Optimization of two‐dimensional warranty policy for repairable products based on age and usage, applicable to lemon law conditions

Abstract

AbstractThis paper proposes a new two‐dimensional warranty policy based on two factors—age and usage—that simultaneously incorporates both the warranty period and the refund period for a repairable product with an increasing failure rate. In this policy, the product is warranted by taking into account both its age and usage, and the warranty expires when the product reaches a specified age or a specified usage, whichever comes first. One unique framework of the policy presented in this work is that, under a specific type of lemon law, it defines a refund period during which the manufacturer must either replace the purchased product or offer a full or partial refund to the buyer if the product fails in such a way that meets certain conditions involving either the number of failures or the length of each repair time. The refund period is generally assumed to be shorter than the warranty period, and each failure that occurs after the refund period is only minimally repaired until the termination of the warranty. In this article, we consider both age and usage in warranting a product and we define an age‐based univariate warranty period based on the usage rate. Under a specified cost structure, we evaluate the expected total warranty cost during the age‐based warranty period and determine an optimal age‐based warranty period from the manufacturer's perspective. We also suggest a heuristic method that can be used to obtain an optimal warranty premium for the two‐dimensional warranty policy considered in this study. Finally, relevant numerical examples are provided to analyze the proposed warranty policy.