Randomized Replacement Rules which Maximize the Expected Cycle Length of Equipment Subject to Markovian Deterioration

A problem of determining the form of optimal replacement policies is treated. Equipment whose changes of state can be described by a finite Markov chain are considered. The objective of the replacement policy is the maximization of the expected time between replacements while keeping the probabilty of an in-service failure below a specified bound. It is shown that, if the equipment "ages," a replacement policy of simple structure called a randomized control limit rule will be optimal. Such a policy can be determined by linear programming.