Optimal maintenance policies during the post-warranty period

This paper develops the optimal periodic preventive maintenance policies following the expiration of warranty. We consider two types of warranty policies to discuss such optimum maintenance policies: renewing warranty and non-renewing warranty. From the user's perspective, the product is maintained free of charge or with prorated cost on failure during the warranty period. However, the users will have to repair or replace the failed product at their own expenses during the post-warranty period. Given the cost structure to the user during the cycle of the product, we derive the expressions for the expected maintenance costs for the periodic preventive maintenance following the expiration of warranty when applying two types of warranty policies and obtain the optimal number and the optimal period for such post-warranty maintenance policies by minimizing the expected long-run maintenance cost per unit time. Explicit solutions for the optimal periodic preventive maintenance are presented for illustrative purposes.