Bayesian Survival Approach to Analyzing the Risk of Recurrent Rail Defects

This paper develops a Bayesian framework to explore the impact of different factors and to predict the risk of recurrence of rail defects, based upon datasets collected from a US Class I railroad between 2011 and 2016. To this end, this study constructs a parametric Weibull baseline hazard function and a proportional hazard (PH) model under a Gaussian frailty approach. The analysis is performed using Markov chain Monte Carlo simulation methods and the fit of the model is checked using a Cox–Snell residual plot. The results of the model show that the recurrence of a defect is correlated with different factors such as the type of rail defect, the location of the defect, train speed limit, the number of geometry defects in the last three years, and the weight of the rail. First, unlike the ordinary PH model in which the occurrence times of rail defects at the same location are assumed to be independent, a PH model under frailty induces the correlation between times to the recurrence of rail defects for the same segment, which is essential in the case of recurrent events. Second, considering Gaussian frailties is useful for exploring the influence of unobserved covariates in the model. Third, integrating a Bayesian framework for the parameters of the Weibull baseline hazard function as well as other parameters provides greater flexibility to the model. Fourth, the findings are useful for responsive maintenance planning, capital planning, and even preventive maintenance planning.