对满意度函数变异性的评估——一种蒙特卡罗方法  

Evaluation of Variation of Desirability Function:A Monte Carlo Approach

作　　者：朱鹏飞[1,2] 何桢[1] 

机构地区：[1]天津大学管理学院,天津300072 [2]中国建设银行苏州分行,江苏苏州215021

出　　处：《管理科学》2011年第4期14-21,共8页Journal of Management Science

基　　金：国家自然科学基金(70931004;70871087)~~

摘　　要：在传统满意度函数法的基础上进一步考虑响应曲面模型的预测误差,根据各个预测响应的均值和标准误得到其概率分布,然后引入蒙特卡罗方法模拟出关于预测响应的大量样本,计算出相应的总体满意度值。在此基础上观察满意度的分布形状并分析其统计规律,从而对给定解的概率风险进行评估。随着各个响应的规格界的给定,多响应问题的可行操作域通常被划分成相互分离的子区域,每个子区域分别对应一个(或多个)最优解,对最优解的选取不能简单的根据它所对应满意度值的高低,还应该考虑满意度波动性的大小。算例结果表明,传统的全局最优解虽然满意度最高,但若考虑到预测响应的变异性,它很可能使满意度波动过大从而带来较高的概率风险;而位于稳健可行域中的局部最优解对预测响应的变异相对不敏感,从而更具有应用价值。This study investigates the impact of prediction errors of response surface models on the desirability function. The mean and standard error of predicted response is deduced and then the probabilistic distribution for it is obtained. The Monte Carlo approach is introduced to generate a large number of sample data for each predicted response, and the correspondence desirability value is calculated for each set of sample. Based on this, we can graphically examine the distribution of the overall desirability and analyze the statistical characteristics for it. As a result, the probabilistic risk of the given solution can be evaluated. When specification limits for each response are given, the feasible operating region might be divided into several disjointed areas, with one （or more） optimum point（s） lying in each sub-region. The choice between these optimum solutions can not be based solely on the single desirability value, but also on the variation of the so-obtained desirability. The case example shows that although the global optimum has the highest desirability value, it might cause large variations on the desirability and has a high probabilistic risk if the variations on predicted responses are considered. In contrast, the local optimum lying in the robust feasible region is relatively insensitive to the variability of predicted responses, which makes more practical benefits.

关 键 词：满意度函数 蒙特卡罗仿真 多响应优化 响应曲面法 

分 类 号：F406.3[经济管理—产业经济]