Computation of optimal policies in replacement models

The problem of optimal replacement for a deteriorating system, subject to inspection at discrete points in time, is considered. It has been established that the optimal replacement policy is of a control-limit type and is fully determined by the knowledge of the hazard function and the associated optimal expected average cost per unit time. Cox's proportional hazards model (PHM) is used to describe the failure rate of the system. Fully parametric specification in the PHM is considered and the analysis is based on the method of maximum likehood. A recursive computational procedure is presented which can be used to obtain the optimal replacement policy and the expected average cost. The classical age-replacement problem is identified as being a special case of the problem discussed.