Collaborative Optimization of Replacement and Spare Ordering of a Deteriorating System with Two Failure Types

Abstract

This paper proposes a model to find optimal ordering and replacement policies for a deteriorating system. Assume that the life time of system has a normal distribution, and it has two failures types, typeⅠfailure is repairable, whereas typeⅡfailure is catastrophic which leads to replacement. A replacement policy N is adopted by which the system will be replaced by an identical new one if available at the time following the Nth typeⅠfailure or the 1st typeⅡfailure whichever occurs first. Furthermore, it considers an ordering policy M in which a spare unit is ordered at the time of the Mth typeⅠfailure or 1st typeⅡfailure, whichever occurs first. The objective is to derive the long-run average cost rate and then find the optimal policy (N,M) such that the average cost rate is minimized. Finally, a numerical example is provided to illustrate the proposed model.