A statistical study of the derailment hazard for U.S. class I railways

A simple probabilistic model is proposed for the collision and derailment experience for freight trains of U.S. Class I railways. By means of this model, asymptotic confidence intervals are constructed for the probability per mile of a derailment accident as a function of train speed and train length which utilize data available from records for U.S. Class I railways kept by the Interstate Commerce Commission and the Association of American Railroads [l]. Allowance is made in the model for the grouping of data by train length and speed. The theory is applied to a particular summary of accident data for all U.S. Class I railways for the years 1952 through 1955. On the basis of this data, confidence intervals for the derailment probability are computed for speeds in excess of 10 mph and train lengths of from 11 to 130 cars in groups of 5 cars. In addition, a statistical test of one of the more crucial model hypotheses is performed. An appendix containing the relevant derivations is included. In particular, a new version of a theorem of Slutsky due to LeCam is stated which greatly facilitates the derivations of the asymptotic distributions for the estimates of the derailment probabilities and the statistic employed in the above mentioned hypothesis test.