A study of the optimal use period and number of minimal repairs of a repairable product after the warranty expires

Abstract

The two-phase warranty models for repairable products are considered. We define the time interval [0, W] as the first phase and the time interval (W, T + W] as the second phase. The products have two types of failures: type I failures (minor failures) and type II failures (catastrophic failures). In the model, type I failures are removed by minimal repairs in the first and the second phases, and type II failures are removed by the replacements in the first phase. If type II failures take place in the second phase, because the type II failures (catastrophic failures) occur in the second phase, catastrophic failures will incur a very large repair cost for the buyer. So, we suppose that the life of products will be ended, that is the buyer will buy another new product. The process of buying a new product is conducted at time T + W, upon type II failures, or the nth of type I failures, whichever occurs first. Whenever each replacement takes place, the spare is ordered, and then delivered. Therefore, the lead time is considered. In this paper, we consider three warranty and maintenance models for seller, buyer and the society. Our objective here is to obtain the optimal minimal repairs n* and use time limit T* when the long-run average cost of society is the smallest. A numerical example is provided.