An optimal maintenace policy of a discrete time markovian deterioration system

Abstract This paper investigates an optimal inspection and replacement problem for a discrete time Markovian deterioration system. It is assumed that the state of the system cannot be identified without inspection. The problem is to determine an optimal inspection and replacement policy which minimizes the expected long-run discounted cost and is formulated as a semi-Markov decision process. Under some conditions reflecting the practical meaning of deterioration, some structural properties of an optimal policy are obtained.