Optimal opportunity-based age replacement policies in discrete time

This paper focuses on discrete-time opportunity-based age replacement models with replacement first and last disciplines, where the expected cost model under each discipline can be further classified into six cases by taking account of the priority of multiple replacement options. We characterize several optimal opportunity-based age replacement policies minimizing the relevant expected costs. Also, we relax assumptions on the deterministic priority and introduce the probabilistic priority to unify six discrete-time opportunity-based age replacement models with deterministic priorities under each discipline. In numerical illustrations, we give a case study to schedule the preventive replacement plan for pole air switches in a Japanese power company and compare all the optimal scheduled preventive replacement times with replacement first and last disciplines.