Selection in Product Plan Alternatives Based on PPHoQ and Stochastic Variable
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摘要:
为了以一种有效的方式反映客观环境的复杂性和备选方案工程特性值的分布特征，首先，结合产品规划质量屋（product planning house of quality，PPHoQ）的相关理论，客户代表使用区间型语言短语表征顾客需求的重要性，进而集结顾客需求与工程特性的关联度以及工程特性的自相关度，得到各项工程特性的重要度；其次，通过对备选方案工程特性目标值分布与最优值的差距分析，计算各个备选方案工程特性差距的总体分布期望值；进一步地，引入随机占优度的思想，构建备选方案两两比较的占优度矩阵；最后，依据工程特性的重要度、占优度矩阵和赋值优先关系矩阵，确定各个备选方案的综合评估指数. 将本文方法应用于某颚式破碎机的设计，项目团队确定了该产品的5项顾客需求和5项工程特性，通过基于产品规划质量屋和随机变量的优选方法对拟定的备选方案进行了选择，最终结果验证了所提方法的可行性.
Abstract:To reflect the complexity of real-life situation and to depict the distribution of engineering characteristic (EC) values associated with each alternative in an effective way, firstly, according to the theory of product planning house of quality (PPHoQ), interval linguistic variables are used by the customer representatives to describe their preferences over the customer requirements (CRs). The aggregation of the correlations between CRs and ECs and the autocorrelations of ECs yield the importance degrees of ECs. Secondly, the gaps between the target values and the optimal ones of ECs are analyzed to calculate the expectations of population distributions for alternative plans. Thirdly, the idea of stochastic dominance theory is introduced to construct the dominance matrix via pairwise comparisons between the alternatives. Finally, the comprehensive evaluation indexes of each alternative are determined as per the importance of ECs, the dominance matrix, and the assignment priority matrix. The proposed method is applied in the product development of jaw crushers, in which five CRs and five ECs are determined by the project team, and the alternatives are selected through the house of quality in product plan and stochastic variables. The outcome of the application validates the proposed approach.
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表 1 备选方案目标值与最优值的差距分布
Table 1. Gaps between target values and the optimal ones for alternatives
备选方案 ${ w_1}$ ${ w_2}$ ${ w_3}$ ${ w_4}$ ${ w_5}$ $ {y_1} $ $ N\left( {963,{{25}^2}} \right) $ $ N\left( {179,{9^2}} \right) $ $ N\left( {255,{{12}^2}} \right) $ $ N\left( {138,{5^2}} \right) $ $ N\left( {51781,{{131}^2}} \right) $ $ {y_2} $ $ N\left( {936,{{25}^2}} \right) $ $ N\left( {164,{9^2}} \right) $ $ N\left( {264,{{12}^2}} \right) $ $ N\left( {151,{5^2}} \right) $ $ N\left( {52149,{{131}^2}} \right) $ $ {y_3} $ $ N\left( {931,{{25}^2}} \right) $ $ N\left( {196,{9^2}} \right) $ $ N\left( {252,{{12}^2}} \right) $ $ N\left( {159,{5^2}} \right) $ $ N\left( {51653,{{131}^2}} \right) $ $ {y_4} $ $ N\left( {955,{{25}^2}} \right) $ $ N\left( {168,{9^2}} \right) $ $ N\left( {258,{{12}^2}} \right) $ $ N\left( {145,{5^2}} \right) $ $ N\left( {51839,{{131}^2}} \right) $ $ {y_5} $ $ N\left( {991,{{25}^2}} \right) $ $ N\left( {173,{9^2}} \right) $ $ N\left( {275,{{12}^2}} \right) $ $ N\left( {144,{5^2}} \right) $ $ N\left( {52096,{{131}^2}} \right) $ 
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表 2 各个备选方案差距值的累积概率分布
Table 2. Cumulative probability distribution of gaps for each alternative
期望值 $ {y_1} $ $ {y_2} $ $ {y_3} $ $ {y_4} $ $ {y_5} $ $ {E_{h,1}} $ 0.1557 0.2209 0.2342 0.1723 0.1292 $ {E_{h,2}} $ 0.1781 0.2817 0.1121 0.2558 0.2190 $ {E_{h,3}} $ 0.2418 0.2058 0.2545 0.2292 0.1659 $ {E_{h,4}} $ 0.3004 0.1907 0.1345 0.2211 0.2288 $ {E_{h,5}} $ 0.1995 0.1130 0.2173 0.1908 0.1232
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表 3 工程特性
${w_1} $ 的随机占优关系Table 3. Stochastic dominance with respect to
$ {{w}_1} $ 备选方案 $ {y_1} $ $ {y_2} $ $ {y_3} $ $ {y_4} $ $ {y_5} $ $ {y_1} $ - - - $ \succ $ $ {y_2} $ $ \succ $ - $ \succ $ $ \succ $ $ {y_3} $ $ \succ $ $ \succ $ $ \succ $ $ \succ $ $ {y_4} $ $ \succ $ - - $ \succ $ $ {y_5} $ - - - -
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表 4 产品规划备选方案在各项工程特性上的信息量
Table 4. Information contents of alternatives with respect to engineering characterisic
备选方案 ${ w_1}$ ${ w_2}$ ${ w_3}$ ${ w_4}$ ${ w_5}$ $ {y_1} $ 0.171 - 0.126 - - $ {y_2} $ - - 0.167 - - $ {y_3} $ - - $ \infty $ - - $ {y_4} $ 0.175 - 0.143 - - $ {y_5} $ 0.132 - $ \infty $ - -
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