#orthogonal-designs

本作者一组有关弱相关试验设计之超立方的博客链接，点击即可浏览。 学习极值原理 回归试验设计的质量要素 弱相关试验设计（修订） 介绍正交超立方试验设计表 正交超立方设计的命名约定 用张量积构造正交超立方存在的缺陷 修正一处认识 同 C.D.Lin 等四博士讨论堆叠法构造正交超立方设计问题 同 C.D.Lin 等四博士讨论堆叠法构造正交超立方设计问题(续1) 同 C.D.Lin

1. 回归试验设计的质量要素 试验设计的品质直接关系到试验的结果，因此，对试验设计需要有一些品质要求。 20 世纪初，试验设计创立时，基于区组设计，费歇提出了实验设计应遵循的三个原则：随机化，局部控制和重复。这一思想当今仍然有效。但试验设计与数据处理技术较那时有了重大进展。各种数据处理技术对试验设计的要求不尽相同。根据回归分析技术的特点，回归试验设计应该具有随机性，均衡性和适度稠密三项品质要素。 2.

综 述 极值原理是最小二乘回归的理论基础，因为最小二乘回归是最重要的数据处理工具，也是试验设计的理论基础，研究优化论必须了解极值原理。为以后叙述和应用方便，这里引述一些有关资料，个别地方作了引伸。 受 HTML 语言的限制，符号不够规范，请查各种数学分析教程。 1. 函数的极值原理 1.1 单变量函数的极值 若函数 f(x) 在点x0 的双侧邻域中有定义，对于|x-x0|<δ 内的一切点

一类试验设计表的命名约定 w17h6o w18h0o w19h7o w20h6o w21h7o w22h0o w23h7o w24h7o w25h7o w26h0o w27h6o w28h7o w29h6o w30h0o w31h6o w32h60 w33h5o w34h0o w35h6o w36h6o w37h6o

W36h6o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 13,22,26,12,07,05,14,05,03,11,29,04,18,12,21,08,23,12,02,09,03,33,04, 34,14,03,28,14,16,34,29,04,10,33,07,25,18,01,16,07,03,24,14,02,10,20,

W35h6o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 20,22,12,33,07,31,23,19,07,02,22,14,15,08,26,09,35,01,34,35,28,21,13, 21,21,32,22,23,16,03,34,11,18,35,35,35,31,06,32,29,32,31,31,18,28,35,

W34h0o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 29,19,28,26,34,02,28,03,20,26,30,04,33,30,12,12,25,30,11,12,27,29,03, 27,25,10,19,14,17,05,33,30,34,04,02,28,08,17,16,04,01,20,11,32,12,12,

W33h5o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 18,29,23,10,26,11,18,06,16,23,22,01,19,24,02,33,27,10,32,31,12,29,25, 27,03,12,11,09,14,28,31,30,32,31,11,30,04,10,27,29,31,11,14,18,10,22,

W32h6o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 02,04,09,18,10,20,03,09,20,07,05,05,28,29,06,30,08,21,05,11,29,19,29, 10,27,19,30,32,10,24,11,07,01,08,26,10,31,15,01,10,28,18,09,10,26,16,

W31h6o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 09,29,16,15,18,17,03,18,29,28,30,26,12,15,11,08,26,05,09,04,19,01,26, 16,30,05,13,07,28,06,09,17,02,16,02,01,14,10,25,17,29,23,24,09,05,14,

W30h0o Author : He Shenze (Email：[email protected] ) Columns 1 to 23 02,02,09,12,08,13,07,30,24,11,12,23,12,13,12,30,13,25,21,01,22,15,24, 15,19,19,27,29,06,20,05,21,13,29,29,26,02,14,09,04,29,06,11,06,10,08,

W29h6 Author : He Shenze (Email：[email protected] ) Columns 1 to 23 20,09,09,05,26,23,22,24,16,08,02,01,11,29,04,14,17,19,06,19,26,02,10, 05,29,23,20,15,29,03,29,14,17,11,24,23,26,26,05,27,08,04,21,12,12,13,

W26H0o Author : He Shenze (Email：[email protected] ) 17,18,08,26,22,24,16,25,05,11,19,08,24,23,20,13,11,18,14,01,23,20,17,13,02, 21,13,07,11,15,12,11,15,16,03,01,26,23,01,24,06,21,01,11,17,20,24,10,17,13,

W18H0o Author : He Shenze (Email：[email protected] ) 03,18,14,15,03,16,12,18,13,16,06,06,11,07,07,14,13, 18,09,01,16,07,07,14,02,12,13,04,01,10,06,11,15,03, 05,12,18,12,08,05,05,05,01,03,14,03,12,10,16,17,08,

W17H6o Author : He Shenze (Email：[email protected] ) 07,05,09,02,10,17,16,12,07,16,10,13,02,02,14,10, 11,02,10,04,11,09,05,08,04,02,13,10,03,14,03,01, 17,10,02,08,14,16,08,15,10,01,03,12,15,09,12,09,

贺深泽 (Email：[email protected] ) 整理说明 本文原稿独立作于2005年，发表于《数学的实践与认识》（Vol.39，No. 3, 99-107）。 经查，零相关与弱相关试验设计的概念与国际上一些数学家的 orthogonal Latin hypercube 及 nearly orthogonal Latin hypercube

W22H0o Author : He Shenze 08,10,11,04,06,20,20,22,07,04,17,19,02,16,06,03,07,09,04,18,05, 16,02,13,08,21,13,22,19,12,22,08,09,09,06,09,18,20,21,10,19,20,

附录：堆叠法 贺深泽 (Email：[email protected] ) 1. 前言 Lin 堆叠法的基本功能是从现有较小运行数的正交超立方构造出较大的正交超立方（OHC）。 本文遵循 Lin 的思路，但从正交阵列的可堆叠性质出发，推导出真正基于堆叠模型的方法。 正交超立方的构造是一类 NP Hard 难题，十分困难。随着运行数 n 的增加，构造难度迅速地增加。 置换集 S

W20H6o Author : He Shenze 09,12,10,20,19,08,05,08,15,07,08,14,08,08,14,19,18,01,18, 15,01,15,11,11,02,10,02,03,17,11,04,02,14,08,08,20,15,11, 18,16,17,04,06,10,20,03,10,01,13,19,05,06,09,16,11,07,04,

作者：贺深泽 (Email：[email protected] ) 1. 前 言 C.Devon Lin, Derek Bingham, Randy R. Sitter and Boxin Tang 联合署名在 The Annals of Statistics 上(2010 Vol.38, No.3,1460-1477) 上发表了一篇论文，题为《A new and flexible method