Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aber-ration criterion has been freque...Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aber-ration criterion has been frequently used; however, for designs with quantitative factors, a polynomial regression model is often established, thus the β-wordlength pattern can be employed to compare different fractional factorial designs. Although the β-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of β-wordlength pattern for four-level designs. These properties can help find better designs with quan- titative factors.展开更多
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
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
<正>Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 o...<正>Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2~r)2~n factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2~r)2~n factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001).展开更多
In constructing two-level fractional factorial designs, the so-called doubling method has been employed. In this paper, we study the problem of uniformity in double designs. The centered L2-discrepancy is employed as ...In constructing two-level fractional factorial designs, the so-called doubling method has been employed. In this paper, we study the problem of uniformity in double designs. The centered L2-discrepancy is employed as a measure of uniformity. We derive results connecting the centered L2-discrepancy value of D（X） and generalized wordlength pattern of X, which show the uniformity relationship between D（X） and X. In addition, we also obtain lower bounds of centered L2-discrepancy value of D（X）, which can be used to assess uniformity of D（X）.展开更多
It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang emplo...It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.展开更多
基金Supported by NSFC(Grant No.11271279)NSF of Jiangsu Province(Grant No.BK2012612)Qing Lan Project
文摘Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aber-ration criterion has been frequently used; however, for designs with quantitative factors, a polynomial regression model is often established, thus the β-wordlength pattern can be employed to compare different fractional factorial designs. Although the β-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of β-wordlength pattern for four-level designs. These properties can help find better designs with quan- titative factors.
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.
文摘<正>Mukerjee and Wu(2001) employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4.In this paper,by introducing a concept of consulting design and based on the connection between factorial design theory and cod- ing theory,we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level (2~r)2~n factorial design to that of its consulting design.Consequently,a general rule for identifying minimum aberration (2~r)2~n factorial designs through their con- sulting designs is established.It is an improvement and generalization of the related result in Mukerjee and Wu(2001).
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.
基金Supported by the National Natural Science Foundation of China(11271147)SRFDP(20090144110002)
文摘In constructing two-level fractional factorial designs, the so-called doubling method has been employed. In this paper, we study the problem of uniformity in double designs. The centered L2-discrepancy is employed as a measure of uniformity. We derive results connecting the centered L2-discrepancy value of D（X） and generalized wordlength pattern of X, which show the uniformity relationship between D（X） and X. In addition, we also obtain lower bounds of centered L2-discrepancy value of D（X）, which can be used to assess uniformity of D（X）.
基金supported by the National Natural Science Foundation of China(Grant Nos.10231030&10571093)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20050055038).
文摘It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.
