An optimal ordering, inspection and replacement policy for a partially observable Markov process maintenance model with non-readily available spares

This paper investigates an optimal inspection, ordering and replacement policy of a system having dynamics described by a discrete-time Markov process. It is assumed that the decision-maker has partial information of the current system on which to base action selection. To know the exact state through inspection, an additional cost has to be incurred. It is also assumed that spares are not readily available. This problem minimizes the expected total discounted cost over an infinite horizon and it is shown that there exists a four region monotonic optimal policy.