Formulation of Opportunity-Based Age Replacement Models with Markovian Arrival Process

In this paper, we consider opportunity-based age replacement models where the arrivals of opportunities follow Markovian arrival process (MAP). The MAP is one of the fairly general point processes capable of representing a wide class of arrival processes including the Poisson process. This work is the first attempt to generalize the arrival process of the preventive replacement opportunities. In particular, this paper focuses on the formulation of long-run average costs for Dekker and Dijkstra's opportunity-based age replacement model (Dekker and Dijkstra 1991) and Zhao and Nakagawa's replacement first and last models (Zhao and Nakagawa 2012) under the assumption that opportunities arise according to a MAP.