An Optimal Inspection and Replacement Policy under Incomplete State Information: Average Cost Criterion

Abstract

An optimal Inspection and replacement problem for a discrete-time Markovian deterioration system is investigated. It is assumed that the system is monitored incompletely by a certain mechanism which gives the decision-maker some Information about the exact state of the system. The problem is to obtain an optimal inspection and replacement policy minimizing the expected average cost per unit time over the infinite horizon and formulated as a partially observable Markov decision process. Under some reasonable conditions reflecting the practical meaning of the deterioration, it is shown that there exists an optimal Inspection and replacement policy in the class of monotonic four region-policies.