Office of Research and Development 

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Validation and Calibration of a Fatigue Assessment Tool 

for Railroad Work Schedules, Summary Report 

U.S. Department of 

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Administration

DOT/FRA/ORD-06/21 Summary Report 

October 2006 

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4. TITLE AND SUBTITLE

Validation and Calibration of a Fatigue Assessment Tool for Railroad Work Schedules, 

Summary Report 

6. AUTHOR(S) Steven R. Hursh, Ph.D., 1 Thomas G. Raslear, Ph.D., 2 A. Scott Kaye,3

and Joseph F. Fanzone, Jr. 

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1

Institutes for Behavior Resources 2Office of Research & Development and 3Office of Safety 

2104 Maryland Avenue Federal Railroad Administration 

Baltimore, MD 21218 Washington, DC 20590 

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COTR: Thomas Raslear, Federal Railroad Administration 

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13. ABSTRACT (Maximum 200 words) 

This report summarizes the results of a project to demonstrate a method to validate and calibrate a fatigue model. The 

project examined 30-day work histories of locomotive crews prior to 400 human factors accidents and 1000 nonhuman 

factors accidents. A biomathematical fatigue model estimated crew effectiveness (the inverse of fatigue) based 

entirely on work schedule information and opportunities to obtain sleep. A reliable linear relationship existed between 

crew effectiveness and the risk of a human factors accident (r = - 0.93); no such relationship was found for nonhuman 

factors accidents. This result satisfied the criteria for model validation. A reliable time of day variation occurred in 

human factors accidents (r = 0.71) but not in nonhuman factors accidents. The risk of human factors accidents was 

elevated at any effectiveness score below 90 and increased progressively with reduced effectiveness. At an 

effectiveness score ≤ 50, human factors accidents were 65 percent more likely than chance. Human factors accident 

risk increases reliably when effectiveness goes below 70, a value that is the rough equivalent of a 0.08 blood alcohol 

level or being awake for 21 hour following an 8-hour sleep period the previous night. Below an effectiveness score of 

70, accident cause codes indicated the kinds of operator errors consistent with fatigue, confirming that the relationship 

between accident risk and effectiveness was meaningful.

15. NUMBER OF PAGES

40 

14. SUBJECT TERMS 

Fatigue, biomathematical fatigue model, work schedules, accidents, train operators, 

performance, effectiveness, risk, safety, freight rail operations, sleep, circadian rhythm, 

model validation. 

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i
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 34

Inches

Centimeters 01 3 26 1 4 5 7 1 1098 1 12

5

3

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

ii
Contents 

Illustrations ..................................................................................................................................... v 

Tables............................................................................................................................................. vi 

Acknowledgements....................................................................................................................... vii 

Preface............................................................................................................................................ ix 

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

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

1.1 Background ................................................................................................................. 3 

1.2 Objectives.................................................................................................................... 3 

1.3 Overall Approach ........................................................................................................ 4 

2. Method of Analysis ..................................................................................................... 5 

2.1 General Method........................................................................................................... 5 

2.2 Validation Method....................................................................................................... 5 

2.3 Sample Size Determination ......................................................................................... 7 

2.4 Selection of Accidents................................................................................................. 7 

2.5 Accident Samples for Each Participating Railroad ..................................................... 8 

2.6 Data Requested............................................................................................................ 8

2.7 The SAFTE Model and the Work Schedule Fatigue Assessment Tool ...................... 8 

3. Results of Analysis.................................................................................................... 11 

3.1 Descriptive Analysis.................................................................................................. 11 

3.2 Validation of a Fatigue Model................................................................................... 13 

3.3 Calibration of a Fatigue Model ................................................................................. 17 

3.4 Other Evidence of Fatigue......................................................................................... 19 

3.5 Interpretation of Effectiveness Scores....................................................................... 21 

3.6 Interpretations and Limitations ................................................................................. 23 

4. Summary and Conclusions........................................................................................ 25 

4.1 Summary ................................................................................................................... 25 

4.2 Conclusion................................................................................................................. 26 

5. References ................................................................................................................. 27 

Abbreviations/Acronyms .............................................................................................................. 29 

iii 
iv 
Illustrations 

Figure 1. Durations of Reported Job-Related Non-Sleep Intervals ............................................. 11 

Figure 2. Frequency of Work Hours by Time of Day, Hours by Consistent Night Workers 

Shown as the Dark Blue Bars at the Bottom and All Others Stacked Above.............. 12 

Figure 3. Accident Risk by Time of Day. Data Have Been Double-Plotted to Show the 

Repeating Circadian Pattern......................................................................................... 13 

Figure 4. Work Interval Effectiveness Distribution for Five Railroads....................................... 14 

Figure 5. Proportion of Time or Accidents as a Function of Predicted Effectiveness Categories. 

Human Factors and Nonhuman Factors Accidents are Indicated as Blue Triangles and 

Green Squares, Respectively........................................................................................ 15 

Figure 6. Human Factors Accident Risk at Each Level of Effectiveness Aggregated from Five 

Railroads ...................................................................................................................... 16 

Figure 7. Nonhuman Factors Accident Risk at Each Level of Effectiveness Aggregated from 

Five Railroads .............................................................................................................. 17 

Figure 8. Human Factors Accident Risk by Criterion Levels of Effectiveness Aggregated for 

Five Railroads .............................................................................................................. 18 

v 
Tables 

Table 1. Human Factors Accident Cumulative Risk at Various Criterion Levels of 

Effectiveness ................................................................................................................. 19 

Table 2. Human Factors Accident Cause Codes Related to Effectiveness ≤ 70.......................... 20 

Table 3. The Relationship Among Various Effectiveness Scores and Other Meaningful Metrics: 

Likelihood of a Lapse, Continuous Hours Awake, and BAC ....................................... 22 

Table 4. The Effects of Various Daily Sleep Patterns on Effectiveness Estimates at 1600 hr and 

0400 hr. Three Schedules: 1, 2, 7 Days at the Specified Sleep Level......................... 22 

vi 
Acknowledgements 

The authors of this report wish to thank the following individuals for their invaluable 

contributions to the analysis, results, and documentation of the procedures: 

• The Federal Railroad Administration for providing funding for this important study. 

• Dr. Timothy Elsmore for the development of the batch processing software that made it 

possible to analyze the enormous amount of work schedule data used in this study. 

• Jeff Moller and Peter French of the Association of American Railroads for encouraging 

this study, interfacing with industry, and assisting in the identification of a suitable 

sample of reportable accidents that formed the basis for the study. 

• The managers and points of contacts of the five participating railroads for cooperation in 

conducting the study and contribution of time and effort to assemble the data needed to 

conduct the study. 

• The Brotherhood of Locomotive Engineers and Trainmen and the United Transportation 

Union labor organizations for their support of the study objectives. 

• Foster-Miller, Inc., the prime contractor, and Judith Gertler, the project manager, for the 

opportunity and generous support to conduct this study. 

vii 
viii 
Preface 

This report is a summary of a major study sponsored by the Federal Railroad Administration 

(FRA) to demonstrate a method to validate and calibrate fatigue models for use in predicting and 

managing fatigue in railroad workers. The summary describes the methods and the major 

findings aggregated from data provided by five freight rail carriers. The researchers are 

preparing a more comprehensive report for FRA that will contain additional details of method 

and results. Furthermore, the researchers will make available the database used for the study for 

future research and analysis, with the contents coded to protect the privacy of the participants. 

ix 
x 
Executive Summary 

Biomathematical fatigue models allow the objective assessment of fatigue so that employees and 

employers can schedule work and rest to minimize the degradation of operator performance by 

fatigue. To be useful, a fatigue model must be validated. Validation means that the model must 

be a predictor of fatigue-related performance errors. Moreover, a model should be calibrated. 

