Abstract: Complex products, such as vehicles and large equipment, are usually provided with a two-dimensional warranty policy. A two-dimensional warranty region is defined by an age limit and a cumulative usage limit. When the optimal two-dimensional warranty policy is designed, from the perspective of the manufacturer, warranty cost is more concerning. However, from the perspective of customers, they are more concerned about the available warranty region according to the usage rate, which leads to various perceptions of the same two-dimensional warranty policy. Due to competition, the manufacturer is motivated to provide an attractive warranty policy for customers with heterogeneous usage rates, to increase the customer’s satisfaction with after-sales and promote sales amount. Therefore, to satisfy the demand of customers for heterogeneous usage rates, a flexible two-dimensional warranty menu design method based on customers’ usage rates is proposed from the perspectives of both the manufacturer and customer.
Firstly, the expected warranty cost of the proposed flexible two-dimensional warranty menu is established based on the assumption of minimal repair under the warranty period. A non-homogeneous Poisson process is modeled to the expected number of warranty claims during the two-dimensional warranty region. Meanwhile, to describe the attractiveness of the warranty region for customers with heterogeneous usage rates, an attractiveness index model for the flexible two-dimensional warranty menu is proposed, which is established based on the available warranty region.
Secondly, both a uniform division strategy and the optimal division strategy for designing the flexible two-dimensional warranty menu are proposed, which maximizes the total expected attractiveness index for customers with a given total expected warranty cost. Design principles to implement the flexible two-dimensional warranty menu are given, and the necessary conditions for obtaining the optimal nominal usage rate and dividing usage rate are discussed. The design procedures for designing a two-dimensional warranty menu are summarized.
A case study of an automobile manufacturer is proposed to illustrate the proposed method, and a sensitivity analysis of the effects of key parameters on the optimal two-dimensional warranty menu is conducted. The findings indicate that the optimal values of uniform division strategy and the optimal values of optimal division strategy for designing the flexible two-dimensional warranty menu are approximate. When the mean value of customers’ usage rate increases, the optimal nominal usage rates of the flexible two-dimensional warranty menu rise. When the variance of customers’ usage rate increases, the total expected attractiveness index for the optimal flexible two-dimensional warranty menu decreases.
The paper considers a flexible two-dimensional warranty menu design considering the heterogeneous usage rates of the customers. An attractiveness index model for the flexible two-dimensional warranty menu is established to describe the various perceptions of the two-dimensional warranty policy for customers with different usage rates. The expected warranty cost of the proposed flexible two-dimensional warranty menu is proposed from the perspective of the manufacturer. Meanwhile, a uniform division strategy and the optimal division strategy for designing the flexible two-dimensional warranty menu are proposed. Design principles and the necessary conditions for obtaining the optimal nominal usage rate and dividing the usage rate are discussed. Through a case study of an automobile manufacturer implementing a flexible two-dimensional warranty menu design, the effectiveness of the proposed method is verified.

Key words: warranty menu, two-dimensional warranty policy, usage rates, attractiveness index

摘要： 对于汽车和工程机械等复杂产品而言,往往具有二维质保策略,包括使用时间和累计使用量两个维度。对于制造商而言,质保成本是质保策略设计的重要内容;而对于用户而言,更关注其使用率下有效的质保面积。这导致了不同使用率用户对二维质保策略感知的差异性。为满足不同使用率用户的个性化需求,本文提出了一种基于用户使用率的柔性二维质保菜单设计方法。首先,基于质保期内失效的最小维修假设,建立了柔性二维质保菜单成本模型。从用户视角,构建了不同使用率用户的二维质保策略吸引力指数模型。其次,分别考虑均匀分组策略和最优分组策略,建立了相应的柔性二维质保菜单最优设计方法,并给出了一般性设计准则和最优解条件。最后,通过汽车柔性二维质保菜单设计案例与敏感性分析验证了所提方法的有效性。

关键词: 质保菜单, 二维质保策略, 使用率, 吸引力指数