产品质量模糊稳健优化设计截集水平解法

Cut set horizontal solution for fuzzy robust optimization design of product quality

综合考虑产品质量设计中的随机不确定性和模糊不确定性,运用概率理论和模糊集合理论,将传统稳健设计思想延展到更一般情形,建立产品质量等级的模糊判定和约束稳健可行域的模糊判别,形成模糊稳健设计的三准则。利用模糊集合理论的分解定理,将复杂的模糊概率运算又回归到常规概率计算,建立了更灵活、更符合工程实际的常规稳健优化数学模型。该模型可根据工程实际,具体设定设计方案的质量水平、合格品率或优质品率,以及设定约束水平、约束概率等关键参数。最后讨论了该模型最优设防水平的求解方法。

The random uncertainty and fuzzy uncertainty have been syntbetieally considered in the quality design of product and u- sing the probability theory and fuzzy set theory to let the traditional thought of robust design be extended to an even more general situation. By establishing the fuzzy judgment of quality grade of product and the fuzzy differentiation of constrained robust feasible region thus formed three criterions of fuzzy robust design. Utilizing the decomposition theorem of fuzzy set theory to let the complicated fuzzy probability operation returned to the conventional probability calculation, more flexible and more accord with the engineering practiced conventional robust optimized mathematical model was established. According to engineering practice this model could concretely enact key parameters of the quality level of designing scheme, qualified product rate or quality product rate and setting the constraint level and the constraint probability etc. Finally the solving method of optimized fortify level of this model has been discussed.