Slide 1
ILLINOIS - RAILROAD ENGINEERING
Xiang Liu, M. Rapik Saat and Christopher P. L. Barkan
Rail Transportation and Engineering Center (RailTEC)
University of Illinois at Urbana-Champaign
15 October 2012

Slide 2
ILLINOIS - RAILROAD ENGINEERING
• Introduction
– Overview of railroad hazmat transportation
– Events leading to a hazmat release incident
• Uncertainties in the risk assessment
– Standard error of parameter estimation
• Hazmat release rate under uncertainty
• Risk comparison

Slide 3
ILLINOIS - RAILROAD ENGINEERING
Overview of railroad hazardous materials transportation
• There were 1.7 million rail carloads of hazardous materials
(hazmat) in the U.S. in
2010 (AAR, 2011)
• Hazmat traffic account for a small proportion of total rail carloads, but its safety have been placed a high priority

Slide 4
ILLINOIS - RAILROAD ENGINEERING
Hazmat Release Risk = Frequency × Consequence
Accident Cause
Track defect
Equipment defect
Human error
Other
This study focuses on hazmat release frequency
Train is involved in a derailment
Number of cars derailed
Derailed cars contain hazmat
Hazmat car releases contents
Release consequences
Influencing
Factors
• track quality
• method of operation
• track type
• speed
• accident cause
• human factors
• equipment design
• railroad type
• traffic exposure etc.
• train length etc.
• number of hazmat cars in the train
• train length
• placement of hazmat car in the train etc.
• hazmat car safety design
• speed, etc.
• chemical property
• population density
• spill size
• environment etc.

Slide 5
ILLINOIS - RAILROAD ENGINEERING
Where:
P (R) = release rate (number of hazmat cars released per train-mile, car-mile or gross ton-miles)
P (A)
P(D i
| A)
= derailment rate (number of derailments per train-mile, car-mile or gross ton-mile)
= conditional probability of derailment for a car in i th position of a train
P (H ij
| D i
, A) = conditional probability that the derailed i th car is a type j hazmat car
P (R ij
| H ij
, D i
, A) = conditional probability that the derailed type j hazmat car in i th position of a train released
L
J
= train length
= type of hazmat car

Slide 6
ILLINOIS - RAILROAD ENGINEERING
• Aleatory uncertainty (also called stochastic, type A, irreducible or variability)
– inherent variation associated with a phenomenon or process (e.g., accident occurrence, quantum mechanics etc.)
• Epistemic uncertainty
(also called subjective, type B, reducible and state of knowledge)
– due to lack of knowledge of the system or the environment (e.g., uncertainties in variable, model formulation or decision)

Slide 7
ILLINOIS - RAILROAD ENGINEERING
Aleatory uncertainty
(stochastic uncertainty)
Sample
(x
1
,..,x n
θ*
)
Epistemic uncertainty
(Statistical uncertainty)

Slide 8
ILLINOIS - RAILROAD ENGINEERING
• The evaluation of hazmat release risk is dependent on a number of parameters, such as
– train derailment rate
– car derailment probability
– conditional probability of release etc.
• The true value of each parameter is unknown and could be estimated based on sample data
• The difference between the estimated parameter and the true value of the parameter is measured by standard error

Slide 9
ILLINOIS - RAILROAD ENGINEERING
• The true value of a parameter is θ. Its estimator is θ*
• Assuming that there are K data samples (each sample contains a group of observations). Each sample has a samplespecific estimator θ k
*
• According to Central Limit Theorem (CLT), θ
1
*,…, θ k
* follow approximately a normal distribution with the mean θ and standard deviation Std( θ*)
– E(θ*) = θ (true value of a parameter)
– Std(θ*) = standard error
θ
1
* θ k
* θ θ
2
*

Slide 10
ILLINOIS - RAILROAD ENGINEERING
95% Confidence Interval
θ* + 1.96Std(θ*)
θ
θ*
θ
θ
θ*-1.96Std(θ*)

Slide 11
ILLINOIS - RAILROAD ENGINEERING
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
<20 MGT and Non-Signaled
≥20 MGT and Non-Signaled
<20 MGT and Signaled
≥20 MGT and Signaled
Class 1 Class 2 Class 3
FRA Track Class
Class 4 Class 5

Slide 12
ILLINOIS - RAILROAD ENGINEERING
95% confidence interval of car derailment probability
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0 20
Upper 95%
Mean
Lower 95%
40 60
Position in Train
80 100

