Warranty servicing for discretely degrading items with non-zero repair time under renewing warranty

This paper considers a repair-replacement strategy for a special class of discretely degrading and repairable products under renewing free replacement warranty. Each product may experience N different working states with different exponential hazard functions, before the warranty contract expires. Once the item enters working state i (i = 1, 2, … , N), it can either fail or move to any of the subsequent working states with different probabilities, given that a transition has been made. In the former case, the best rectification action, replacement or minimal repair, regarding the failure status, i.e., the product degradation level at the failure time and the remaining warranty time, should be conducted to put the item into operation. It is assumed that replacement of the faulty item occurs instantly and the product warranty is renewed, but non-zero repair time has been included in the model. We derive the optimal replacement-repair policy to minimize the manufacturer’s expected warranty servicing cost per item sold. The Adomian decomposition method is used to find an analytic approximate solution for a special case with two working states. For N > 2, a simulation based optimization method has been developed to analyze the expected warranty cost. Some numerical examples in each section are given to clearly demonstrate the application of this model.

► We develop a new model to analyze rectification costs for a multi state degrading item under renewing free replacement warranty. ► Adomian decomposition method applied to analytically find the optimal parameters of the model for special cases. ► A simulation based optimization procedure proposed to analyze the warranty cost function for general models. ► Using the methodology provided in this study, enable manufacturers to provide maintenance services for warranted items with minimum possible costs.