Preventive maintenance with age-reduced nonhomogeneous Poisson process model for a fleet of repairable systems

Planning preventive maintenance (PM) actions for a fleet of repairable systems is not simple due to their complex dependent structure and variability among systems. An optimal PM policy can be established by considering a tradeoff between system reliability and maintenance costs over the lifespan of repairable systems. In this paper, we propose age-reduced nonhomogeneous Poisson process (NHPP) models for doubly-censored (left- and right-censored) or bathtub-shaped recurrent failure data from multiple repairable systems. We apply modeling frameworks of mixed-effects and frailty to the proportional age-reduced NHPP model, of which parameters are estimated by the maximum likelihood (ML) method, except for the improvement factor that is assumed to be known. The proposed models explicitly involve between-system variation through random-effects or frailty, along with a common baseline for all the systems through fixed-effects for non-normal data. Given the estimates for the proposed models, we derive the optimal aperiodic PM policy by considering whole population of repairable systems rather than a single system to reflect practical environments where the PM executes imperfect repairs on same-typed systems following the same schedule in a lump. The optimal policy aims at determining irregular PM check-points and useful lifetime with the objective of minimizing the expected total maintenance cost per unit of time. Analytical results of two real-world examples show prominent applications of the proposed models and methods to doubly-censored or bathtub-shaped failure patterns from a fleet of repairable systems for the purpose of reliability prediction and maintenance optimization.