1. 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

2. 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

3. 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

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

5. Modeling hazmat car release rate Where: P (R) = release rate (number of hazmat cars released per train-mile, car-mile or gross ton-miles) P (A) = derailment rate (number of derailments per train-mile, car-mile or gross ton-mile) P(Di | A) = conditional probability of derailment for a car in ith position of a train P (Hij | Di, A) = conditional probability that the derailed ith car is a type j hazmat car P (Rij| Hij, Di, A) = conditional probability that the derailed type j hazmat car in ithposition of a train released L = train length J = type of hazmat car

6. 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)

7. Comparison of two uncertainties Aleatory uncertainty (stochastic uncertainty) Population f(x;θ) Sample (x1,..,xn) θ* Epistemic uncertainty (Statistical uncertainty)

8. 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

9. 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 θand standard deviation Std(θ*) • E(θ*) = θ (true value of a parameter) • Std(θ*) = standard error θ1* θk* θ2* θ

10. Confidence interval of a parameter estimate 95% Confidence Interval θ* + 1.96Std(θ*) θ Small to Large θ* θ θ*-1.96Std(θ*) θ

11. 95% confidence interval of train derailment rate

12. 95% confidence interval of car derailment probability

13. 95% confidence interval of conditional probability of release Conditional Probability of Release (CPR) Tank Car Type

14. Standard error of risk estimates • Previous research focused on the single-point risk estimation • This research analyzes the uncertainty (standard error) of risk estimate

15. 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)

16. Hazmat release rate under uncertainty Hazmat release rate = train derailment rate × car derailment probability × conditional probability of release If X, Y, Z are mutually independent = 0.34 × 0.165 × 0.084 0.0047 (0.026 cars released per million train-miles)

17. Standard error of risk estimate If Xi are mutually independent 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.

18. 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)

19. 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

20. 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. Z-Test Conclusion Hypothesis Ho: µ1 = µ2 Ha: µ1 ≠ µ2 The two routes have different risks Route 1 has a higher risk Ho: µ1 = µ2 Ha: µ1 > µ2 Ho: µ1 = µ2 Ha: µ1 < µ2 Route 1 has a lower risk

21. 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

22. Xiang (Shawn) Liu Ph.D. Candidate Rail Transportation and Engineering Center (RailTEC)Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-ChampaignOffice:(217) 244-6063Email: liu94@illinois.edu Rail Transportation and Engineering Center (RailTEC)http://ict.illinois.edu/railroad Thank You!