非正规正交设计的分辨度及其应用  

Resolution of nonregular design and its applications

作　　者：陈雪平[1,2] 陈绚青[2] 盛永健 林金官[1] 

机构地区：[1]东南大学数学系,南京211189 [2]江苏理工学院数理学院,常州213001

出　　处：《东南大学学报（自然科学版）》2015年第2期413-416,共4页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11301073;11401094);教育部博士点专项基金资助项目(20120092110021);江苏省自然科学基金资助项目(BK20141326);江苏省普通高校研究生科研创新计划资助项目(2014KYZZ0068);东南大学优秀博士学位论文基金资助项目(YBJJ1444)

摘　　要：为实现非正规正交设计的最优选择,提出了一种基于矩阵象的广义分辨度指标.首先,定义了高阶交互作用之间的混杂度量值,其计算不依赖于水平数的选取,不仅适用于等水平正交设计,还适用于混合水平正交设计;然后,替换广义方差分析模型中的混杂度量值,得到了一个非正规正交设计的广义分辨度指标,满足水平置换不变性.实例分析结果表明,所提的广义分辨度对非正规正交设计具有较好的区分能力,可实现对非正规正交设计的排序和最优选择.由不同水平上因子的投影频数分布可知,该广义分辨度能够反映出设计点在整个空间中的均匀性,从而建立了广义分辨度准则和均匀性的联系.To realize optimal selection for nonregular orthogonal designs,a generalized index of resolution based on matrix images is proposed. First,the measure of confounding betw een high-order interactions is defined. The confounding values do not depend on the numbers of levels. Hence,this measure can be applied to both the orthogonal designs with fixed-levels and those with mixed-levels.Then,by substituting the confounding values in generalized models of analysis of variance,a generalized index of resolution for nonregular orthogonal designs is obtained,which satisfies the property of coding invariant. The results of the real data analysis demonstrate that the proposed generalized resolution has good classification capacity and can be used for ranking and optimally selecting nonregular orthogonal designs. Moreover,from the distribution of the projected frequencies on different levels,it is show n that the generalized resolution can reflect the uniformity of the design points in overall space,thus the relationship betw een the generalized resolution criterion and uniformity is established.

关 键 词：正交设计 工业设计 分辨度 混杂 矩阵象 

分 类 号：O212.6[理学—概率论与数理统计] TP391[理学—数学]