals

97 1 2 3 4 5

Symptoms due to one-time exposure 

 to loud noise

98 1

Symptoms due to one-time 

 inhalation exposure to 

 airborne contaminants

9A 1 2

Medical removal (under OSHA requirements) 9B 1 2 3 4 5

All other injuries 99 1 2 3 4 5
26

An FRA report (Reinach and Gertler, 2001), An Examination of Railroad Yard Worker Safety, 

suggests a way to determine the average severity of various injuries. Table 16 of that report 

shows the number of LWDs (or days absent) and the number of injuries for the same injury 

codes listed in Table 4. Table 5 shows the mean number of LWDs per injury and the mean 

MAIS for each injury code based on Table 4. The same accident codes that were highlighted in 

Table 4 are highlighted in Table 5.

Table 5. LWDs, Number of Injuries, and Mean MAIS for FRA Injury Codes

Injury Code Injuries LDWs

LWDs per

Injury

Mean 

MAIS

10 655 29533 45.09 1

13 2.5

20 2643 173355 65.59 1.5

30 296 11170 37.74 1.5

35 35 989 28.26 1.5

36 2.5

40 19 621 32.68 3

50 28 455 16.25 3

60 60 6336 105.60 2

70 396 26477 66.86 2.5

71 2.5

72 3.5

74 2

75 2 48 24.00 1.5

80 46 6450 140.22 2.5

90 6

91 59 165 2.80 1.5

92 56 3635 64.91 2

93 22 1472 66.91 3.5

94 1 167 167.00 1.5

95 7 905 129.29 4

96 4

97 19 271 14.26 3

98 7 267 38.14 1

9A 1.5

9B 25 1900 76.00 3

99 158 11166 70.67 3
27

Table 6 shows average accident cost as a function of MAIS level, based on Table 5. MAIS 

levels 3.5 and 5 do not have any LWD data, and LWD for MAIS level 6 would be infinity. It is 

also apparent in Table 6 that the mean LWD for MAIS 3 is an outlier. This is more easily seen 

in Figure 12, which plots MAIS as a function of mean LWDs. The red square is the MAIS level 

3 datum. The remainder of the data are well-fit by a straight line (correlation coefficient = 0.965, 

p < 0.01).

Table 6. Mean LWD and MAIS Level

MAIS LWD

1 41.6157

1.5 54.2301

2 85.2554

2.5 103.539

3 46.128

3.5 -

4 129.286

5 -

6 -

Figure 13. MAIS Level as a Function of LWDs
28

The best linear fit to the data is defined in equation (1):

MAIS = 0.031 LWD – 0.373. (1)

With the equation (1), MAIS level can be estimated from LWD. Mathematically relating the 

cost of injuries to MAIS level from Table 2 is the next logical step. The relationship between 

MAIS and cost, however, is not mathematically tractable. The relationship is approximately a 

power function (r = 0.993), but the best-fitting line underestimates the cost of MAIS 5 by 

34.4 percent. At MAIS 5, the true cost is $4,575,000, but the cost predicted by a power function 

is only $3,000,000. 

An alternative is to construct a look-up table based on the true values and values interpolated for 

intermediate MAIS levels. This is presented in Table 7. For the economic analysis of accident 

costs related to estimate effectiveness level and fatigue, equation (1) was used in conjunction 

with the VSL levels in Table 1, rounding off levels to the nearest whole number. On the basis of

Table 7, this approach may underestimate injury costs in some categories but is efficient when 

applied across this large data set.

Table 7. MAIS Level and LWDs

Expanded

MAIS

Fraction

of VSL Dollars LWDs

1 0.002 $12,000 46.82482

1.25 0.005375 $32,250 54.31657

1.5 0.00875 $52,500 61.80832

1.75 0.012125 $72,750 69.30007

2 0.0155 $93,000 76.79182

2.25 0.026 $156,000 84.28357

2.5 0.0365 $219,000 91.77532

2.75 0.047 $282,000 99.26707

3 0.0575 $345,000 106.7588

3.25 0.09 $540,000 114.2506

3.5 0.1225 $735,000 121.7423

3.75 0.155 $930,000 129.2341

4 0.1875 $1,125,000 136.7258

4.25 0.33125 $1,987,500 144.2176

4.5 0.475 $2,850,000 151.7093

4.75 0.61875 $3,712,500 159.2011

5 0.7625 $4,575,000 166.6928

5.25 0.821875 $4,931,250 174.1846

5.5 0.88125 $5,287,500 181.6763

5.75 0.940625 $5,643,750 189.1681

6 1 $6,000,000 -
29

Abbreviations and Acronyms

FAST Fatigue Avoidance Scheduling Tool

FRA Federal Railroad Administration

HF human factor

LWD lost workday(s)

MAIS Maximum Abbreviated Injury Scale

mph mile(s) per hour

NHF nonhuman factor

SAFTE Sleep, Activity, Fatigue, and Task Effectiveness model

VSL value of a statistical life