Calibration means that the predictions from a model can be related to the level of risk of failures 

of human performance. One method of validating and calibrating a biomathematical fatigue 

model is to demonstrate that the model can predict an increased likelihood of human factors 

accidents relative to nonhuman factors accidents under conditions of fatigue. A valid fatigue 

model should predict higher levels of fatigue (based on opportunities to sleep and an accident’s 

time of day) when a greater likelihood of a human factors accident exists. By comparison, 

fatigue levels should have a weaker or no relationship to the likelihood of nonhuman factors 

accidents. The Federal Railroad Administration (FRA) Office of Research and Development and 

the Office of Safety have partnered with the railroad industry to demonstrate a method to 

validate and calibrate fatigue models. This study collected 30-day work histories of locomotive 

crews prior to 400 human factors and 1000 nonhuman factors accidents to demonstrate this 

validation method. A total of over 1 million 30-minute work intervals before the accidents, 

covering over 57,000 work starts, were evaluated for effectiveness (the inverse of fatigue) 

predicted by the Sleep, Activity, Fatigue, and Task Effectiveness (SAFTE) model using the 

Fatigue Avoidance Scheduling Tool (FAST). This served as the baseline of exposure to various 

levels of effectiveness. In addition, the effectiveness at the time of each accident was calculated. 

The analysis used two criteria to evaluate if the SAFTE biomathematical fatigue model was a 

valid predictor of fatigue-related accidents: 

• The proportion of human factors accidents that occur at low levels of effectiveness 

should be greater than the proportion of time working at those levels of effectiveness 

(exposure level). If the proportion of human factors accidents is reliably greater than the 

exposure level, and there is a statistically reliable relationship between decreases in 

effectiveness and an increase in human factors accident risk, then low levels of 

effectiveness (increased fatigue) predict increased human factors accident risk. 

• By comparison, there should not be a statistically reliable relationship between 

effectiveness and nonhuman factors accident risk, and at low levels of effectiveness 

(increased fatigue), the risk of human factors accidents should be greater than the risk of 

nonhuman factors accidents. If the human factors accident risk is reliably greater than 

the nonhuman factors accident risk, then low effectiveness is associated with the kinds of 

accidents that would be expected to be related to fatigue. 

The statistical reliability of relationships was based on finding significant correlation coefficients 

(r). The chi square (χ

2

) statistic was used to compare the distributions of human factors and 

nonhuman factors accidents to demonstrate significantly different distributions of risk. In each 

case, the researchers rejected the null hypothesis (the hypothesis that there is no correlation (i.e., 

r = 0) or that there is no difference in the distributions of human factors and nonhuman factors 

accidents) when the chance probability of a finding was less than 5% (p < 0.05). 

1 
The results of the study indicated that the biomathematical fatigue model met both criteria for 

validation and the results were statistically reliable: 

• The biomathematical fatigue model estimates of effectiveness were significantly 

correlated with human factors accident risk (r = -0.93, p < 0.01, Figure 6). 

• The biomathematical fatigue model distinguished between human factors and nonhuman 

factors accidents. Nonhuman factors accident risk was not correlated with estimated 

effectiveness (r = -0.14, p > 0.05, Figure 7), and at low estimated effectiveness the 

relative risk of human factors and nonhuman factors accidents were significantly 

different (χ

2 = 7.201, p < 0.01). 

This study found that an elevated risk of human factors accidents occurs at any effectiveness 

score below 90, and accident relative risk increased as effectiveness decreased. A reliable 

increase in human factors accident risk occurred when effectiveness scores were below 70 but 

nonhuman factors accident risk was not consistently elevated. Based on other research, 

effectiveness scores below 70 are the rough equivalent of a 0.08 blood alcohol level or being 

awake for 21 hours (hr) following an 8-hr sleep period the previous night. 

An analysis of the cause codes associated with accidents that occurred at or below an 

effectiveness score of 70 showed an overrepresentation of the type of human factors accidents 

that might be expected of a fatigued crew (e.g., failure to comply with a stop signal). This 

confirms that the relationship between reduced effectiveness and elevated human factors 

accident risk is meaningful and not a mere correlation. 

The study also demonstrated that human factors accidents follow a circadian pattern that is 

significantly correlated with the circadian rhythm of a fatigue model (r = 0.71, p < 0.05). The 

same model rhythm is not correlated with nonhuman factors accidents. The maximum human 

factors accident risk due to time of day alone was increased by less than 20 percent, while the 

maximum accident risk due to reduced effectiveness (fatigue) was increased by 65 percent, 

reflecting the combined effects of time of day and sleep opportunities. 

This study was designed to demonstrate a method to test the validity of fatigue models. The data 

used accidents and the 30-day work histories that preceded them were not a random sample of all 

workers in freight rail operation. Hence, the levels of effectiveness calculated by the SAFTE 

model should not be interpreted as representative of the freight railroad work force in general. 

The study was not designed to determine the extent of fatigue in the freight rail industry. 

Furthermore, given the well-known variations in individual sleep requirements and absence of 

specific information on individual sleep habits, health, and circumstances, it was not the intent of 

this study to validate fatigue models based entirely on work schedule data as tools for 

determining the fatigue of particular individuals. 

This study provides the first evidence that a biomathematical fatigue model can relate work 

schedules to an elevated risk of railroad accidents. This provides a strong scientific basis for 

evaluating work schedules with valid mathematical models to reduce worker fatigue. A 

mathematical model for detecting elevated fatigue risk could be part of a nonprescriptive, 

performance-based fatigue management plan that would supplement current regulations. 

Although fatigue models do not identify all sources of fatigue and will require a cooperative 

partnership among management, labor, and government regulators, they are an important tool in 

the identification of one of the causes of fatigue in the railroad industry. 

2 
1. Introduction 

FRA has sponsored a research program to demonstrate a method to validate and calibrate fatigue 

models for use in predicting and managing fatigue in railroad workers. Fatigue models allow the 

objective assessment and forecasting of fatigue so that employees and employers can schedule 

work and rest to minimize degradation of operator performance by fatigue. To be useful, a 

fatigue model must be validated. Validation means that a fatigue model predicts changes in job 

performance and/or job-related errors, such as incidents and accidents, caused by fatigue. A 

useful fatigue model must be calibrated. Calibration means that the predictions from the model 

can be related to the risks of meaningful failures of human performance. This report describes 

the results of the research program to demonstrate a method to validate and calibrate fatigue 

models. 

1.1 Background 

Human factors accidents have increased as a proportion of FRA reportable accidents over the 

past 5 years. No question exists that fatigue may be a factor in many human factors accidents. 

Without a detailed history of work and rest before an accident, however, it is difficult to 

determine the role of fatigue in that accident. The analysis of work/rest histories to rule out 

fatigue can be accomplished with a number of software models associated with fatigue, but until 

now none of these models has been validated in commercial transportation operations. In the 

interest of developing validated fatigue models, the Office of Research and Development and the 

Office of Safety sponsored a study of work histories of locomotive crews associated with 

accidents to provide the necessary data to validate fatigue models. This report describes the 

details of the data collection, the methods used to analyze the data for signs of fatigue, and the 

results of the analysis. 

1.2 Objectives 

One method of validating and calibrating a fatigue model is to demonstrate that the model can 

predict an increased likelihood of human factors accidents relative to nonhuman factors accidents 

under conditions of fatigue. A valid fatigue model should predict higher levels of fatigue (based 

on opportunities to sleep and the time of day of an accident) when a greater likelihood of a 

human factors accident exists. By comparison, fatigue levels should have a weaker or no 

relationship to the likelihood of nonhuman factors accidents. The present study determined 

cognitive effectiveness (a predictor of speed of reactions and vigilance in laboratory tests that is 

inversely related to fatigue) from 30-day work histories of locomotive crews prior to 400 human 

factors and 1000 nonhuman factors accidents. The objective was to determine if a statistically 

reliable relationship exists between reductions in effectiveness and the risk of human factors 

accidents. Further, the study determined if the relationship of effectiveness to human factors 

accidents was larger and more consistent than that of nonhuman factors accidents, which would 

be expected to be much less sensitive to the effects of fatigue. The second objective was to 

determine the level of effectiveness at which an elevated likelihood of human factor accidents 

occurs relative to chance. That result served to calibrate the fatigue model for aggregate work 

schedule analyses of fatigue. The goal was to determine the nature of the relationship between 

effectiveness scores and statistically elevated accident risk. Given the well-known variations in 

individual sleep requirements and absence of specific information on individual sleep habits, 

3
health, and circumstances, it was not the intent of this study to validate fatigue models based 

entirely on work schedule data as tools for determining the fatigue of particular individuals. 

