Optimum block replacement policy for a system operating under a random time horizon

In this paper we consider the block replacement policy (BRP) for a system operating over a random time horizon. Under such a policy, a system is replaced by a new one either at failure or at a given time interval. The optimality criterion is the expected total replacements cost. Conditions under which an optimal replacement period exits are given. It is shown that BRP over an infinite time horizon is obtained as a particular case of the present work. A numerical example is given to illustrate the proposed replacement model.