Two Simple Control Policies for a Multicomponent Maintenance System

Abstract

Optimal group maintenance policies for a set of M identical machines subject to stochastic failures are considered. The control of the system is not based on the complete age configuration of all components, nor on the number of failed components only. We compromise between these two extreme cases by introducing four possible states for each component: good, doubtful, preventive maintenance is due, and failed. Two types of control policies are considered, both based on the number of doubtful components at component failure epochs. Starting from a general model with general (but identical) lifetime distributions for the individual components, we introduce an approximate model in which the four possible states are identified with certain age intervals for each individual component. The sojourn times in the good and the doubtful state are supposed to be exponentially distributed. For this resulting approximate model, explicit expressions are derived for various performance measures, like the time to system replacement and the average costs per unit time. By making use of the results obtained for the approximate model several approximations for the performance measures of the original model are presented. Validation of these approximations is performed by simulation.