Two-stage failure modeling and optimal periodic inspection policy during the extended warranty period

Abstract

ABSTRACTThe increased complexity of products and failure-induced costs add more pressure on the dealers of extended warranty (EW) contracts. In such conditions, conducting periodic inspection over the EW time-span may provide an opportunity to identify and repair defects before product failure. In this study, for a product with a two-stage failure process, the delay time model is applied to derive the failure process of the product. Considering a periodic inspection policy, the effects of identifying and removing defects on the failure process of the product and its corresponding cost are modeled. Then, a mathematical optimization model is derived to minimize the expected servicing cost for the dealer over the EW period. In the presented model, the number of inspections is assumed to be the dealer’s decision variable. Adopting a real case study from the literature, a numerical example is presented to clarify the model. Moreover, an extensive sensitivity analysis is conducted to study the effect of parameters on the optimal solution. The results show that considering periodic inspection may help pinpoint and remove defects, reduce failures, and minimize the expected servicing cost for the dealer.