平衡区组设计(BBD)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十四

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

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。作为系列论文的第十四篇,利用拉丁矩阵构造平衡区组设计(BBD),并对平衡区组设计的试验因子、区组因子及其总体均值是否显著的问题进行了统计分析。

Abstract：This series of articles, based on ＂Multilateral Matrix Theory＂ and inspired by the Eastern ho- listic thinking,are trying to provide and improve a whole set of powerful mathematical tools to handle complex multi-target 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 fourteenth paper of the series, the balanced block design （BBD） has been constructed by Latin matrix structure. The sta- tistical analysis has been made of the significance of the balanced block design factor, block factor and total mean value.