Optimizing imperfect preventive maintenance in multi-component repairable systems under [formula omitted]-dependent competing risks

Abstract

Existing maintenance optimization models for single-component repairable systems are extensively studied. However, maintenance optimization in multicomponent reparable systems (MCRS) is still a challenging problem, especially when dealing with stochastic dependent (s-dependent) competing risks between components. This paper develops a novel reliability-centered maintenance optimization model for MCRS operating under s-dependent competing risks. The s-dependency is captured by the joint reliability function constructed using Copula method and unknown parameters are estimated by maximum likelihood estimations (MLE). Maintenance strategies are carried out both at components and system levels. At components level, a preventive maintenance (PM) is performed whenever the reliability of the MCRS reaches a given threshold. PM actions are imperfect and modeled using the hybrid hazard rate approach. At system level, the whole system is preventively replaced after a certain number of PM cycles. The objective of the proposed maintenance strategies is to determine the optimal reliability threshold together with the optimal number of PM cycles that minimize the total expected maintenance cost rate in the infinite time horizon. The optimality conditions of the resulting maintenance optimization problem are formally discussed via two propositions. A case study that investigates a ball screw mechanism with multiple components is provided to validate the proposed approaches.