 The biomathematical fatigue model used for these studies, the SAFTE model, was originally 

developed for the U.S. Army and Air Force to predict potential fatigue from work schedules 

(Hursh, Redmond, Johnson, Thorne, Belenky, Balkin, Storm, Miller, and Eddy, 2004). The 

model has been incorporated into a fatigue assessment tool (Hursh, Balkin, Miller, and Eddy, 

2004) called FAST. FAST uses work schedule information to estimate the amount of sleep and 

cognitive effectiveness. Cognitive effectiveness is a metric that tracks speed of performance on 

a simple reaction time test and is strongly related to overall response speed, vigilance, and the 

probability of lapses (Hursh, et al., 2004; Van Dongen, 2004). Cognitive effectiveness can be 

interpreted as the inverse of fatigue. 

1.3 Overall Approach 

FRA and the Association of American Railroads (AAR) determined which human factors 

accident cause codes would be appropriate to use. This was important since work histories for 

locomotive crews would be analyzed to determine effectiveness, and, therefore, only cause codes 

that related to locomotive crew errors would be relevant. FRA and AAR also determined which 

nonhuman factors accident cause codes would be appropriate to use as a control group. Finally, 

the kinds of track and equipment most likely to be associated with irregularly scheduled line haul 

(between cities or terminals) freight service was determined. For each accident, the researchers 

requested from that railroad the 30-day work history of the train crew just before the accident. 

The work histories were used to estimate the effectiveness of the crew at the time of the event 

and to determine the overall percentage of time typically spent at work at various levels of 

effectiveness. This information was used to determine the ability of the fatigue model to predict 

increases in human factors accident risk relative to chance. It was also used to determine if the 

relationship between effectiveness and accident risk was stronger for human factors than 

nonhuman factors accidents. Little or no relationship should exist between effectiveness and 

nonhuman factors accident risk. The reduction in effectiveness associated with statistically 

reliable cumulative increases in accident risk was determined in order to calibrate the 

effectiveness scores. Additionally, human factors accidents that were overrepresented at reduced 

levels of effectiveness were examined to determine if these accidents were consistent with the 

expected effects of crew fatigue (e.g., lapses increase with fatigue and are consistent with 

accidents in which signals are passed at danger). Descriptive information regarding work 

patterns and accident patterns that were independent of the model predictions were also 

developed. 

4
2. Method of Analysis 

2.1 General Method 

The general method of the study was to use a biomathematical fatigue model (SAFTE) to 

estimate the cognitive effectiveness of locomotive crews at the time of accidents to determine if 

low levels of effectiveness are associated with higher than expected rates of accidents. The 

model computes cognitive effectiveness (the inverse of fatigue) from opportunities to sleep and 

the time of day during the 30 days before the accident and at the time of the accident. To control 

for extraneous factors, the analysis compared human factors and nonhuman factors accidents 

using the same methods. The following sections describe the validation method, the sample 

determination, the data requested from the railroads that describe the accidents, and the 30-day 

work histories of the associated train crews. 

2.2 Validation Method 

Thirty-day work histories were collected for train crews who were involved in FRA reportable 

accidents. FAST processed these histories with the SAFTE model to determine the crew’s 

cognitive effectiveness at the time of the accidents. The histories were also used to estimate the 

proportion of time spent working at various levels of effectiveness during the preceding 30 days. 

This is the exposure of the locomotive crews to fatigue. If fatigue is not associated with 

accidents, then the proportion of accidents at each effectiveness level should be similar to fatigue 

exposure. Fatigue exposure provides an expected proportion of accidents at each effectiveness 

level. An easy way to see if the obtained proportion of accidents matches the expected 

proportion is to divide the obtained proportion by the expected proportion. If accidents are 

independent of fatigue, the ratio should be close to one. This ratio is the accident risk. 

Statistically reliable deviations in the ratio indicate increased or decreased risk, depending on 

whether the ratio is greater or less than one. This analysis yields a function that relates accident 

risk to levels of effectiveness and estimates fatigue-associated risk. 

It was expected that if fatigue is a factor in some accidents, then accident risk should be higher at 

lower levels of effectiveness (increased levels of fatigue), and the risk should be greater for 

human factors accidents than for nonhuman factors accidents. Testing these hypotheses takes 

several steps and makes several assumptions. 

2.2.1 Assumptions 

First, it is assumed that loss of alertness, confusion, or slowed reaction time causes some railroad 

accidents. These are all performance changes that are associated with fatigue. Since these 

accidents are the result of human error, it was expected that fatigue-associated accident risk 

would be greater for human factors than for nonhuman factors accidents. 

Second, it is assumed that when the model predicts a loss in cognitive effectiveness, an increase 

occurs in the probability of a human error that could result in a railroad accident. For example, 

when the model predicts reduced effectiveness, the train crewmen are more likely to miss a 

signal or run through a switch. This connection is not deterministic; reduced effectiveness 

increases the probability of an error but does not determine that an error will occur. 

Furthermore, a similar error could occur in the absence of unusual fatigue, such as caused by a 

distraction, so that not all occurrences of a particular sort of error can be attributable to fatigue. 

5
Hence, a fatigue model can predict an increase in fatigue-associated risk, not the specific 

occurrence of an accident. 

Third, the SAFTE model incorporated in FAST makes a number of assumptions about the 

amount of sleep that can be achieved under specific work schedules, the amount of sleep the 

average person requires, and the susceptibility of the average person to time of day variations in 

alertness. Wide variations exist in individual sensitivity to the factors that cause fatigue, so, 

again, fatigue models can only predict an increased risk of fatigue, not a specific individual 

person’s level of fatigue or performance. 

2.2.2 Validation Criteria 

If the fatigue model is valid, it will show that human factors related accidents are more likely to 

occur at decreased levels of crew effectiveness, while the likelihood of nonhuman factors-related 

accidents are the same regardless of crew effectiveness. 

The fatigue model estimates effectiveness during each work shift of each worker in the database 

up to the time of an accident and records the mean effectiveness level across each 30-minute 

work interval. From all work histories combined, the approximate proportion of work time spent 

by workers at given effectiveness levels can be computed. This is the exposure to fatigue and, as 

noted above, determines the expected proportion of accidents at any given effectiveness level. 

The model also estimates the crew effectiveness at the time of the accident. From these data the 

proportion of accidents occurring at any given crew effectiveness level can be computed. 

Combining the two proportions defines the risk ratio: 

( ) ( )

( ) atTimeWork Effectiven Leveless ( TimeWorkTotal )

atAccidents Effectiven Leveless Total ofNumber Accidents Ratio Risk =

Accident risk, as used in this report, is defined entirely in terms of the risk ratio specified above. 

If operator effectiveness is unrelated to accident occurrence, then the proportion of accidents 

occurring at any given level of effectiveness should be approximately equal to the proportion of 

work time spent at that effectiveness level (i.e., the accident risk should be close to 1). If lower 

effectiveness is related to a greater likelihood of an accident, then accident risk should increase 

with decreasing effectiveness (i.e., be greater than 1 at lower effectiveness levels and less than 1 

at higher effectiveness levels). 

Therefore, model-derived estimates of effectiveness that show the following would constitute 

validation that the model provides a measure of fatigue-associated accident risk: 

1. A statistically reliable relationship between decreases in effectiveness and an increase in 

human factors accident risk 

2. The absence of a statistically reliable relationship between effectiveness and nonhuman 

factors accident risk, and a greater risk of human factors versus nonhuman factors 

accidents at low levels of effectiveness 

The statistical reliability of relationships was based on finding significant correlation coefficients 

(r). The chi square (χ

2

) statistic was used to compare the distributions of human factors and 

nonhuman factors accidents to demonstrate significantly different distributions of risk. In each 

case, we rejected the null hypothesis (the hypothesis that there is no correlation, i.e., r = 0, or that 

there is no difference in the distributions of human factors and nonhuman factors accidents) 

when the chance probability of a finding was less than 5 percent (p < 0.05). 

6
2.2.3 

2.2.4 

Calibration of the Fatigue Model 

Up to this point, the analysis method has referred to low levels of effectiveness and levels of 

fatigue without specifying what those levels might be. This is because it is not known in 

advance how much fatigue or reductions in cognitive effectiveness are sufficient to cause a 

detectable increase in accidents or a detectable difference between human and nonhuman factors 

accidents. The level of effectiveness for human factor accidents that yields a reliable increase in 

accidents relative to chance and the effectiveness level for human factor accidents that is reliably 

different from the level for nonhuman factors accidents were used to calibrate the model. 

