An optimal replacement problem using two monotone processes

This paper studies a simple repairable system assuming that the system after repair is not ‘as good as new’ and also the successive working times form a decreasing α -series process and exposing to exponential failure law, while the successive repair times form an increasing geometric process and exposing to Weibull failure law. Under these assumptions we study an optimal replacement policy N under which we replace the system when the number of failures reaches N. We derive an explicit expression of the long-run average cost per unit time and determine an optimal repair replacement policy N* such that the long run average cost per unit time is minimized. Numerical results are provided to support the theoretical results.