Optimal Prophylaxis Policy Under Non-monotone Degradation

Abstract

A stationary server system with observable degradation is considered. An optimization problem for choice of a time to begin a prophylactic repair of the system is being investigated. A mathematical problem is to choose a Markov time on a random process which is optimal with respect to some criterion. A necessary condition for the time to be optimal is such that it determines a unique solution for monotone random processes. For non-monotone processes this necessary condition determines a set of Markov times containing a time of the first fulfilment of the condition (trivial solution), if this set is not empty. The question arises: Is the trivial solution optimal? We show that it depends on parameters of the process and mainly on difference between the hazard rate and the rate of useful output of the system. For Markov processes the following alternative is true: either the trivial time is optimal or there exist no optimal times.