Variables Not Considered 

Given the nature of this analysis of historical work times associated with reportable accidents, 

the biomathematical fatigue model was not able to consider some variables that might ordinarily 

be part of an analysis. The database included work start and stop times, typical call times for 

each location, and estimated average commute times for each location. The analysis could not 

consider each worker’s usual sleep habits or actual sleep times, quality of the sleep environment, 

or schedule predictability. The analysis did not consider the use of fatigue countermeasures or 

additional naps. The analysis could not consider unusual events that might have interfered with 

usual sleep opportunities. The analysis could not consider schedule delays or misinformation, 

medical conditions and sleep disorders, medications and/or drug use, observations of operator 

performance and appearance, concurrent stress, family issues, work demands, or crew resource 

management issues, such as communication problems. Many of these factors could cause 

additional fatigue or performance disruptions. Some of these factors could reduce fatigue, such 

as the use of napping strategies. The analysis had to assume that each individual obtained as 

much sleep as was afforded by the schedule, call times, commute times, and personal 

obligations, up to a nominal level of 8 hrs of sleep per day. Given these limitations, the 

predicted levels of effectiveness reported in this study are not necessarily the same as might be 

obtained if an accident investigator performed a detailed fatigue analysis at the time of the 

accident and caution should be exercised in extending the calibration levels to that application.

2.3 Sample Size Determination 

A statistical process called power analysis, based on the results of a pilot study to evaluate the 

odds of finding a statistically significant difference in fatigue between human factor and 

nonhuman factor accidents given various sample sizes and assumptions about the signal to noise 

ratio, was used to determine sample size. The power analysis indicated that sufficient accidents 

occur within a 21⁄2-year period to reach an acceptable statistical power with a sample size of 400 

human factors cases and 1000 nonhuman factors cases. Since usually two employees are on each 

locomotive, an engineer and conductor, this results in approximately 2800 work histories and 

accident cases. 

2.4 Selection of Accidents 

Accidents that were assigned a human factors cause code (Hxxx) for either the primary or 

secondary cause were considered human factors accidents. Human factors accidents caused by 

actions of non-operational personnel, such as maintenance or signal workers, cannot logically be 

associated with the fatigue or effectiveness levels of the crew operating the train. Accidents with 

cause codes of H305, H402, H501, H993, H994, and H997 were, therefore, excluded from the 

7
list of human factors accidents considered. All track- and equipment-related accident cause 

codes (Txxx or Exxx) were included for the nonhuman factors accidents. 

2.5 Accident Samples for Each Participating Railroad 

To achieve the sample size specified in Section 2.3, it was estimated that data would be needed 

for all non-excluded human factors accidents occurring during calendar years 2003, 2004, and 

the first 6 months of 2005 on mainline, siding, and industry track involving freight trains. All 

track- and equipment-caused accidents occurring over the same period on mainline, siding, and 

industry track involving freight trains were used as a comparison set of nonhuman factors 

accidents. The 5 participating railroads—BNSF, CSX, Kansas City Southern (KCS), Norfolk 

Southern (NS), and Union Pacific (UP)—provided data on a total of 405 non-excluded human 

factors accidents and 1015 nonhuman factors accidents reported in this interval, which 

constituted the study sample.

2.6 Data Requested 

Each participating railroad provided work schedule data for each worker for the 30 days 

before each of the identified accidents. A template file was provided for the railroads to 

use to construct the data tables and is described in the full report. Most critical to the 

analysis was a record of the reporting and release date/times of each work episode, 

including deadhead and limbo times, which for analytical purposes were combined as 

unavailable for sleep. (The duty periods reported are not all regulated by hours of service 

rules and may exceed the allowable limit of 12 hr on duty.) Data on terminals, standard 

call times, and estimated commute times were also requested and applied to further limit 

opportunities to sleep. Worker identification was used solely to associate each work 

history with the accident involved and was coded to insure confidentiality. 

2.7 The SAFTE Model and the Work Schedule Fatigue Assessment Tool 

The biomathematical fatigue model used for this specific analysis was the SAFTE model. 

The U.S. Air Force and FRA have sponsored the development of a scheduling tool based 

upon the model that can be used to assess and manage fatigue in aircrews and railroad 

workers. The software is called FAST. For assessment of aggregate fatigue in a work 

force, FRA sponsored the development of a work schedule fatigue assessment tool based 

on FAST that can process hundreds of work histories compiled in a database and provide 

aggregate estimates of fatigue across workers and for specific times associated with 

accidents. This project used the batch processing version of FAST. 

8

2.7.1 The Work Schedule Fatigue Assessment Process 

In general, the batch processing involves the following steps. First, the data are entered 

into a set of databases. Second, the program processed those work histories to determine 

when sleep could have occurred, given that workers normally cannot sleep at work, 

generally do not sleep after they are called to work, and must commute to and from their 

place of work. The tool uses an algorithm called AutoSleep to estimate how much sleep 

the average railroad worker would get given the sleep opportunities afforded by the work 

schedule and the call/commute times. AutoSleep is based on a study of railroad engineer 

work/rest diaries (Pollard, 1996) and is described in more detail in the full report. The 

third step was to estimate the cognitive effectiveness of each worker for every minute that 
the worker was awake, using the SAFTE model. A detailed description of the SAFTE 

model has been previously published (Hursh, et al., 2004). Simply stated, crew 

effectiveness1

 is an estimate of the speed of reaction time and alertness. Estimated 

effectiveness varies with the combined effect of the time of day and the pattern of sleep. 

Crew effectiveness follows a daily (circadian) rhythm that is much lower between 0000 

and 0600 hr than between 1200 and 1800 hr. In addition, the model keeps track of the 

amounts of sleep opportunities a person gets as it contributes to performance and 

progressively degrades performance if the person experiences a loss of sleep from the 

nominal requirement of 8 hr per day. The batch processor summarized these detailed 

effectiveness estimates into 30-minute averages during every work period in the database. 

The program also summarized effectiveness in 30-minute intervals around the clock to 

provide a time of day estimate of work effectiveness. The analysis summarized 

effectiveness for each person’s work shift by describing the distribution of the amount of 

time spent at work as a function of effectiveness. Finally, and most importantly, the 

program estimated the effectiveness of each worker at the time he/she was reported to 

have been involved in an accident. 

2.7.2 

 

The Dimensions of the Analysis 

The batch processor created a schedule file for each worker that could be viewed in the 

standard version of FAST. These schedule files were used to troubleshoot any unusual 

values and in several cases led to corrections to the database. Of the 2962 workers 

involved in accidents (approximately 2 crewmembers per accident) that were reported, 

valid work histories were available for 2843 workers, a 96 percent success rate. Of those, 

790 were involved in human factors accidents, and 2053 were involved in nonhuman 

factors accidents. Each work history was composed of a series of records that constituted 

a work shift. Across the five railroads, the analysis processed 57,537 work shifts. In 

total, the results reported are based on over 1 million 30-minute work intervals. Hence, 

the effectiveness exposure estimates and accident effectiveness values were based on 

over 2800 work histories, and the results of all crewmembers contributed equally to the 

findings. The data were not coded in such a way to permit estimates of effectiveness by 

craft (engineer or conductor). 

1

 Crew effectiveness can have values in the range of 0 to 100. A person who consistently obtains 8 hr of 

good quality sleep would have a peak effectiveness score of 100 during the following waking period. 

9
10
3. Results of Analysis 

3.1 Descriptive Analysis 

The first results are simple descriptions of various features of the work schedule and 

accident data without any reference to the fatigue model predictions of effectiveness. 

The three basic descriptive charts are: 

 Work Durations 

 Clock Time of Work 

 Accidents by Time of Day 

For this and all other sections of the report, the results are shown as an aggregate of the 

findings based on the data from all railroads. 

3.1.1 Job-Related Non-Sleep Durations 

The railroads reported all times crewmembers were doing work related activities, such as 

performing as a crewman, deadheading, or in limbo time before release. Together, these 

constituted job-related times unavailable for sleep. Figure 1 shows the number of these 

intervals sorted by duration in hourly intervals. Relatively few intervals were shorter 

than 5-hr long. Work periods were about equally distributed from lengths of greater than 

6 hr to less than 11 hr. 

