Maintenance optimization for second-hand products following periodic imperfect preventive maintenance warranty period

The maintenance policy for a product's life cycle differs for second-hand and new products. Although several maintenance policies for second-hand products exist in the literature, they are rarely investigated with reference to periodic inspection and preventive maintenance action during the warranty period. In this research, we study an optimal post-warranty maintenance policy for a second-hand product, which was purchased at age x with a fixed-length warranty period. During the warranty period, the product is periodically inspected and maintained preventively at a prorated cost borne by the user, while any product failure is only minimally repaired by the dealer. After the warranty expires, the product is self-maintained by the user for a fixed-length maintenance period and the costs incurred during this time are fully borne by the user. At the end of the maintenance period, the product is replaced with a product of the user's choice. This study is focused on the determination of an optimal length for the maintenance period after the warranty expiration. As a criterion for the optimality, we adopt the long-run mean cost during the second-hand product's life cycle from the user's perspective. Finally, our results are analyzed numerically for sensitive analysis of several relevant factors, assuming that the failure distribution follows a Weibull distribution.