广义正交表和正交表的裂区试验设计法的比较  

Comparison of Split Plot Experiment Design Method Based on Orthogonal Arrays and Generalized Orthogonal Arrays

作　　者：杨林[1] 吴亚桢[1] 廖靖宇[1] 张应山[2] YANG Lin WU Ya-zhen LIAO Jing-yu ZHANG Ying-shan(School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China School of Finance and Statistics, East China Normal University, Shanghai 200241, China)

机构地区：[1]许昌学院数学与统计学院,河南许昌市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》2017年第10期191-208,共18页Mathematics in Practice and Theory

基　　金：教育部高等学校博士学科点专项基金资助(44k550500);国家自然科学基金(11101381);河南省高等学校青年骨干教师基金资助(211GGJS-182);许昌市科技计划基金资助(1106008)

摘　　要：裂区试验设计方法是在正交表的基础上进行的.根据试验设计的数据分析结论要求具有再现性这一原理,将证明这种裂区试验设计法要有条件的使用才是合理的.由于广义正交表是保证设计表具有再现性的基本设计表,根据广义正交表来研究这种裂区试验设计方法的合理性.研究结果显示在裂区试验设计法对应的设计表是广义正交表,并且相应的数据分析方法采用广义正交表的数据分析方法时,才能保证其数据分析结论具有客观一致性和可重复再现性.The method of experimental design for split-plot was conducted on the basis of the orthogonal arrays. According to the requirements of the principle of reproducibility of the design experiment data analysis, this paper proposes that it is reasonable for the usage of the method of experimental design for split-plot under some conditions. Since the generalized orthogonal array is a basic design array of reproducibility, the rationality of the method of experimental design for split-plot will be studied in the present paper. The results show the corresponding array of the method of experimental design for split-plot is generalized orthogonal arrays. In addition, if the corresponding data analysis method using data analysis method of generalized orthogonal arrays, it can ensure that the conclusion of data analysis is objective consistent and repeatable reproducibility.

关 键 词：广义正交表 裂区法 自由函数模型 最小二乘无偏估计 方差分析 

分 类 号：O212.6[理学—概率论与数理统计]