以制造商质保成本最小化为目标，考虑使用时间和使用量相关性对产品故障率的影响，利用Copula函数建立二维基本质保优化模型. 在质保期内采用最小维修和非等强度周期预防性维修，优化基本质保期内产品的维修策略. 通过分析基本质保期和价格对产品销量的影响，建立产品利润模型. 考虑制造商提供标准质保和柔性质保等两种基本质保策略，分别优化基本质保期的长度和价格. 案例研究表明：质保成本最小化并不能保证制造商获得最大利润；而增加质保策略的柔性，可以帮助制造商提升顾客满意度、获取更高的利润.
To minimize the warranty cost of manufacturers, a two-dimensional basic warranty optimization model is established based on Copula function. The influence of usage time and usage rate on product failure rate is considered. Moreover, minimal repair and non-equal-strength periodic preventive maintenances are adopted, and the maintenance policies during the warranty period are optimized. By considering the influence of basic warranty period and sale price on product sales, a profit model is established. Considering that manufacturers provide two types of warranty policies, i.e. normative warranty policy and flexible warranty policy, for customers, the basic warranty period and its prices are optimized respectively. The result shows that minimizing warranty cost cannot ensure the maximization of manufacturers’ benefits. However, by increasing the flexibility of warranty policy, customer satisfaction can be promoted, which helps to gain more profits for manufacturers.
［1］SU C, WANG X L. A two-stage preventive maintenance optimization model incorporating two-dimensional extended warranty［J］. Reliability Engineering & System Safety, 2016, 155: 169-178.
［2］YEH C W, FANG C C. Optimal decision for warranty with consideration of marketing and production capacity［J］. International Journal of Production Research, 2015, 53(18): 5456-5471.
［3］PARK M, JUNG K M, PARK D H. A generalized age replacement policy for systems under renewing repair-replacement warranty［J］. IEEE Transactions on Reliability, 2016, 65(2): 604-612.
［4］XIE W, YE Z S. Aggregate discounted warranty cost forecast for a new product considering stochastic sales［J］. IEEE Transactions on Reliability, 2016, 65(1): 486-497.
［5］SHAFIEE M, CHUKOVA S. Maintenance models in warranty: A literature review［J］. European Journal of Operational Research, 2013, 229(3): 561-572.
［6］WU S M, ZUO M J. Linear and nonlinear preventive maintenance models［J］. IEEE Transactions on Reliability, 2010, 59(1): 242-249.
［7］HUANG Y S, HUANG C D, HO J W. A customized two-dimensional extended warranty with preventive maintenance［J］. European Journal of Operational Research, 2017, 257(3): 971-978.
［8］PAN E S, LIAO W Z, ZHUO M L. Periodic preventive maintenance policy with infinite time and limit of reliability based on health index［J］. Journal of Shanghai Jiao Tong University (Science), 2010, 15(2): 231-235.
［9］MOSKOWITZ H, CHUN Y H. A poisson regression model for two-attribute warranty policies［J］. Naval Research Logistics, 1994, 41(3): 355-376.
［10］WANG J T, ZHOU Z, PENG H. Flexible decision models for a two-dimensional warranty policy with periodic preventive maintenance［J］. Reliability Engineering & System Safety, 2017, 162: 14-27.
［11］SHAHANAGHI K, NOOROSSANA R, JALALI-NAINI S G, et al. Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts［J］. Engineering Failure Analysis, 2013, 28: 90-102.
［12］SU C, WANG X L. Modeling flexible two-dimensional warranty contracts for used products considering reliability improvement actions［J］. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2016, 230(2): 237-247.
［13］TANG X S, LI D Q, ZHOU C B, et al. Impact of copulas for modeling bivariate distributions on system reliability［J］. Structural Safety, 2013, 44: 80-90.
［14］JACK N, ISKANDAR B P, MURTHY D N P. A repair-replace strategy based on usage rate for items sold with a two-dimensional warranty［J］. Reliability Engineering & System Safety, 2009, 94(2): 611-617.
［15］HE S G, ZHANG Z M, ZHANG G H, et al. Two-dimensional base warranty design based on a new demand function considering heterogeneous usage rate［J］. International Journal of Production Research, 2017, 55(23): 7058-7072.