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

<= 1 1<=2 2<=3 3<=4 4<=5 5<=6 6<=7 7<=8 8<=9 9<=10 10<=11 11<=12 >12

Hours

Number of shifts re

ported

 Figure 1. Durations of Reported Job-Related Non-Sleep Intervals 

The most frequent job-related intervals were those between 11 and 12 hr and longer than 

12 hr. This may not be surprising considering that these intervals would include 

deadhead time and limbo time. For example, if a typical deadhead time is at least 3 hr 

11
long, then duty shifts of 9 hr or longer that were combined with deadhead time would all 

fall in the longer than 12 hr category. 

3.1.2 

3.1.3 

Clock Time of Work 

Figure 2 shows the number of work hours that occurred at hourly intervals around the 

clock. This analysis indicates the frequency of work at varying times of day and shows 

that, in general, work was fairly evenly distributed around the clock. For the population 

at large (the full height of the bars in Figure 2), work is a bit more concentrated between 

0800 and 1600 hr and diminishes between 1600 and 0500 hr. A detailed analysis 

revealed that in the overall population involved in accidents, a subgroup of workers 

existed who started a majority of their work periods between 2200 and 0400 hr. These 

workers are termed consistent night workers. Their data were separated from the larger 

population and evaluated as a distinctly different group. Their distribution of work is 

understandably more concentrated between 0000 and 1200 hr, shown as the dark blue 

bars in the graph. The remainder of this report focuses on the findings with those who 

were not consistent night workers. The full report includes the analysis of night workers. 

0

5,000

10,000

15,000

20,000

25,000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour of Day (0000-2300)

Number of Hours 

All Other Workers

Consistent Night Workers

Figure 2. Frequency of Work Hours by Time of Day, Hours by Consistent Night 

Workers Shown as the Dark Blue Bars at the Bottom and All Others Stacked Above 

3.1.4 Accidents by Time of Day 

Figure 3 shows the risk of human factors and nonhuman factors accidents in 3-hr 

intervals around the clock. For each clock interval the analysis calculated the proportion 

of accidents that occurred in that interval and divided that proportion by the proportion of 

work times that occurred at that clock time based on the work interval values in Figure 2. 

If accidents were randomly distributed around the clock, then the points would have a 

value of 1.0 and fall on the dashed line. The blue triangles in Figure 3 are for human 

factors accidents, and the green squares are for nonhuman factors accidents. A clear 

12
circadian pattern of human factors accident risk exists. Taking into consideration the 

distribution of work around the clock, accidents are relatively more likely in the early 

morning hours from 0000 to 0300 hr (the circadian nadir) and in the early afternoon from 

1200 to 1500 hr (the postprandial dip). Accidents are much less likely in the late 

morning (0900 to 1200 hr) and in the early evening (1500 to 1800 hr). These patterns are 

predicted by a circadian pattern generated by the SAFTE model, shown as a red line. 

Since effectiveness is thought to decline with increased fatigue, the inverse of 

effectiveness is plotted against the right-hand axis. The maximum value of inverse 

effectiveness corresponds to the early morning peak in accident risk. The data are plotted 

twice along the x-axis to illustrate the rhythmic pattern of the results. Human factors 

time of day accident risk is reliably correlated with the circadian pattern derived from the 

fatigue model (r = 0.71, p < 0.05). Circadian rhythms account for 51 percent of the 

variance in the time of day at which human factors accidents occur. By comparison, 

circadian rhythms only account for 6 percent of the variance in the time of day at which 

nonhuman factor accidents occur. 

0.6

0.8

1.0

1.2

1.4

00 - 03 03 - 06 06 - 09 09 - 12 12 - 15 15 - 18 18 - 21 21 - 00 00 - 03 03 - 06 06 - 09 09 - 12 12 - 15 15 - 18 18 - 21 21 - 00

Hour of Day

Risk of Accidents

0.90

1.00

1.10

1.20

1.30

1.40

 Inverse Effectiveness

Human Factors Nonhuman Factors (Random value) Inverse Effectiveness

R2 to HF Incidents = 0.51

R2

 to NHF Incidents = 0.06

Correlation Coefficient = 0.71, p< 0.05

3.2.1 

Figure 3. Accident Risk by Time of Day. Data Have Been Double-Plotted to Show 

the Repeating Circadian Pattern 

3.2 Validation of a Fatigue Model 

Work Time in Effectiveness Categories 

Figure 4 shows the distribution of 30-minute work intervals as a function of 

effectiveness. The figure shows the proportion of time spent at work with an 

effectiveness score between 90 and 100, between 80 and 90, between 80 and 70, and so 

on down to the lowest bin with scores of 50 or less effectiveness. The right-hand axis 

shows that 42 percent of the time locomotive crews have effectiveness scores above 90. 

13
Another 23 percent of the time, they have effectiveness scores between 80 and 90. 

Hence, 65 percent of the time, locomotive crews have scores above 80. The percent of 

time declines consistently with decreasing effectiveness, and less than 5 percent of the 

time effectiveness is below a score of 50. 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

≤ 50% 50% ≤ 60% 60% ≤ 70% 70% ≤ 80% 80% ≤ 90% > 90%

Effectiveness

 Proportion of Work Intervals

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

 Percent of Work Intervals

Five Railroads

Results excluding consistent night workers

Figure 4. Work Interval Effectiveness Distribution for Five Railroads 

These data provide an important reference for interpreting the estimated effectiveness 

values associated with accidents. If accidents are independent of effectiveness (or 

fatigue), then when accidents are sorted by crew effectiveness at their time of occurrence, 

the accidents should distribute exactly as work time effectiveness is distributed in Figure 

4. On the other hand, if accidents are caused, in part, by low effectiveness (fatigue or 

lack of alertness), then one would expect that a greater proportion of human factors 

accidents would occur at low levels of effectiveness than the proportion of time or 

exposure to those levels of effectiveness. In other words, if the fatigue model is 

predictive of accidents, then low effectiveness should be associated with an elevated risk 

of an accident. 

3.2.2 Effectiveness at the Time of the Accident 

Figure 5 shows the distributions of human factors and nonhuman factors accidents by 

effectiveness scores of the locomotive crews at the time of the accidents. Figure 5 also 

shows the mean work interval effectiveness distribution from Figure 4 for comparison. 

The y-axis is logarithmic, so that the distance between the accident distribution lines and 

the time distribution line at any effectiveness level reflects the degree of risk at that level; 

the greater the distance between the lines, the larger the ratio that defines risk (see 

Section 2.2.2). 

14
Figure 5 shows that the proportion of accidents that occur above an effectiveness score of 

90 is less than expected by the distribution of time, indicating reduced risk. Below an 

effectiveness score of 90, the rate of human factors accidents is consistently above the 

work-time distribution (heavy line) and gradually separates from the line as effectiveness 

decreases. For nonhuman factors accidents, the proportion is sometimes above the line 

and sometimes below the line, and no consistent relationship exists between nonhuman 

factors proportions and decreases in effectiveness. 

0.01

0.02

0.04

0.06

0.10

0.20

0.40

0.60

1.00

<50 50-60 60-70 70-80 80-90 90-100+

0.01

0.02

0.04

0.06

0.10

0.20

0.40

0.60

1.00 Time

Human Factors Accidents

Nonhuman Factors Accidents

Log scale: distances between lines reflect size of risk ratio

Effectiveness

Proportion of Time or Accidents

Figure 5. Proportion of Time or Accidents as a Function of Predicted Effectiveness 

Categories. Human Factors and Nonhuman Factors Accidents are Indicated as 

Blue Triangles and Green Squares, Respectively 

3.2.3 Accident Risk as a Function of Effectiveness 

As discussed in Section 2.2.2, if effectiveness (fatigue) is not associated with accidents, 

then the ratio that defines relative risk will be equal to 1.0. In other words, if being 

exposed to a certain level of effectiveness (fatigue) does not alter chances of having an 

accident, then accident risk is approximately 1.0. On the other hand, a ratio greater than 

1.0 indicates that accidents are more likely than chance at that level of effectiveness. A 

ratio of 1.5 means that a 50 percent increase in the risk of having an accident occurred at 

that level of effectiveness. To show the relationship between risk and effectiveness, the 

data points from Figure 5 were used to compute the risk ratio (using the expression from 

Section 2.2.2) for each effectiveness category. Figures 6 and 7 show the accident risk for 

the aggregated data from all five railroads for human factors and nonhuman factors 

accidents, respectively. 

