THE OPTIMAL REPLACEMENT OF A MARKOVIAN DETERIORATIVE SYSTEM UNDER STOCHASTIC SHOCKS

This paper discusses the optimal replacement of a discrete Markovian d eteriorative system which is subject to random shocks from its environ ment. Besides the inherent deterioration, the system is deteriorated b y the shocks. For the discounted finite and infinite horizon and avera ge objectives, we prove the existence of optimal stationary policies w hich are extended control limit policies. And under a weak condition, the countable physical state set can be gathered to a finite set, whic h offers us great convenience for computing the optimal policies.