平衡区组正交表的分层叠加技术  

Layered Stack Technology of Balance Block Orthogonal Arrays

作　　者：廖靖宇[1] 杨林[1] 张应山[2] 张明珠[1] 吴亚桢[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》2013年第24期113-122,共10页Mathematics in Practice and Theory

基　　金：教育部高校博士点专项基金(44K55050);河南省基础研究计划项目(132300410322);河南省教育厅科学技术研究重点资助项目(13A110753);许昌市科技计划项目(1106008)

摘　　要：平衡区组正交表是一种类似于正交表的新设计,它相应的区组设计要求相遇平衡、组间平衡和正交性.它是正交表的推广,它可以像正交表一样进行试验设计和数据分析,但试验次数大幅减少.平衡区组正交表的构造技术,也和正交表类似.在正交表的构造技术中,基于矩阵象理论,相关文献,推导出了一个简单的分层叠加技术,对于两个只有一列水平数不一定相同的正交表,先将这两列的水平重新编号,叠加形成一个高水平列,其水平数是原来两个正交表对应列的水平数之和,其它列保持不变分层叠加在一起,就形成新的具有一列高水平的正交表.将证明这种正交表分层叠加技术也适用于平衡区组正交表的构造.最后通过算例验证了这种技术的有效性.Balance block orthogonal array is a kind of the new design similar to the orthog- onat array, its corresponding block design requirements to meet balanced between its levels, balanced between blocks and orthogonality between columns. It is the promotion of orthogonal arrays, it can seem like orthogonal arrays as the experimental designs and data analysis,but the number of experiments is greatly reduced. Balance block orthogonal arrays structure tech- nology, and orthogonal arrays similar. In the orthogonal arrays structure technology, based on the matrix image theory, Pang and Zhang （2001） had deduced, it is a simple layered stack technology. For two orthogonal arrays, each of them has a lot of columns with the same level numbers but only a column whose level number may be not necessarily the same number of other array, the first two columns stack to form a high level column, the level number of columns is corresponding to the the sum of level numbers of two columns, other columns keep the same layers added together, they form a new orthogonal array whose columns have a high level number. This paper will show the orthogonal array layered stack technology can also be applied to balance block orthogonal array structure. Finally, the verified the effectiveness of this technique.

关 键 词：平衡区组正交表 广义正交表 分层叠加技术 

分 类 号：O212[理学—概率论与数理统计]