Determination of optimal post-warranty variable maintenance period for repairable second-hand product based on mean residual life

Abstract

Due to the increased transactions of second-hand products in the market, the optimization of maintenance strategy for the second-hand product has become very important issue to attract a great attention from many researchers of late. This paper proposes a new post-warranty strategy with a variable self-maintenance period for the second-hand product, assuming that the product is replaced by another one on the first failure following a fixed length of post-warranty self-maintenance period. During the non-renewing 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. The main goal of this study is to determine an optimal length of post-warranty self-maintenance period which minimizes the expected cost rate per unit time during the product’s life cycle from the user’s perspective. This approach considers not only the periodic preventive maintenance during the warranty period, but also the remaining life distribution of the product after the warranty expires, which is the significant difference of this work from many existing maintenance policies. For this purpose, we formulate the expected length of life cycle and evaluate the expected total cost incurred during the life cycle of the second-had product which is purchased at the age of $\mathit{x}(>0).$ The existence of the optimal self-maintenance period is proved analytically under mild conditions and the proposed maintenance model is compared with an existing model with regard to the expected cost rate. Finally, assuming that the life distribution of the product follows a Weibull distribution, the effect of relevant parameters on the optimal self-maintenance period is analyzed numerically.