Optimal minimal-repair and replacement problem of discrete-time Markovian deterioration system under incomplete state information

Abstract

Abstract In this paper, we investigate an optimal minimal-repair and replacement problem of a discrete-time Markovian deterioration system. It is assumed that the system is partially observable through a certain monitoring mechanism which yields a signal relating probabilistically to the exact level of its deterioration. The problem is to find an optimal minimal-repair and replacement policy of minimizing the expected total discounted cost over the infinite horizon. It is formulated as a Markov decision process whose state contains probability distribution of deterioration level of the system. Introducing the likelihood-ratio ordering between the probability distributions, we show that, under some reasonable assumptions, both of the optimal cost function and the optimal policy have monotone properties with respect to this ordering. This is an extension of the past studies on the time-based maintenance problems and the condition-based maintenance problems for the perfectly observable system.