(An) optimal age replacement policy for an equipment monitored by a stochastically failing indicator

Abstract

In this study, we present an age replacement policy for the system composed of a single equipment and an indicator, where the state of the equipment (good or failed) is monitored by the indicator attached to it and both equipment and indicator are subject to stochastic failures. Such failures are assumed to cause stochastic system charges associated with either the decision of preventive maintenance or failure replacement. In addition, system-down cost due to undetected failures is assumed to be incurred. Based on these cost informations, a long-run expected average cost function is derived by use of renewal theory. Then, some numerical examples are treated to obtain the optimal system replacement time by a search method, at which the long-run expected average cost is minimized.