15
r 2

 = 0.86

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

35 45 55 65 75 85 95

Effectiveness

Human Factors

 Risk 

Mean NHF

< 50 50-60 60-70 70-80 80-90 90-100+

Random

Correlation Coefficient = -0.93, p < 0.01

Figure 6. Human Factors Accident Risk at Each Level of Effectiveness Aggregated 

from Five Railroads 

In Figure 6, the solid blue circles and the heavy solid line fit to them show the increase in 

risk for human factors accidents as a function of decreases in effectiveness (increasing 

fatigue) at the time of the accident. A risk value of 1.0 indicates no effect of fatigue on 

accident occurrence. The dashed line shows the mean accident risk of nonhuman factors 

accidents. As can be seen from Figure 6, human factors accident risk is well described by 

a linear function. The line that is fit to these data accounts for 86 percent of the variance 

in human factors accident risk, and a significant inverse correlation exists between 

accident risk and effectiveness, the inverse of fatigue (r = -0.93, p < 0.01). The data 

show that for effectiveness scores between 90 and 100 (values associated with optimal 

prior sleep), a reduction of risk occurs. At effectiveness scores below 90, risk 

progressively increases. At the lowest level of effectiveness, a 65 percent increase in 

accident risk occurs (for effectiveness scores equal to or less than 50). The consistent 

relationship between reduced effectiveness (increased fatigue) and elevated risk indicates 

that the additional risk is associated with fatigue. 

• This finding satisfies the first criterion for model validation: There was a 

significant correlation between model predicted reductions in effectiveness and an 

increase in human factors accident risk. 

Importantly, the maximum increase in accident risk due to time of day alone was less 

than 20 percent (Figure 3), while the maximum increase in accident risk due to reduced 

effectiveness (fatigue) was 65 percent (Figure 6), reflecting the combined effects of time 

of day and sleep opportunities. 

Figure 7 shows the risk for nonhuman factors accidents as a function of effectiveness. In 

Figure 7 no consistent, statistically reliable relationship exists between risk and 

effectiveness. Data points fall above and below the line, showing a risk value of 1.0. 

16
The best fitting straight line has a slope that is not reliably different from zero, indicating 

that no consistent relationship exists between nonhuman factors accident risk and 

effectiveness (r = -0.14, p > 0.05). Only 2 percent of the variance in risk is accounted for 

by a linear function. 

r 2 = 0.02

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

35 45 55 65 75 85 95

Effectiveness

Nonhuman Factors

Risk 

< 50

Mean NHF

< 50 50-60 60-70 70-80 80-90 90-100+

Random

Correlation Coefficient = -0.14

Figure 7. Nonhuman Factors Accident Risk at Each Level of Effectiveness 

Aggregated from Five Railroads 

A large difference in relative risk occurred between human factors and nonhuman factors 

accidents in the lowest category of effectiveness, and this difference was statistically 

reliable (χ

2

 = 7.201, p < 0.01). The full report includes details of the statistical analysis. 

• These findings satisfy the second criterion for model validation: There was no 

reliable relationship between effectiveness and nonhuman factors accident risk, 

and at low levels of effectiveness, human factors accident risk was elevated more 

than nonhuman factors accident risk. 

3.3 Calibration of a Fatigue Model 

3.3.1 Accident Likelihoods at Selected Criterion Levels 

In addition to validating that a fatigue model can associate reductions in effectiveness 

with a reliable increase in human factors accidents, this study sought to calibrate the level 

of reduced effectiveness below which there is a reliable increase in accident risk 

(cumulative risk). To do this, a somewhat different analysis was conducted. In this case, 

a criterion level was set to include the proportion of all accidents that occurred with an 

effectiveness score at or below that level. The analysis then compared that proportion to 

the proportion of exposure time that occurred at or below that level. If the ratio of the 

two values is reliably greater that 1.0 at a particular criterion level, then that level could 

be considered the effectiveness level below which an increased cumulative risk of 

17
accidents would exist. As before, the analysis was conducted on the aggregated data, 

excluding the consistent night workers. Figure 8 shows the results, while Table 1 

summarizes them. The blue symbols are the cumulative human factors fatigue-associated 

accident risk, the black line is the expected cumulative risk of accidents if they are 

distributed as work interval effectiveness exposure (see Figure 4), and the dashed line is 

the mean cumulative risk ratio for nonhuman factors accidents. 

Each point shows the 95 percent confidence limits. If the lower confidence limit is above 

the black line (risk = 1), then the bar is reliably greater than 1.0 (chance). Interestingly, 

for any effectiveness criterion score below 90, human factors accidents have a cumulative 

risk reliably greater than expected by chance. Below an effectiveness score of 70, human 

factors cumulative risk is reliably greater than nonhuman factors cumulative risk and 

reliably greater than chance. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

40 50 60 70 80 90 100 110

Effectiveness Criterion (≤ Value)

Human Factors

Cumulative Risk 

 >90

Mean NHF

Figure 8. Human Factors Accident Risk by Criterion Levels of Effectiveness 

Aggregated for Five Railroads 

Table 1 summarizes the results in Figure 8, along with the percent of work time and 

accidents at each criterion level. Several things are clear. First, no specific threshold 

defines the beginning of the relationship between estimated effectiveness and accident 

risk. At any criterion level of effectiveness below a score of 90, a significant, albeit a 

small, increase in risk occurs. Effectiveness above a score of 90 is actually protective; 

accident likelihood is significantly less than chance for both human factors and 

nonhuman factors accidents. An effectiveness level of 90 is meaningful; the average 

daytime worker who consistently gets 8 hr of sleep each night will never have an 

effectiveness score below 90 according to the model used here. If a person works at 

night or consistently misses some sleep, effectiveness drops below a score of 90, at least 

some of the time. Here the analysis indicates that whenever workers are below an 

18
effectiveness level of 90, they have a statistically significant increase in accident risk. 

However, an increase in risk, while detectable, may not be operationally meaningful. For 

example, Figure 2 indicates that a considerable amount of work occurs at night, which is 

an operational necessity. Undoubtedly, effectiveness is below a score of 90 for some or 

all of that time for those workers; however, that degradation is biologically determined. 

An 11 percent increase in accident risk may be an operational cost inherent to any 

industry that operates at night. What is more important to note is that fatigue risk 

gradually escalates with progressively lower levels of effectiveness. 

Table 1. Human Factors Accident Cumulative Risk at Various Criterion Levels of 

Effectiveness

Criterion 

Effectiveness#

Score

Human Factors 

Accident Risk 

(%)

Percent of 

Work Time

Human Factors Cases 

 Number (Percent)+

> 90 - 16 * 42 259 (35%) 

≤ 90 + 11 * 58 472 (65%) 

≤ 80 + 14 * 35 289 (40%) 

≤ 70 + 21 * 19 166 (23%) 

≤ 60 + 39 * 7 71 (10%) 

≤ 50 + 65 * 2.7 33 (4.5%) 

* Significantly different from chance (p < 0.05). 

#

 Effectiveness at accident time based on 30-day work histories processed using the 

SAFTE biomathematical fatigue model. 

+ Human factors cases (two crewmembers per accident) in 21⁄2 yrs, excluding accidents 

involving consistent night workers. The percentages above and below 90 sum to 100 

percent. The percentages below 90 are cumulative and do not sum to 100 percent. 

Choosing a criterion level for effectiveness, below which risk is intolerable, is an 

economic, operational, and safety decision beyond the scope of this report. From a 

purely statistical point of view, however, a criterion set at 70 and below indicates the 

point at which human factors fatigue-associated accident risk is reliably greater than 

chance and the risk for nonhuman factors accidents. 

3.4 Other Evidence of Fatigue 

The validation and calibration analyses documented in Figures 6 and 8 highlight human 

factors accidents that occur below an effectiveness score of 70 as the accidents most 

strongly related to the influence of fatigue or low effectiveness. The relationship between 

estimated effectiveness and accident risk is merely a correlation. This relationship could 

be due to fatigue, or it could be due to some other extraneous factor that is associated 

19
with this method for determining effectiveness. One way to more strongly implicate 

fatigue as an important part of this relationship is to identify evidence that the accidents 

were caused by errors that are typical of a fatigued state. To pursue this evidence, the 

analysis determined which cause codes were involved in the human factors accidents 

with effectiveness scores at or below 70 to see if they were the type of accident expected 

to be related to fatigue. If those accidents were caused by human errors that might 

reasonably be expected to result from fatigue, then that would constitute further 

validation of this method and increase confidence that the reliable statistical relationship 

is not a coincidental result of some extraneous factor(s). 

