2m-pⅣ设计的弱最小低阶混杂与最多纯净两因子交互效应

纯净准则和最小低阶混杂准则是选择部分因析设计的两个重要准则.通过研究纯净两因子交互效应的个数,证明了某些2m-p设计具有弱最小低阶混杂,并给出了2m-p设计具有弱最小低阶混杂并包含最多纯净两因子交互效应的一些条件.同时给出了几个弱最小低阶混杂2m-p设计的例子,并构造了两个非同构的弱最小低阶混杂213-6设计.     

利用2Ⅳ^m-p设计的纯净两因子交互效应个数判断低阶混杂

根据纯净两因子交互效应的数量证明某些2Ⅳ^m-p设计在一定条件下具有弱最小低阶混杂，并且给出了一组既具有弱最小低阶混杂又包含最大数量纯净两因子交互效应的2Ⅳ^m-p设计．     

2_(IV)~(m-p)设计的弱最小低阶混杂与最多纯净两因子交互效应

纯净准则和最小低阶混杂准则是选择部分因析设计的两个重要准则.通过研究纯净两因子交互效应的个数,证明了某些2_(IV)~(m-p)设计具有弱最小低阶混杂,并给出了2_(IV)~(m-p)设计具有弱最小低阶混杂并包含最多纯净两因子交互效应的一些条件.同时给出了几个弱最小低阶混杂2_(IV)~(m-p)设计的例子,并构造了两个非同构的弱最小低阶混杂2_(IV)~(13-6)设计.     

利用2m-pⅣ设计的纯净两因子交互效应个数判断低阶混杂

根据纯净两因子交互效应的数量证明某些2m-pⅣ设计在一定条件下具有弱最小低阶混杂,并且给出了一组既具有弱最小低阶混杂又包含最大数量纯净两因子交互效应的2m-pⅣ设计.     

一类包含最大数量纯净两因子交互效应的2IV^m-p设计

2IV^m-p设计包含纯净两因子交互效应的个数是衡量该设计优良性的重要标准之一．本文证明了某些最小低阶混杂的2IV^m-p设计包含最大数量的纯净两因子交互效应；并在文章的末尾给出了一类既具有最小低阶混杂又包含最大数量纯净两因子交互效应的2IV^m-p设计．     

一类包含最大数量纯净两因子交互效应的2Ⅳm-p设计

2Ⅳm-p设计包含纯净两因子交互效应的个数是衡量该设计优良性的重要标准之一.本文证明了某些最小低阶混杂的2Ⅳm-p设计包含最大数量的纯净两因子交互效应;并在文章的末尾给出了一类既具有最小低阶混杂又包含最大数量纯净两因子交互效应的2Ⅳm-p设计.     

2IVm- p设计的弱最小低阶混杂与最多纯净两因子交互效应

纯净准则和最小低阶混杂准则是选择部分因析设计的两个重要准则. 通过研究纯净两因子交互效应的个数, 证明了某些2_IV^{m- p}设计具有弱最小低阶混杂, 并给出了2_IV^{m- p}设计具有弱最小低阶混杂并包含最多纯净两因子交互效应的一些条件. 同时给出了几个弱最小低阶混杂2_IV^{m- p}设计的例子, 并构造了两个非同构的弱最小低阶混杂2_IV^{m- p}设计.     

某些包含最多纯净两因子交互效应2_Ⅲ~(m-(m-k))设计的一种构造方法(英文)

本文给出了构造包含最多纯净两因子交互效应2Ⅲm-(m-k)设计的一种方法.对于某些设计参数m和k,验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al.(2002)所构造的设计.并且所构造的设计都给出了格子点表示.     

某些包含最多纯净两因子交互效应2m-(m-k)Ⅲ设计的一种构造方法

本文给出了构造包含最多纯净两因子交互效应2m-(m-k)Ⅲ设计的一种方法.对于某些设计参数m和k,验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al.(2002)所构造的设计.并且所构造的设计都给出了格子点表示.     

某些包含最多纯净两因子交互效应$2_{\rm{III}}^{m-(m-k)}$设计的一种构造方法

本文给出了构造包含最多纯净两因子交互效应$2_{\text{III}}^{m-(m-k)}$设计的一种方法.对于某些设计参数$m$和$k$, 验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al. (2002)所构造的设计. 并且所构造的设计都给出了格子点表示.     

Weak minimum aberration and maximum number of clear two-factor interactions in 2_(IV)~(m-p) designs

Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2IVm-p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2IVm-p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm-p designs are provided for illustrations and two non-isomorphic weak minimum aberration 2IV13-6 designs are constructed at the end of this paper.     

Weak minimum aberration and maximum number of clear two-factor interactions in 2m-p Ⅳ designs

Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2m-p Ⅳ designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs.And some conditions are provided, under which a 2m-p Ⅳ design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time.Some weak minimum aberration 2m-p Ⅳ designs are provided for illustrations and two nonisomorphic weak minimum aberration 213-6 Ⅳ designs are constructed at the end of this paper.     

Weak minimum aberration and maximum number of clear two-factor interactions in $$2_{IV}^{m - p} $$ designs

Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration designs are provided for illustrations and two nonisomorphic weak minimum aberration designs are constructed at the end of this paper.     

A NOTE ON 2_(IV)~(m-p) DESIGNS WITH THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS

In this article, the authors obtain some theoretical results for 2_(IV)~(m-p) designs to have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2_(IV)~(m-p) designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration.     

A NOTE ON 2IVm-p DESIGNS WITH THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS

In this article, the authors obtain some theoretical results for 2_IV^m-p designsto have the maximum number of clear two-factor interactions by considering the number of two-factor interactions that are not clear. Several 2_IV^m-p designs with the maximum number of clear two-factor interactions, judged using these results, are provided for illustration.     

ON WEAK MINIMUM ABERRATION AND NUMBER OF CLEAR TWO-FACTOR INTERACTION COMPONENTS IN s_Ⅳ～(m-p) DESIGNS

This article obtains some theoretical results on the number of clear two-factor interaction components and weak minimum aberration in an s_Ⅳ～(m-p) design,by considering the number of not clear two-factor interaction components of the design.