正规s^(n-p)部分因子设计最优区组和折叠反转方案

Optimal blocking and foldover plans for regular s^(n-p) designs

讨论了同时应用区组方案和折叠反转技巧时在sn-p正规部分因子设计中选择最优设计的问题,其中s是一个素数或素数幂.以分区组sn-p正规部分因子设计折叠反转的一般结构为基础,给出了组合区组设计的处理和区组裂区字长型的定义.该文证明了,对于已分区组的初始设计,它的组合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,其组合区组设计定义的区组和折叠反转方案有最小混杂的充分必要条件是在不考虑区组方案时折叠反转方案有最小混杂,在不考虑折叠反转方案时区组方案有最小混杂.

This article studies the issue of choosing optimal designs of regular s^n-p fractional factorial designs when both blocking and foldover techniques are simultaneously employed, here s is a prime or prime power. Based on a general decomposition structure, the treatment and block split word length 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 also 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 mini- mum aberration without consideration of blocking plans and the blocking plan has minimum aberration without consideration of foldover plans.