The optimal replacement model under the warranty policies

This article considers the warranty policies of a repairable system consisting of one component, involving two kinds of the new warranty policies: the free warranty and the pro rata warranty. Assume that the system after repair is not “as good as new”, by using the geometric process, we examine the long-run expected costs under these policies for both consumer costs and manufacturer costs. The explicit expression of the costs can be found. Also, the optimal warranty period is derived analytically or numerically.