Optimization of Preventive Maintenance and Replacement Strategies for Nonrenewing Two-Dimensional Warranty Products Experiencing Degradation and External Shocks

Abstract

“Vehicle damage insurance” in China, “Protection Plus Mobile Elite” launched by Samsung, “iPhone Apple Care +” offered by Apple, and so on are special warranty services aiming at external shocks. These warranty terms, named accident insurance, exist widely in the marketplace. Considering the effect of external shocks on degradation, a two-dimensional preventive maintenance and replacement strategy for products, sold with a nonrenewing and two-dimensional rectangle warranty service, is proposed in this paper. Under this strategy, preventive maintenance actions are scheduled based on units of age or usage, which occurs first. There is a reduction in the intensity function after a preventive maintenance action. Each shock before the Nth shock causes a failure of the product or an increase in product failure rate. The product is replaced by a new one on the Nth shock if it survives the N − 1 shocks. From the view of manufacturers, the mean warranty servicing cost over the whole warranty region is obtained by using the renewal theory. Based on direct numerical Riemann–Stieltjes integration, an approximation algorithm of the cost is also given. The mean cost is minimized by the optimization of preventive maintenance interval and the number of shocks N. A numerical example is given to illustrate the feasibility of the proposed strategy. The effects of maintenance cost, the arrival rate of the shocks, and other model parameters on the optimal strategy are also investigated numerically.