1. Slide 1 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

2. Slide 2 ILLINOIS - 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

3. 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

4. Slide 4 ILLINOIS - RAILROAD ENGINEERING 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 defect Equipment defect Human error Other track quality method of operation track type human factors equipment design railroad type traffic exposure etc. Influencing Factors Accident Cause This study focuses on hazmat release frequency

5. Slide 5 ILLINOIS - RAILROAD ENGINEERING 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 (H ij | D i, A) = conditional probability that the derailed i th car is a type j hazmat car P(D i | A) = conditional probability of derailment for a car in i th position of a train 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 = train length J = type of hazmat car Where:

6. Slide 6 ILLINOIS - 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)

7. Slide 7 ILLINOIS - RAILROAD ENGINEERING Comparison of two uncertainties Population f(x;θ) Sample (x 1,..,x n ) θ* Aleatory uncertainty (stochastic uncertainty) Epistemic uncertainty (Statistical uncertainty)

8. Slide 8 ILLINOIS - 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

9. Slide 9 ILLINOIS - RAILROAD ENGINEERING 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 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 θ2*θ2* θ1*θ1* θk*θk*

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

11. Slide 11 ILLINOIS - RAILROAD ENGINEERING 95% confidence interval of train derailment rate

12. Slide 12 ILLINOIS - RAILROAD ENGINEERING 95% confidence interval of car derailment probability

13. Slide 13 ILLINOIS - RAILROAD ENGINEERING 95% confidence interval of conditional probability of release Conditional Probability of Release (CPR) Tank Car Type

14. Slide 14 ILLINOIS - RAILROAD ENGINEERING 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. Slide 15 ILLINOIS - RAILROAD ENGINEERING 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. Slide 16 ILLINOIS - RAILROAD ENGINEERING Hazmat release rate under uncertainty Hazmat release rate = train derailment rate × car derailment probability × conditional probability of release 0.0047 = 0.34 × 0.165 × 0.084 (0.026 cars released per million train-miles) If X, Y, Z are mutually independent

17. Slide 17 ILLINOIS - RAILROAD ENGINEERING Standard error of risk estimate 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 X i are mutually independent

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

19. Slide 19 ILLINOIS - RAILROAD ENGINEERING 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. Slide 20 ILLINOIS - RAILROAD ENGINEERING A statistical test for risk difference There are two hazmat routes, whose mean risk estimates and standard errors are (R 1,S 1 ) and (R 2, S 2 ), respectively. Z-TestConclusion The two routes have different risks Route 1 has a higher risk Route 1 has a lower risk H o : µ 1 = µ 2 H a : µ 1 µ 2 H o : µ 1 = µ 2 H a : µ 1 > µ 2 H o : µ 1 = µ 2 H a : µ 1 < µ 2 Hypothesis

21. Slide 21 ILLINOIS - RAILROAD ENGINEERING 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. Slide 22 ILLINOIS - RAILROAD ENGINEERING Thank You! 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