This article obtains some theoretical results on the number of clear two-factor interaction components and weak minimum aberration in an sm-pIVdesign, by considering the number of not clear two-factor interaction comp...This article obtains some theoretical results on the number of clear two-factor interaction components and weak minimum aberration in an sm-pIVdesign, by considering the number of not clear two-factor interaction components of the design.展开更多
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 ...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.展开更多
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...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.展开更多
Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maxi...Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.展开更多
It is useful to know the maximum number of clear two-factor interactions in a 2Ⅲ^[m-（m-k）] design. This paper provides a method to construct a 2Ⅲ^[m-（m-k）] design with the maximum number of clear two-factor inte...It is useful to know the maximum number of clear two-factor interactions in a 2Ⅲ^[m-（m-k）] design. This paper provides a method to construct a 2Ⅲ^[m-（m-k）] design with the maximum number of clear two-factor interactions. And it is proved that the resulting designs have more dear two-factor interactions than those constructed by Tang et al. Moreover, the designs constructed are shown to have concise grid representations.展开更多
基金supported by the China Postdoctoral Science Foundation (20060390169)the Philosophy and Social Science Foundation of China (07CTJ002)+1 种基金the National Natural Science Foundation of China (10671099)Program for New Century Excellent Talents in University(NCET-08-0909)
文摘This article obtains some theoretical results on the number of clear two-factor interaction components and weak minimum aberration in an sm-pIVdesign, by considering the number of not clear two-factor interaction components of the design.
基金partially supportcd by the National Natural Science Foundation of China(Grant Nos.10171051,10301015)the Science and Technology lnnovation Fund of Nankai University.
文摘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.
基金Research supported by the NNSF of China (10301015: 10571093)the SRFDP of China (20050055038)the China Portdoctoral Science Foundation (20060390169)Liu and Zhang's research was also supported by the Visiting Scholar Program at Chern Institute of Mathematics.
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571093,10671099and 10771123)the Research Foundation for Doctor Programme (Grant No. 20050055038)+1 种基金the NaturalScience Foundation of Shandong Province of China (Grant No. Q2007A05)Zhang’s research was also supportedby the Visiting Scholar Program at Chern Institute of Mathematics
文摘Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.
基金Supported by the National Natural Science Foundation of China(No.10301015)
文摘It is useful to know the maximum number of clear two-factor interactions in a 2Ⅲ^[m-（m-k）] design. This paper provides a method to construct a 2Ⅲ^[m-（m-k）] design with the maximum number of clear two-factor interactions. And it is proved that the resulting designs have more dear two-factor interactions than those constructed by Tang et al. Moreover, the designs constructed are shown to have concise grid representations.
基金supported by the Philosophy and Social Science Foundation of China(07CTJ002)the China Postdoctoral Science Foundation(20060390169)the National Natural Science Foundation of China(10671099)
文摘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.
基金supported by the NNSF of China(10826059,10901092)the NSF of Shandong Province of China (Q2007A05)the China Postdoctoral Science Foundation(20090451292)
