多响应三水平部分因子试验设计的建模与优化

Modeling and optimization of three-level fractional factorial experiments with multiple responses

针对多响应三水平部分因子试验,当筛选试验中候选变量个数大于试验样本数时,本文提出了一种考虑因子效应原则的建模与优化方法.首先,构建三水平对照试验,并结合二元变量指示器构建Bayesian Lasso模型;其次,根据因子效应原则,分三个阶段逐步更新二元变量指示器的先验信息,并利用变量指示器的后验概率来识别显著性变量,确定模型结构;然后,在此基础上结合贝叶斯抽样技术构建多变量过程能力指数函数,并通过最大化该函数获得最佳的参数设计值;最后,实际案例的结果表明:本文所提方法不仅能够有效地筛选出多响应三水平部分因子试验的显著性变量,而且能够获得最佳的参数设计值.

As for three-level fractional factorial experiments with multiple responses,this paper proposes a modeling and optimization method considering factorial effect principles when the number of candidate variables is greater than the number of experiment samples in the screening experiment.Firstly,a three-level controlled trial is created,and then a Bayesian Lasso model combing binary variable indicators is constructed in this paper based on the factorial effect principles.Secondly,the prior information of the binary variable indicator is gradually updated in three stages.Then,significant variables and the model structure can be identified by the posterior probability of the variable indicator.Thirdly,a multivariate process capability index function is constructed by Bayesian sampling technique,and the optimal parameter value is obtained by maximizing the function.Finally,the results of actual examples reveal that the proposed method not only can effectively screen out significant variables of three-level fractional factorial experiments with multiple responses,but also can obtain the optimal parameter values.