Table 2. Human Factors Accident Cause Codes Related to Effectiveness ≤ 70

Rank Cause 

Code 

Frequency w/ 

Effectiveness 

≤ 70 

Frequency 

Total

Relative 

Likelihood Category Description 

1 H400 15 40 1.53 Main Track Authority 

2 H700 42 149 1.15 Use of Switches 

All Human Factors Cause Codes, 

Primary and Secondary Total All HF 215 880

Rank Cause 

Code 

Frequency w/ 

Effectiveness 

≤ 70 

Frequency 

Total 

Relative 

Likelihood 

Individual Cause Code 

Description 

Spring switch not cleared before 

reversing 1 H701 4 4 4.09 

Moving cars while loading ramp, 

hose, or chute not in proper place 2 H311 5 7 2.92 

Failure to release hand brake on 

cars 

3 H019 8 15 2.18 

Automatic block or interlocking 

signal displaying other than stop 

indication–failure to comply 

4 H222 4 8 2.05 

5 H404 7 17 1.69 Train order, etc., failure to comply 

Buffing or slack action excessive, 

train makeup 6 H504 4 10 1.64 

Automatic block or interlocking 

signal displaying stop indication–

failure to comply 

7 H221 12 31 1.58 

Failure to comply with restricted 

speed in connection with the 

restrictive indication of a block or 

interlocking signal 

8 H605 18 53 1.39 

9 H399 4 12 1.36 Other general switching rules 

Buffing or slack action excessive, 

train handling 10 H503 20 60 1.36 

Top 10 most overrepresented ≤ 70, excluding those with < 3 occurrences. 

Note: A human factors accident could have two human factors cause codes; hence, more cases of human 

factors cause codes than human factors accidents occurred. 

20
About 400 human factors accidents occurred, and usually two crew members were 

associated with each. Hence, about 800 cases occurred in which an effectiveness score 

was associated with a human factors accident, and 880 human factors cause codes were 

assigned since an accident could have more than one human factors cause code. Table 2 

displays those categories of cause codes and individual cause codes that were 

overrepresented in human factors accidents with an effectiveness score below 70: the 

proportion of these accidents at an effectiveness score below 70 was greater than their 

overall proportion for all human factors accidents. The top two rows of Table 2 indicate 

the only two categories of causes that were overrepresented as a class: main track 

authority and use of switches. The lower part of the table lists the 10 most 

overrepresented individual codes, excluding those that were rare (less than three 

occurrences in the entire sample). Most of these cause codes are associated with human 

errors that would be expected to increase with fatigue. The analysis cannot determine if 

these elevated risks are statistically reliable because the sample of events is too small, but 

this analysis suggests that the relationship between effectiveness and human factors 

accident risk is meaningful and not due to extraneous factors. 

3.5 Interpretation of Effectiveness Scores 

The results of this analysis of freight railroad accident risk indicate a reliable relationship 

between reduced effectiveness and an increased risk of human factors accidents. Below 

an effectiveness level of 70, the risk of human factors accidents is increased by about 20 

percent; below an effectiveness level of 50, it is elevated by 65 percent. In this section, 

the effectiveness metric is related to various other metrics and sleep histories to provide a 

context for understanding and appreciating the kinds of circumstances that can lead to 

reduced levels of effectiveness of this magnitude. 

The effectiveness values shown in Table 3 were derived from the SAFTE model and are 

based on an average person getting 8 hrs of sleep, awakening at 0700 hr, and remaining 

awake for the amount of time specified. A lapse is defined as an excessively long 

reaction time caused by loss of alertness or a micro-sleep. Lapse likelihood is the ratio of 

the expected frequency of lapses at an effectiveness level to the frequency of lapses of a 

well-rested person during a normal work day. A lapse likelihood score of 8 means that 

expected lapses are 8 times more frequent than for a well-rested person (Hursh, et al., 

2004). The effects of wakefulness are based on studies of laboratory subjects who were 

kept awake after a full night of sleep and tested repeatedly on cognitive tests throughout 

the period of wakefulness (Angus and Heslegrave,1985; Belenky, et al., 1994). The 

blood alcohol concentration (BAC) equivalence is based on studies comparing the effects 

of alcohol and sleep deprivation on performance on a driving simulator (Arnedt, Wilde, 

Munt, and MacLean, 2001) and cognitive test performance (Dawson and Reid, 1997). As 

an example, Table 3 shows that at an effectiveness score of 70, lapses are 5 times more 

likely than for a well-rested person and that this score is the equivalent of being awake 

for 21 hr after awakening at 0700 hr or having a BAC of 0.08. 

21
Table 3. The Relationship Among Various Effectiveness Scores and Other 

Meaningful Metrics: Likelihood of a Lapse, Continuous Hours Awake, and BAC 

Effectiveness 

Score 

Lapse 

Likelihood 

Hours Awake 

(Hr:Min) 

BAC 

Equivalent 

98 0.2 14:00 

94 1.0 15:10 

90 1.5 16:00 

80 3 18:00 

77 4 18:30 0.05 

70 5 21:00 0.08 

69 5.4 22:00 

60 8 40:50 

50 12 42:30 

40 18 64:00 

Another way to understand effectiveness values is to consider the kinds of sleep patterns 

and times of day that can lead to different levels of effectiveness. The values in Table 4 

were derived from the SAFTE model and are based on an average person awakening at 

0700 hr after getting the hours of sleep shown in the first column or losing the amount of 

sleep (relative to 8 hr per day) in the second column. Performance at 1600 hr reflects 

near optimal performance for a person on that schedule; performance at 0400 hr reflects 

the combined effects of prior sleep, time of day, and 21 hr of wakefulness. The values at 

0400 hr do not consider benefits of an evening nap; for example, a 2-hr nap at 2000 hr 

improves performance at 0400 hr by 4-6 percent. 

Table 4. The Effects of Various Daily Sleep Patterns on Effectiveness Estimates at 

1600 hr and 0400 hr. Three Schedules: 1, 2, 7 Days at the Specified Sleep Level 

Effectiveness Score After: 

One Day Two Days Seven Days 

Prior Daily 

Sleep 

(Hr) 

Prior Daily 

Sleep 

Loss (Hr) 1600 hr 0400 hr 1600 hr 0400 hr 1600 hr 0400 hr 

8 0 97 70 97 70 97 70 

7 1 96 69 95 68 93 67 

6 2 94 68 92 66 88 63 

5 3 92 65 89 62 82 57 

4 4 90 63 84 58 72 48 

3 5 87 59 78 51 57 34 

2 6 83 55 70 42 * * 

1 7 78 49 58 30 * * 

0 8 73 43 46 15 * * 

* No data available for these conditions

Relating Table 4 to Table 1, the analysis shows that if a person gets less than 8 hr sleep 

on a regular basis, then effectiveness at 0400 hr (the circadian minimum) will be below a 

score of 70, and accident risk will be elevated by at least 21 percent. If the person gets 

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less than 4 hr sleep, then effectiveness at 0400 hr is below a score of 65 in 1 day, less 

than a score of 60 in 2 days, and less than a score of 50 in 7 days, at which point accident 

risk is elevated by 65 percent. After 7 days of 4 hr sleep per day, effectiveness at the 

circadian peak (about 1600 hr) is nearing a score of 70 or an elevated risk of 14-21 

percent in the day time. 

3.6 Interpretations and Limitations 

This study was designed to test the validity of biomathematical models of fatigue, here 

the SAFTE model and the FAST software, as tools for evaluating schedules for increased 

risk of fatigue-related accidents. The data considered–accidents and the 30-day work 

histories that preceded them–were not a random sample of all locomotive crews in freight 

rail operations. Hence, the levels of effectiveness calculated by the model should not be 

interpreted as representative of the railroad work force in general. The study was not 

designed to determine the extent of fatigue in the freight rail industry. The objective was 

to test the validity of the mathematical model and to calibrate the model so that one could 

relate the effectiveness estimates to an estimate of elevated accident risk. 

While the biomathematical model used is typical of other sleep and performance models 

and is designed to simulate the effects of circadian rhythms and sleep patterns on fatigue, 

it is important to emphasize that the data that drove these predictions were entirely related 

to work schedule and opportunities to obtain sleep. The study did not measure sleep 

duration and quality directly, nor did the study directly measure cognitive performance. 

