Post on 31-Mar-2015
Slide 1ILLINOIS - RAILROAD ENGINEERING
Railroad Hazardous Materials Transportation Risk Analysis Under Uncertainty
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 2ILLINOIS - RAILROAD ENGINEERING
Outline
• 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 3ILLINOIS - 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
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Chain of events leading to hazmat car release
Hazmat Release Risk = Frequency × Consequence
Number of cars
derailed
• speed
• accident cause
• train length etc.
Derailed cars contain hazmat
• number of hazmat cars in the train
• train length
• placement of hazmat car in the train etc.
Hazmat car releases contents
• hazmat car safety design
• speed, etc.
Release consequences
• chemical property
• population density
• spill size
• environment etc.
Train is involved in
a derailment
Track defectEquipment defectHuman errorOther
• track quality
• method of operation
• track type
• human factors
• equipment design
• railroad type
• traffic exposure etc.
InfluencingFactors
Accident Cause
This study focuses on hazmat release frequency
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Modeling hazmat car release rate
P (A) = derailment rate (number of derailments per train-mile, car-mile or gross ton-mile)
P (R) = release rate (number of hazmat cars released per train-mile, car-mile or gross ton-miles)
P (Hij | Di, A) = conditional probability that the derailed i th car is a type j hazmat car
P(Di | A) = conditional probability of derailment for a car in i th position of a train
P (Rij | Hij, Di, A) = conditional probability that the derailed type j hazmat car in i th position of a train released
L = train length
J = type of hazmat car
Where:
Slide 6ILLINOIS - RAILROAD ENGINEERING
Types of uncertainty
• 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)
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Comparison of two uncertainties
Population
f(x;θ)
Sample
(x1,..,xn
)θ*
Aleatory uncertainty(stochastic
uncertainty)
Epistemic uncertainty(Statistical
uncertainty)
Slide 8ILLINOIS - RAILROAD ENGINEERING
Uncertainties in hazmat risk assessment
• 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
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Standard error of a parameter estimate
• 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 sample-specific estimator θk*
• According to Central Limit Theorem (CLT), θ1*,…, θk* 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 θ2*θ1
* θk*
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Confidence interval of a parameter estimate
θ*-1.96Std(θ*)
θ* + 1.96Std(θ*)
θ*
θ
θ
θ
Sm
all
to L
arg
e
95% Confidence Interval
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95% confidence interval of train derailment rate
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Class 1 Class 2 Class 3 Class 4 Class 5
<20 MGT and Non-Signaled <20 MGT and Signaled
≥20 MGT and Non-Signaled ≥20 MGT and Signaled
Cla
ss I
Mai
nlin
e Tr
ain
Der
ailm
ent
Rat
e p
er B
illio
n G
ross
To
n-M
iles
FRA Track Class
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95% confidence interval of car derailment probability
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0 20 40 60 80 100
Upper 95%
Lower 95%
Mean
Position in Train
Ca
r D
era
ilm
en
t P
rob
ab
ilit
y
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95% confidence interval of conditional probability of release
Co
nd
itio
nal
Pro
bab
ilit
y o
f R
elea
se
(CP
R)
Tank Car Type
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Standard error of risk estimates
• Previous research focused on the single-point risk estimation
• This research analyzes the uncertainty (standard error) of risk estimate
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Numerical Example
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)
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Hazmat release rate under uncertainty
Hazmat release rate = train derailment rate × car derailment probability × conditional probability of release
( ) ( ) ( ) ( )E XYZ E X E Y E Z
0.0047 = 0.34 × 0.165 × 0.084
(0.026 cars released per million train-miles)
Train Derailment Rate per Billion
Gross Ton-MilesCar Derailment
ProbabilityConditional of
Release Estimate 0.34 0.165 0.084Standard Error 0.026 0.008 0.00595% Confidence Interval (0.295,0.395) (0.1496,0.1797) (0.0742,0.0930)
If X, Y, Z are mutually independent
Slide 17ILLINOIS - RAILROAD ENGINEERING
Standard error of risk estimate
Train Derailment Rate per Billion
Gross Ton-MilesCar Derailment
ProbabilityConditional of
Release
Hazmat Release Rate per Billon
Gross Ton-MilesEstimate 0.34 0.165 0.084 0.0047Standard Error 0.026 0.008 0.005 0.00049695% 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.
If Xi are mutually independent
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Route-specific hazmat release risk
• Route-specific risk
– Estimate = R1 + R2 + … + Rn
– Standard error =
Segment 1
Segment 2
Segment n
R1
Std(R1)R2
Std(R2)Rn
Std(Rn)
2 2 21 2 nStd(R ) +Std(R ) +...+Std(R )
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Risk comparison under uncertainty
• 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
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A statistical test for risk difference
• There are two hazmat routes, whose mean risk estimates and standard errors are (R1,S1) and (R2, S2), respectively.
1 2/22 2
1 2
R Rz
s s
a
Z-Test Conclusion
The two routes have different risks
1 2
2 21 2
R Rz
s sa
1 2
2 21 2
R Rz
s sa
Route 1 has a higher risk
Route 1 has a lower risk
Ho: µ1 = µ2
Ha: µ1 ≠ µ2
Ho: µ1 = µ2
Ha: µ1 > µ2
Ho: µ1 = µ2
Ha: µ1 < µ2
Hypothesis
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Conclusions
• 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 22ILLINOIS - RAILROAD ENGINEERING
Thank You!
Xiang (Shawn) LiuPh.D. Candidate
Rail Transportation and Engineering Center (RailTEC)Department of Civil and Environmental Engineering
University of Illinois at Urbana-ChampaignOffice:(217) 244-6063
Email: liu94@illinois.edu
Rail Transportation and Engineering Center (RailTEC)http://ict.illinois.edu/railroad