Optimal Post-Warranty Maintenance Strategy for the Second-Hand Product

Since the market share of the second-hand product has increased, there is a growing interest among the second-hand product users regarding a self-maintenance strategy after the warranty expires as well as warranty service provided by dealers. In this research, we study an optimal maintenance strategy following warranty expiration for the second-hand product which was purchased at age x with a fixed length of warranty period. During the warranty period, the product is subject to preventive maintenance periodically at a prorated cost while only minimal repair is implemented at each failure by the dealer. After the warranty expires, the second-hand product is maintained for a fixed length of period by the user and is replaced at the first failure after the self-maintenance period. The main goal of this study is to determine an optimal length of maintenance period after the warranty expires. To this end, we derive the expected length of life cycle and formulate the expected total cost incurred during the cycle. We show that existence and uniqueness of the optimal maintenance period which minimizes the expected cost rate per unit time during the second-hand product's life cycle from the user's perspective. Finally, assuming that the life distribution of the product follows Weibull distribution, we present the numerical example for the purpose of illustrating our results and analyzing the effect of relevant parameters on the optimal maintenance period.