Optimal condition-based warranty policy for multi-state products with three guarantees service

ABSTRACT Within a certain period of time after products are sold, many manufacturers offer free repairing, replacing and refunding for the defective products, referred to as three guarantees service. Under the assumption that the working states of the product can be partitioned into three non-overlapping sets and its degradation can be modeled by homogeneous Markov chain, a three-stage and conditioned-based warranty model is proposed. Under the model, the whole warranty period is divided into a compulsory replacement period, a condition-based maintenance period, and a minimal repair period. Over the condition-based maintenance period, depending on the state set that the working state before the failure belongs to, failed products are rectified minimally, imperfectly, replaced by an identical one and the warranty terms are renewed, respectively. Markov process and renewal process theories are used to analyze the failure process and the warranty servicing cost over the whole warranty period. Based on double Riemann sum, a recursive algorithm for finding the optimal partition method of working states and the warranty period is proposed. A numerical example is given to illustrate the validity of the warranty strategy.