Optimal group preventive maintenance of a system with observable state parameter

Abstract

A group of n independent identical machines with exponential lifetimes is considered. Repair is made simultaneously for all failed machines. It is possible to observe the ‘state parameter', i.e. the number of operating machines. It is proved that for two types of critieria (minimal cost per time unit and maximal return per time unit) the optimal repair policy is of the following type: repair when the number of failed machines reaches some prescribed number .