An Optimal Inspection Policy for a Markovian Deterioration System with Geometrically Decreasing Lifetime

Abstract

In this paper we consider a Markovian deterioration system with geometrically decreasing lifetime and study a sequential inspection strategy. Our objective is to provide an iterative algorithm to derive an optimal inspection policy that minimizes the expected total long-run average cost per-unit time. We show that as the degree of the deterioration increases, the optimal time interval between two successive inspections becomes shorter and shorter and a control limit rule holds. Also we numerically investigate several properties related to the optimal policy when the number of repairs increases.