基于权矩阵和正交阵的筛选设计  

A Screening Design Based on Weighting Matrix and Orthogonal Arrays

作　　者：李婉玉 周永道[1] LI Wanyu;ZHOU Yongdao(College of Mathematics,Sichuan University,Chengdu 610000,China)

机构地区：[1]四川大学数学学院

出　　处：《成都师范学院学报》2019年第11期96-102,共7页Journal of Chengdu Normal University

基　　金：国家自然科学基金项目“研发新型材料的试验设计研究”(11471229)

摘　　要：传统的筛选设计,比如正规部分因子设计和Plackett-Burman设计,它们的因子水平仅仅是两水平的。尽管主效应之间是相互独立的,但是不能唯一地识别具有强曲率效应的因子,文章在传统筛选设计的基础上提出来一个新设计OAW。OAW设计由三部分组成,第一部分是由两水平的部分因子设计组成,第二部分是由一些中心点组成,第三部分采用权矩阵和它的翻转矩阵。研究OAW设计列与列之间的相关性以及D效率,研究结果表明,OAW设计的主效应之间是相互独立的,主效应与二次效应之间是相互独立的,主效应与两因素交互效应之间的相关性也有一定规律。OAW设计在某些条件下的D效率比以前提出来的设计的D效率要大。Traditional screening designs such as regular fractional factorial and Plackett-Burman designs employ factors at two levels only.Though they have orthogonal linear main effects,such designs cannot uniquely identify factors with strong curvature effects.Therefore,a new design named OAW was proposed.The new design OAW constructed with three parts.The first part is 2-level factorial design,the second part includes some center points,and the third part adopts weighting matrix and its foldover.Correlations between design columns and D-efficiency were discussed.The results show that the main effects of OAW designs are independent of each other,the main effects are independent of the pure-quadratic effects,and the correlation of two-factor effects and main effects show apparent rules.D-efficiency of OAW designs is more efficient than that of former designs constructed by others.

关 键 词：筛选设计 权矩阵 会议矩阵 相关性 D效率 翻转设计 

分 类 号：O212.6[理学—概率论与数理统计]