Optimal warranty policy design for deteriorating products with random failure threshold

With the rapid development of technologies and increasing availability of degradation data, the design of appropriate warranty policy for products subject to performance deterioration has hitherto received more attention in boosting profits and improving the competition of enterprises. In most existing works, a product is considered to have failed and trigger a warranty service when the degradation level exceeds the constant failure threshold. However, the stochastic nature of failure threshold exists in many applications. In this study, firstly, two truncated distributions are employed to model the random failure threshold. Then we propose three types of warranty policies-free replacement, full refund and partial refund, that take into account the random failure threshold based on the degradation model. Under the first policy, the manufacturer’s total expected profit is maximized to determine the optimal price and warranty period, besides these, the prescribed maintenance times can also be obtained under the other two policies. We further compare these warranty policies under random failure threshold characterized by different distributions. Finally, a numerical example is presented along with sensitivity analysis to illustrate and compare the proposed warranty policies, showing that the parameters of degradation model and random failure threshold can lead to different expected profits.