正交平衡区组设计(OBBD)的一种构造方法及其统计分析——处理复杂系统的新思维系列之十五  

A Constructive Method and Its Statistical Analysis of the Orthogonal Balanced Block Design(OBBD)——New Thinking of Dealing with Complex Systems Series Fifteen

作　　者：罗纯[1,2] 王萌[2] 张应山[2] 

机构地区：[1]上海应用技术学院理学院,上海201418 [2]华东师范大学金融与统计学院,上海200241

出　　处：《上海应用技术学院学报（自然科学版）》2013年第1期61-68,共8页Journal of Shanghai Institute of Technology: Natural Science

基　　金：教育部高等学校博士学科点专项基金资助项目(44K55050)

摘　　要：本系列论文基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统多指标问题、非均匀性问题、非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明。作为系列论文的第十五篇,利用正交拉丁矩阵构造正交平衡区组设计(OBBD),并对正交平衡区组设计的试验因子和区组因子及其总体均值是否显著的问题进行统计分析。This series of articles, based on ＂Multilateral Matrix Theory＂ and inspired by the Eastern holistic thinking, are trying to provide and improve a set of powerful mathematical tools to handle multitarget local issues, non-uniformity problems and nonlinear problems of complex system ranging from the whole to the part with rigorous theoretical analysis and proof. As the fifteenth paper of the series, the orthogonal balanced block design （OBBD） has been constructed by orthogonal Latin matrix. The statistical analysis has been made on the significance of the orthogonal balanced block design factor, block factor and total mean value.

关 键 词：拉丁矩阵 正交平衡区组设计 平衡不完全区组设计 方差分析 

分 类 号：N941.4[自然科学总论—系统科学] O212.1[理学—概率论与数理统计]