Slide 13
0,06
0,04
0,02
0,00
ILLINOIS - RAILROAD ENGINEERING
0,10
0,08
105J300W
Tank Car Type
105J600W

Slide 14
ILLINOIS - RAILROAD ENGINEERING
• Previous research focused on the single-point risk estimation
• This research analyzes the uncertainty (standard error) of risk estimate

Slide 15
ILLINOIS - RAILROAD ENGINEERING
The objective is to estimate hazmat release rate (number of cars released per traffic exposure) based on track-related and train-related characteristics
• Track characteristics:
– FRA track class 3
– Non-signaled
– Annual traffic density below 20MGT
• Train characteristics
– Two locomotives and 60 cars
– Train speed 40 mph
– One tank car in the train position most likely to derail
(105J300W)

Slide 16
ILLINOIS - RAILROAD ENGINEERING
Hazmat release rate = train derailment rate × car derailment probability
× conditional probability of release
Estimate
Standard Error
Train Derailment
Rate per Billion
Gross Ton-Miles
0.34
0.026
Car Derailment
Probability
0.165
0.008
Conditional of
Release
0.084
0.005
95% Confidence Interval (0.295,0.395) (0.1496,0.1797) (0.0742,0.0930)
If X
,
Y, Z are mutually independent
( )

E X )

E Y

E Z
0.0047
= 0.34 × 0.165 × 0.084
(0.026 cars released per million train-miles)

Slide 17
ILLINOIS - RAILROAD ENGINEERING
If X i are mutually independent
Estimate
Standard Error
Train Derailment
Rate per Billion
Gross Ton-Miles
0.34
0.026
Car Derailment
Probability
0.165
0.008
Conditional of
Release
0.084
0.005
Hazmat Release
Rate per Billon
Gross Ton-Miles
0.0047
0.000496
95% Confidence Interval (0.295,0.395) (0.1496,0.1797) (0.0742,0.0930) (0.0037,0.0057)
Source: Goodman, L.A. (1962). The variance of the product of K random variables.
Journal of the American Statistical Association. Vol. 57, No. 297, pp. 54-60.

Slide 18
ILLINOIS - RAILROAD ENGINEERING
Segment 1 Segment 2 Segment n
R
1
Std(R
1
)
R
2
Std(R
2
)
R n
Std(R n
)
• Route-specific risk
– Estimate = R
1
+ R
2
+ … + R n
– Standard error = 2 2
Std(R ) +Std(R ) +...+Std(R )
1 2 n
2

Slide 19
ILLINOIS - RAILROAD ENGINEERING
• The uncertainty in the risk assessment should be taken into account to compare different risks
• For example, assuming a baseline route has estimated risk 0.3, an alternative route has estimated risk 0.5, is this difference large enough to conclude that the two routes have different safety performance?
– It depends on the standard error of risk estimate on each route

Slide 20
ILLINOIS - RAILROAD ENGINEERING
• There are two hazmat routes, whose mean risk estimates and standard errors are (R
1
,S
1
) and (R
2
, S
2
), respectively.
Conclusion Z-Test
R
1

R
2 s
1
2  s
2
2
 z a / 2
Hypothesis
H o
: µ
1
H a
: µ
1
= µ
2
≠ µ
2
The two routes have different risks
R
1

R
2 s
1
2  s
2
2
 z a
R
1

R
2 s
1
2  s
2
2
  z a
H o
: µ
1
H a
: µ
1
= µ
2
> µ
2
H o
: µ
1
H a
: µ
1
= µ
2
< µ
2
Route 1 has a higher risk
Route 1 has a lower risk

Slide 21
ILLINOIS - RAILROAD ENGINEERING
• Risk analysis of railroad hazmat transportation is subject to uncertainty due to statistical inference based on sample data
• These uncertainties affect the reliability of risk estimate and corresponding decision making
• In addition to single-point risk estimate, its standard error and confidence interval should also be quantified and incorporated into the safety management

Slide 22
ILLINOIS - RAILROAD ENGINEERING
Xiang (Shawn) Liu
Ph.D. Candidate
Rail Transportation and Engineering Center (RailTEC)
Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
Office:(217) 244-6063
Email: liu94@illinois.edu
Rail Transportation and Engineering Center (RailTEC) http://ict.illinois.edu/railroad