Operationally, this study related work schedule to accident risk using a sophisticated 

mathematical algorithm, but it did not directly measure fatigue or the performance 

manifestations of fatigue. The relationships observed are entirely correlational, not 

causal. It is theoretically conceivable that some other factor correlated with the same 

work schedule factors considered by the fatigue model was the real operational cause of 

the elevated accident risk. That possibility cannot be entirely eliminated with the sorts of 

data used in this study. In practice, however, that logical possibility may not matter if 

elimination of those work schedule risk factors results in improved safety. The 

encouraging results of this study provide justification for such an experiment. 

The inferences of sleep opportunity are based on a sleep estimation algorithm called 

AutoSleep, and the calculated effectiveness values were partly dependent on the settings 

of AutoSleep. Studies are currently underway to measure actual sleep under typical 

railroad schedules, and those findings may lead to improvements in the sleep estimation 

accuracy of AutoSleep, which may lead to greater accuracy in estimates of the true risk of 

fatigue. 

The accident risk levels that were found must be carefully limited to the operational 

factors that were considered: work schedule, time of day, call times, and commute times. 

Accidents that were estimated to have occurred with relatively high levels of 

effectiveness could have been fatigue related if the fatigue were caused by factors not 

considered by the analysis, such as sleep disorders, poor sleep hygiene, unusual 

circumstances in the operator’s life, such as illness or family demands, or unusual sleep 

needs. This sort of error might be called a miss, a case of fatigue that was misidentified 

as not fatigue. 

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Even in cases where the fatigue model judged that fatigue could have occurred, it is 

possible that the human factors accident was caused by some other human error, such as 

distraction or poor training. This sort of error might be termed a false alarm, a case in 

which the analysis suspected fatigue as the cause but was really some other cause. These 

two sorts of errors, misses and false alarms, are typical of discriminations involving 

noise, unidentified factors that lead to error in judgment. When making such judgments, 

the user of the model must weigh the relative costs associated with the two kinds of errors 

and set a criterion value for using the model, based on Table 1, that is operationally, 

economically, and socially optimal. Making that decision is beyond the scope of this 

study. 

Furthermore, fatigue models based entirely on the sorts of data used in this study are not 

suitable for determining the fatigue of particular individuals because of the kinds of 

inaccuracies discussed above, especially the wide variation in individual sleep 

requirements and absence of specific information on individual sleep habits, health, and 

circumstances. On the other hand, by adding such additional information to a fatigue 

analysis, it is possible to reduce the error sufficiently to use fatigue models as tools in 

accident investigations, combined with other important information about the 

performance of the individuals. That sort of detailed analysis, however, was clearly 

beyond the scope of this study. 

Finally, it is important to properly interpret the risk values in Table 1. Those values 

represent the percent change in human factors accidents relative to the expected 

distribution of accidents based on work time effectiveness. The results indicate that the 

lower the effectiveness level, the greater the elevation of human factors accident risk. 

The percent changes in risk (second column, Table 1) are not to be confused with the 

percentages of human factors accidents associated with that level of risk (fourth column, 

Table 1). The percentages in second column represent the increase (or decrease) in the 

risk of fatigue-associated human factors accidents compared to chance when at a 

particular level of effectiveness. 

The overall probability of a particular railroad worker on a particular work shift having a 

human factors accident is extremely low. This study only considered work histories 

related to accidents, not all work histories. Consequently, an overall probability of 

fatigue-caused human factors accidents in freight service cannot be calculated, but that 

probability will be a number with four or five zeros after the decimal point. 

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4. Summary and Conclusions 

4.1 Summary 

This report summarized the results of a project sponsored by FRA’s Office of Research 

and Development and Office of Safety to develop a methodology to validate and calibrate 

biomathematical fatigue models for use as fatigue management tools. This study 

assessed whether a fatigue model can predict an increased risk of human factors caused 

accidents. Using 21⁄2 years of accident data from five Class I freight railroads, the fatigue 

model used 30-day work histories before a sample of human factors and nonhuman 

factors accidents to determine the relationship between accident risk and crew 

effectiveness (the inverse of fatigue). This report summarized the scope of that effort, the 

methods used to conduct the analysis, and the results of the analysis to date. The study 

considered approximately 2800 crew member work histories associated with 1400 

accidents, 400 of which involved human factors errors. A biomathematical fatigue model 

(SAFTE) evaluated a total of over 1 million 30-minute work intervals, covering over 

57,000 work starts, for predicted effectiveness. The 2800 work histories served as a basis 

for determining the exposure level to various levels of fatigue in these locomotive crews. 

In addition, the fatigue model calculated estimated effectiveness at the time of each 

accident, again based on 2800 estimates of effectiveness at the time of the accidents. The 

following summarizes the results of the study. 

Human factors accidents follow a circadian pattern that is significantly correlated with 

the circadian rhythm of a fatigue model (r = 0.71, p < 0.05). The same model rhythm is 

not correlated with nonhuman factors accidents. The maximum human factors accident 

risk due to time of day alone was increased less than 20 percent (Figure 3), while the 

maximum increase in accident risk due to reduced effectiveness (fatigue) was 65 percent 

(Figure 6), reflecting the combined effects of time of day and sleep opportunities. 

• Validation. The fatigue model met two validation criteria. 

1. Accident risk was significantly correlated with effectiveness for human 

factors accidents (r = -0.93, p < 0.01, Figure 6). 

2. The model distinguished between human factors and nonhuman factors 

accidents. Nonhuman factors accident risk was not correlated with 

estimated effectiveness (r = -0.14, p > 0.05, Figure 7), and the relative risk 

of human factors and nonhuman factors accidents were significantly 

different at low effectiveness levels (χ

2 = 7.201, p < 0.01). 

• Calibration. Effectiveness has a reliable correspondence to increases in accident 

risk. 

1. Risk is a relatively smooth increasing function with decreases in 

effectiveness. 

2. Above an effectiveness score of 90, risk is significantly reduced relative to 

chance. 

3. Below an effectiveness score of 70, risk is significantly elevated relative to 

nonhuman factors risk. 

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4. Overall, railroad workers in this study spent about 40 percent of work time 

above an effectiveness score of 90 and about 20 percent of work time 

below an effectiveness score of 70. 

• An effectiveness score of 90 is the minimum level for a person getting 8 hrs sleep 

per day and awake from about 0700 to 2300 hr (day shift). 

• An effectiveness score of 70 is the minimum level for a rested person after being 

awake for 21 hr at 0400 hr. 

• An effectiveness score of 70 is about equal to the effects of 0.08 BAC and lapse 

likelihood five times greater than a well-rested person during the daytime. 

An analysis of the cause codes associated with the accidents that occurred at 

effectiveness at or below an effectiveness score of 70 indicated an overrepresentation of 

human factors errors associated with main track authority and use of switches. Most of 

the overrepresented individual cause codes reflect the kinds of operator errors one might 

expect of persons who are fatigued. This finding confirms that the relationship between 

effectiveness and human factors accident risk is meaningful and not a circumstantial 

coincidence. 

4.2 Conclusion 

This project established that a biomathematical fatigue model can be used to assess how 

much work schedule factors can contribute to increased fatigue and an elevated risk of 

railroad accidents. The virtue of having a validated fatigue model, especially if it is 

calibrated to accident likelihood, is that a carrier could use it to do a self-assessment of 

fatigue across its system. By evaluating work histories on a terminal by terminal basis 

and using the scores from the model as a metric, the carrier could determine which 

terminals are experiencing schedules that might be generating increased risk of fatigue in 

train operators. Perhaps none of the terminals have a problem, perhaps just a few. In any 

case, the carrier would be in a position to use this objective assessment as a way to focus 

its fatigue management efforts where the greatest payoff would be expected. This study 

provides evidence that such a strategy, using a validated fatigue model, can identify work 

schedule-related fatigue factors that contribute to an elevated risk of accidents. 

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Abbreviations/Acronyms 

AAR Association of American Railroads 

BAC blood alcohol concentration 

BNSF BNSF Railway 

CSX CSX Transportation Inc. 

FAST Fatigue Avoidance Scheduling Tool 

FRA Federal Railroad Administration 

KCS Kansas City Southern Railway Company 

NS Norfolk Southern Railway Company 

SAFTE Sleep, Activity, Fatigue, and Task Effectiveness Model 

UP Union Pacific Railroad 

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