Optimal inspection policy for a second-hand product with a two-dimensional warranty

This paper studies the situation in which a manufacturer acts as a dealer and buys a second-hand product from one customer and sells it with a two-dimensional warranty to another customer. The manufacturer plans to inspect the product during the warranty period to identify and remove hidden defects and hence prevent failure as well as their corresponding cost. We describe a two-dimensional delay time model in which the customer's usage rate affects both the time to defect and delay time. This concept is then used to derive a new class of failure models, namely, the two-dimensional and two-stage failure model. The number and time of inspections are determined to minimize the service cost during the warranty period under periodic and sequential inspection policies. Our approach is illustrated using an example from the automobile industry. A sensitivity analysis evaluates the effect of changes in the parameters of the model. Results indicate that the proposed model can aid the decision-making of a manufacturer, particularly in relation to the effect of customers' usage and the effect of inspection upon the service cost during the warranty period.