Reliability modelling of wheel wear deterioration using conditional bivariate gamma processes and Bayesian hierarchical models

Wear of wheel profiles is a common degradation process that significantly impacts the reliability of wheelsets. In this study, a conditional bivariate Gamma process is constructed to characterize wheel wear, and hierarchical Bayesian models are employed to identify the differences in wear between each vehicle within a train. Before computation, the field data are modified by isotonic regression and monotone cubic Hermite interpolants. Due to the failure modes involving flange thickness and wheel diameter difference, the distributions of first-passage times are calculated using an analytical approach and kernel density estimation, respectively. The proposed model is validated with a real-world case study of a train consisting of eight vehicles. The results indicate that the laws of wear vary throughout the train, besides left and right wheels. Based on the results, conclusions can be drawn that the first and last vehicles in a train have higher mean wear rates than others, and that different vehicles have different levels of reliability during different stages; the early failure rates are close to zero, but they rapidly increase in the late stage.