(s^r)×s^n正规部分因子设计最优区组和折叠反转方案

Optimal Blocking and Foldover Plans of Regular(s^r)×s^n Fractional Factorial Designs

讨论了在同时应用区组和折叠反转技巧时,在(s^r)×s^n正规部分顺子设计中选择最优设计的问题,其中r(≥2)是一个整数,s是一个素数或素数幂,以分区组(s^r)×s^n正规部分因子设计折叠反转的一般结构为基础,给出了扩大区组设计的处理和区组裂区字长型的定义.可以证明,扩大区组设计的处理和区组裂区字长型与区组折叠反转方案无关.对于一个未分区组的初始设计,针对扩大区组设计定义的区组和折叠反转方案有最小混杂当且仅当不考虑区组方案时折叠反转方案有最小混杂;不考虑折叠反转方案时区组方案有最小混杂.

This article considers the problem of choosing optimal designs of regular(s^r)×s^n fractional factorial designs when both blocking and foldover techniques are employed,here r(≥2) is an integer and,s is a prime or prime power.Based on a general decomposition structure of blocked regular(s^r)×s^n fractional factorial designs,the treatment and block split wordlength patterns of the combined blocked design under a general foldover plan are defined. They are proved to be independent of the choice of the block foldover plans.It is shown that, for an initial unblocked design,a pair of blocking and foldover plans has minimum aberration for the combined blocked design if and only if the foldover plan has minimum aberration without consideration of blocking plans and the blocking plan has minimum aberration without consideration of foldover plans.