Optimal ordering and replacement policies of a deteriorating system

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 gamma distribution, and it has two failures types, type I failure is repairable, whereas type II failure 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 N th type I failure or the 1st type II failure whichever occurs first. Furthermore, it considers an ordering policy M(0≤M<;N) in which a spare unit is ordered at the time of the M th type I failure or at the time of the 1st type II failure, whichever occurs first. The objective is to derive the long-run average cost rate and then find the optimal two-dimensional policy (N,M) such that the average cost rate is minimized. Finally, a numerical example is provided to illustrate the proposed model.