Design and optimization of warranty period of new products with two-parameter degradation
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摘要:
由于新研产品缺乏外场故障数据和历史保修索赔记录，难以开展科学合理的质保成本预测及质保期优化。考虑到产品不同性能参数退化过程之间的相互影响，提出了一种基于Copula理论的双参数退化型新研产品质保期设计与优化方法。根据实验室加速退化试验数据建立产品单参数性能退化模型，采用Copula方法量化退化过程之间的相关性，同时考虑产品在外场的动态运行环境，给出其外场可靠性模型。采用维修改善因子模型量化维修过程中的不完美维修情形，并基于蒙特卡罗仿真计算产品的预计失效数，建立质保成本模型。在此基础上，利用Glickman-Berger模型量化质保期对产品销售量的影响，构建以制造商利润最大化为目标的质保期优化模型。以某型电子组件为例，开展产品质保期设计优化与敏感性分析，验证了模型的有效性和适用性。
Abstract:Due to the lack of outfield failure data and historical warranty claim records of new products, it is difficult to carry out scientific and reasonable warranty cost prediction and warranty period optimization. Considering the interaction between the degradation processes of different product performance parameters, this paper proposed a method for the design and optimization of the warranty period of new products with two-parameter degradation based on Copula theory. Firstly, a single parameter performance degradation model was established according to the laboratory accelerated degradation test data. Copula theory was used to quantify the correlation between degradation processes. In addition, the outfield reliability model was given by quantifying the dynamic operating environment of the outfield. Secondly, the maintenance improvement factor model was used to quantify the imperfect maintenance situation in the process of maintenance, and the Monte Carlo simulation was employed to calculate the predicted number of product failures. Moreover, the warranty cost model was established. Then, the Glickman-Berger model was used to quantify the impact of the warranty period on product sales, and an optimization model of the warranty period was constructed to maximize the manufacturer’s profit. Finally, by taking a certain type of electronic component as an example, the design and optimization of the warranty period of products and sensitivity analysis were carried out to verify the validity and applicability of the model.
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图 1 两性能参数退化过程失效机制
Figure 1. Two performance parameter degradation process failure mechanism
图 2 两性能退化型产品不完美维修策略
Figure 2. Imperfect maintenance strategy for products with two performance parameter degradation
图 3 两性能退化型产品的预计失效数仿真算法流程图
Figure 3. Flow chart of simulation algorithm for predicted number of failures of products with two performance parameter degradation
图 6 两参数退化型产品失效概率密度函数
Figure 6. Failure probability density function of products with two-parameter degradation
图 7 第1次维修前两参数退化型产品可靠度函数
Figure 7. Reliability function of products with two-parameter degradation before first maintenance
表 1 常见的二元Copula函数
Table 1. Common binary Copula functions
Copula函数 分布函数$ C({u_1},{u_2},\theta ) $ Clayton $ {({u_1}^{ - \theta } + {u_2}^{ - \theta } - 1)^{ - \frac{1}{\theta }}} $ Frank $ - \dfrac{1}{\theta }\ln \left( {1 - \dfrac{{\left( {1 - {{\text{e}}^{ - \theta {u_1}}}} \right)\left( {1 - {{\text{e}}^{ - \theta {u_2}}}} \right)}}{{1 - {{\text{e}}^{ - \theta }}}}} \right) $ Gumbel $\exp \left\{ { - {{\left[ {{{\left( { - \ln {u_1}} \right)}^\theta } + {{\left( { - \ln {u_2}} \right)}^\theta }} \right]}^{{1 \mathord{\left/ {\vphantom {1 \theta }} \right. } \theta }}}} \right\}$ 
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表 2 退化模型参数表
Table 2. Parameters of degradation model
退化参数 ak bk σk 功率 6.873 9 −4 639.611 9 0.087 6 噪声 18.229 8 −9 230.483 6 0.082 4
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表 3 Copula函数选取
Table 3. Copula function selection
Copula参数 θ AIC 排序 Gumbel Copula 8.370 1 −36 317 2 Clayton Copula 10.721 2 −23 038 3 Frank Copula 35.701 4 −39 081 1
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表 4 制造商利润模型相关参数表
Table 4. Parameters of manufacturer’s profit model
参数 数值 来源 参数 值 来源 p 6 假设 k1 1.2 假设 CM 2 假设 k2 2 假设 CF 0.28 假设 $ \gamma $ 1.2 假设 CA 0.35 假设 $ \eta $ 0.8 假设
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