Superposed Poisson process models with a modified bathtub intensity function for repairable systems

Bathtub-shaped failure intensity is typical for large-scaled repairable systems with a number of different failure modes. Sometimes, repairable systems may exhibit a failure pattern different from the traditional bathtub shape, due to the existence of multiple failure modes. This study proposes two superposed Poisson process models with modified bathtub intensity functions to capture this kind of failure pattern. The new models are constructed by the superposition of the generalized Goel–Okumoto process and power law process (or log-linear process). The proposed models can be applied to masked failure-time data from repairable systems where the modes of collected failure-times are unobserved or unavailable. Bayesian posterior computation algorithms based on the data augmentation method are developed for the inference on the parameters or their functions of the superposed Poisson process models. This study also examines the best model selection among the candidate models in the Bayesian framework and modeling check using the residuals. A practical case study with a data set of unscheduled maintenance events for complex artillery systems illustrates potential applications of the proposed models for the purpose of reliability prediction for the repairable systems.