An Optimal Replacement Problem of A Semi-Markovian Deteriorating System

Abstract

This paper discusses an optimal replacement problem of a multi-state system when the deterioration of the system state is described by a semi-Markov process. It is assumed that the system has operating costs and replacement costs depending on its states. The problem is to derive a replacement policy which minimizes the expected average cost per unit time over the infinite horizon. Moreover, under some reasonable conditions reflecting the physical and economical meaning of the deterioration, we show that an optimal replacement policy has a monotone structure.