具有整体平衡性质的广义正交表的替换构造及其应用  

Replacement Structure and Its Application for Generalized Orthogonal Arrays with the Overall Balance

作　　者：王楠[1] 邹科发[1] 张应山[2] 张燕[1] 王惠婷[1] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]华东师范大学金融与统计学院,上海200241

出　　处：《数学的实践与认识》2015年第10期302-308,共7页Mathematics in Practice and Theory

基　　金：河南省科技厅项目(142300410103);河南省高等学校骨干教师资助计划(2013GGJS-169);许昌市科技局项目(5014)

摘　　要：广义正交表是一种能够保证试验因子的数据分析结论具有再现性的最基本的设计表.试验设计的整体平衡性是关于系统中心、区组因子(可观测的干扰因子)、试验因子(可控因子)、试验误差(未知不可控因子)整体全面思维角度的一种平衡.具有整体平衡性质的广义正交表是在整体全面思维的角度能够保证总体均值、区组因子、试验因子、试验误差标准差的估计具有再现性的设计表.设计表的构造是试验设计的重要问题之一.类比正交表的替换构造方法,提出了一种具有整体平衡性质的广义正交表的一种替换构造方法,并通过算例说明此种构造方法的实用性.Generalized orthogonal array is a kind of the most basic design, which can ensure the data analysis of experimental factors having the reproducibility. Is the overall balance of the design of experiment about the system center, block factor （observable interference factors）, experimental factors （controllable factors）, experimental error （unknown uncontrollable factors） overall thinking Angle of a balance. Generalized orthogonal array with overall balance is the most basic design, which is in the nature of the overall balance in the overall comprehensive thinking Angle to ensure that the overall average, block factor, experiment factors and error estimates of the standard deviation with reproducibility. The structure of the design is one of the important problems of experiment design.Replacing construction method of analogy to the orthogonal arrays, this paper puts forward a kind of generalized orthogonal arrays being in the nature of the overall balance of a replacement method, to illustrate the usefulness of this method by an example.

关 键 词：广义正交表 整体平衡性 正交表 替换构造 

分 类 号：O212.6-4[理学—概率论与数理统计] G642[理学—数学]