Degradation data analysis for samples under unequal operating conditions: a case study on train wheels

Traditionally, reliability assessment of devices has been based on life tests (LTs) or accelerated life tests (ALTs). However, these approaches are not practical for high-reliability devices which are not likely to fail in experiments of reasonable length. For these devices, LTs or ALTs will end up with a high censoring rate compromising the traditional estimation methods. An alternative approach is to monitor the devices for a period of time and assess their reliability from the changes in performance (degradation) observed during the experiment. In this paper, we present a model to evaluate the problem of train wheel degradation, which is related to the failure modes of train derailments. We first identify the most significant working conditions affecting the wheel wear using a nonlinear mixed-effects (NLME) model where the log-rate of wear is a linear function of some working conditions such as side, truck and axle positions. Next, we estimate the failure time distribution by working condition analytically. Point and interval estimates of reliability figures by working condition are also obtained. We compare the results of the analysis via an NLME to the ones obtained by an approximate degradation analysis.