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.
Highlights
Due to the rapid technological development and fierce competition in the marketplace, it is crucial for manufacturers to make scientific and reasonable decisions on maintenance strategies
Considering the effect of external shocks on products, a 2D preventive maintenance (PM) and replacement strategy is proposed in this paper. e mean cost over the warranty region is minimized by the optimization of the PM interval or the joint optimization of the PM interval and the number of shocks before replacing
Setting N 3, let average cost per minor repair, Cm, change from 4 to 12 by Step 2 and the other product parameters be the same to those in Section 4.1. e optimal strategies (K∗, L∗) and its corresponding mean cost C(3, K∗, L∗) are presented in Table 4 and illustrated in Figure 4. e table and figure indicate that the mean cost increases and the optimal age and usage PM intervals decrease with the increase of Cm
Summary
Due to the rapid technological development and fierce competition in the marketplace, it is crucial for manufacturers to make scientific and reasonable decisions on maintenance strategies. Under the assumption that the failure time of a deteriorating product depends both on its age and a stationary Wiener process, Zheng and Zhou [7] analyzed the warranty servicing costs of three preventive maintenance policies (no inspection, continuous inspection, and periodic inspection) in the Markov decision process framework. Considering the effect of external shocks on products, a 2D PM and replacement strategy is proposed in this paper. E impact of the increase of the product failure rate on shocks and the replacement cost on the optimal PM interval is insignificant. Ck(t): the mean total warranty cost over (0, t), given the number of shocks on the first renew over (0, t) in the case that at least one shock occurs and the product is replaced C(N, K, L): the total mean warranty servicing cost over the two-dimensional rectangle warranty region
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