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Accid Anal Prev. 2017 Oct;107:164-172. doi: 10.1016/j.aap.2017.07.007.

Analysis of multiple tank car releases in train accidents.

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Department of Civil and Environmental Engineering, Rutgers University, United States. Electronic address:
Department of Statistics, Rutgers University, United States.
Department of Statistics, Virginia Tech, United States.


There are annually over two million carloads of hazardous materials transported by rail in the United States. The American railroads use large blocks of tank cars to transport petroleum crude oil and other flammable liquids from production to consumption sites. Being different from roadway transport of hazardous materials, a train accident can potentially result in the derailment and release of multiple tank cars, which may result in significant consequences. The prior literature predominantly assumes that the occurrence of multiple tank car releases in a train accident is a series of independent Bernoulli processes, and thus uses the binomial distribution to estimate the total number of tank car releases given the number of tank cars derailing or damaged. This paper shows that the traditional binomial model can incorrectly estimate multiple tank car release probability by magnitudes in certain circumstances, thereby significantly affecting railroad safety and risk analysis. To bridge this knowledge gap, this paper proposes a novel, alternative Correlated Binomial (CB) model that accounts for the possible correlations of multiple tank car releases in the same train. We test three distinct correlation structures in the CB model, and find that they all outperform the conventional binomial model based on empirical tank car accident data. The analysis shows that considering tank car release correlations would result in a significantly improved fit of the empirical data than otherwise. Consequently, it is prudent to consider alternative modeling techniques when analyzing the probability of multiple tank car releases in railroad accidents.


Correlated binomial model; Hazardous materials; Safety; Tank car release; Transportation risk

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