Opportunity-based age replacement: Exponentially distributed times between opportunities

This article gives a full analysis of a component-replacement model in which preventive replacements are only possible at maintenance opportunities. These opportunities arise according to a Poisson process, independently of failures of the component. Conditions for the existence of a unique average optimal control limit policy are established and an equation characterizing the optimal policy and minimal average cost is derived. An important result is that the optimal policy can be described as a so-called one-opportunity-look-ahead policy. Such policies play an important role as heuristics in more general models. It is shown that there is a correspondence with the well-known age-replacement model, which can be considered as an extreme case of the model. Finally, some numerical results are given.