Warranty cost analysis for second-hand products under a two-stage repair-or-full refund policy

Abstract

With this paper, we consider an optimal warranty policy for second-hand products based on a two-stage repair-or-full-refund maintenance strategy to determine an optimal length of warranty period from the dealer's point of view. Because replacing failed products may not be an option with second-hand products, we newly introduce in this paper the concept of full refund rather than replacement. We pre-specify a repair time threshold and define the length of maintenance period during which the dealer will maintain the product as the product maintenance cycle. Following this policy, if the product failure cannot be repaired within the repair time threshold during the warranty period, the user receives a full refund and the maintenance cycle ends. Otherwise, the user receives only minimal repairs to the product, and if the dealer does not issue a full refund during the warranty period, the maintenance cycle ends when the warranty expires. Given a certain cost structure charged to the dealer, we derive mathematical formulas to evaluate the expected length of a maintenance cycle and the expected total maintenance cost during the cycle. As a criterion for the optimality of the warranty policy, we utilize the expected cost during the product maintenance cycle to propose the optimal warranty policy. Assuming the power law model for product failures and a two-parameter Weibull distribution for the repair times, we illustrate our proposed warranty policy numerically and conduct sensitivity analysis to study the impacts of several relevant parameters on the optimal warranty policy.