Note—A Replacement Problem using a Wald Identity for Discounted Variables

A fundamental model is presented for determining optimal replacement times for stochastically deteriorating equipment. It is an elementary Markov decision model in which an optimal policy is to replace an item when and only when its operating cost reaches a certain level Wald type identities for discounted random variables are introduced to derive a tractable method for computing these replacement levels. The analysis herein simplifies and corrects earlier work in this area.