Maintenance policies for quality improvement with consideration of renewable warranty

In this paper, we consider a renewable warranty policy and propose an optimal maintenance model after the expiration of the warranty. Such a model adopts new warranty during the warranty period and follows a certain type of system maintenance policy during the post warranty period. As for the criteria for optimality, we use the expected cost rate per unit time during the life cycle of the system, which has been frequently used in many existing maintenance models. Based on the cost structure defined for each failure of the system, we formulate the expected cost rate during the life cycle of the system, assuming that a renewable warranty policy is provided to the user during the warranty period. Once the warranty is expired, the maintenance of the system is the user's sole responsibility. New warranty which is subject to two factors, repair time and failure time, is assumed, and its warranty cost incurred during the warranty period is investigated as well. We derive the expected cost rate per unit time during the life cycle of the system on the perspective of the user and obtain the optimal maintenance model following the expiration of the warranty period by minimizing such cost rate. Numerical examples are presented to exemplify the applicability of the methodologies proposed in this paper.