Optimal replacement policy for a semi-Markov shock model

Abstract

We examine a failure model for a system subject to a sequence of randomly occuring shocks. A shock is any perturbation to the system which causes a random amount of damage to the system. Any of the shocks can cause the system to fail at shock times. The amount of damage at each shock is a function of the sum of the magnitudes of damage caused from all previous shocks. The times between shocks form a sequence of independent and identically distributed random variables. The system must be replaced upon failure at some cost but it also can be replaced before failure at a lower cost. The goal of this research is to investigate optimal replacement policies using the long-term expected cost per unit time criterion. The optimal replacement policy is characterized under appropriate regularity conditions and then an algorithm for finding the optimal policy is developed. Finally, comparisons are made between our algorithm and those currently available.