Optimal post-warranty replacement policy based on number of product failures for the second-hand product

This paper deals with a post-warranty maintenance model for the second-hand product as follows. The second-hand product of age [Formula: see text], which is assumed to be positive, is purchased with a fixed length of non-renewing warranty, during which the product is given a fixed number of preventive maintenances periodically by the dealer. At each preventive maintenance, the failure rate of the product is adjusted to some extent for the purpose of reducing the likelihood of product failure. At the expiration of warranty, the user starts to self-maintain the product until a pre-determined number of failures occur, at which time the product is replaced by another one. For each post-warranty failure, only a minimal repair is taken to restore the failed product to its previous functioning state. This paper aims to determine an optimal number of post-warranty product failures that minimizes the expected cost rate during the second-hand product’s life cycle. To this end, we derive a formula to evaluate the expected cost rate during the second-hand product’s life cycle by assuming a certain cost structure for maintaining the product during the life-span of the product and determine an optimal number of post-warranty product failures from the user’s perspective. And we provide a numerical example to illustrate our proposed optimal maintenance model by assuming a Weibull failure distribution. The main contribution of this work is to use the number of post-warranty failures to propose a maintenance model for the second-hand product, where the number of failures is in general easier to observe than the failure times.