railroad hazardous materials transportation risk analysis under uncertainty

ILLINOIS - 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


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


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


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


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:


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)


Comparison of two uncertainties

Population

f(x;θ)

Sample

(x1,..,xn

)θ*

Aleatory uncertainty(stochastic

uncertainty)

Epistemic uncertainty(Statistical

uncertainty)


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


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*


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


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


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


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


Standard error of risk estimates

• Previous research focused on the single-point risk estimation

• This research analyzes the uncertainty (standard error) of risk estimate


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)


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


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


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 )


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


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


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


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: [email protected]

Rail Transportation and Engineering Center (RailTEC)http://ict.illinois.edu/railroad

railroad hazardous materials transportation risk analysis under uncertainty

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