Optimal post-warranty maintenance policy with repair time threshold for minimal repair

In this paper, we consider a renewable minimal repair–replacement warranty policy and propose an optimal maintenance model after the warranty is expired. Such model adopts the repair time threshold during the warranty period and follows with a certain type of system maintenance policy during the post-warranty period. As for the criteria for optimality, we utilize 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 minimal repair–replacement warranty policy with the repair time threshold 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. The life cycle of the system is defined on the perspective of the user and the expected cost rate per unit time is derived in this context. We obtain the optimal maintenance policy during the maintenance period following the expiration of the warranty period by minimizing such a cost rate. Numerical examples using actual failure data are presented to exemplify the applicability of the methodologies proposed in this paper.