Optimal replacement in the proportional hazards model

In this paper, the authors examine a replacement problem for a system subject to stochastic deterioration. Upon failure the system must be replaced by a new one and a failure cost is incurred. If the system is replaced before failure a smaller cost is incurred. The failure of the system depends both on its age and also on values of a diagnostic stochastic process observable at discrete points of time. Cox’s proportional hazards model is used to describe the failure rate of the system. The authors consider the problem of specifying a replacement rule which minimizes the long-run expected average cost per unit time. The form of the optimal replacement policy is found and an algorithm based on a recursive computational procedure is presented which can be used to obtain the optimal policy and the optimal expected average cost.