Optimal replacement policies for multistate deteriorating systems

The authors consider state-age-dependent replacement policies for a multistate deteriorating system. They assume that operating cost rates and replacement costs are both functions of the underlying states. Replacement times and sojourn times in different states are all state-dependent random variables. The optimization criterion is to minimize the expected long-run cost rate. A policy-improvement algorithm to derive the optimal policy is presented. The authors show that under reasonable assumptions, the optimal replacement policies have monotonic properties. In particular, when the failure-rate functions are nonincreasing, or when all the replacement costs and the expected replacement times are independent of state, they show that the optimal policies are only state dependent. Examples are given to illustrate the structure of the optimal policies in the special case when the sojourn-time distribution are Weibull.