The factorial design within a conditional model is utilized when the effects of one factor in a factorial experiment hold greater significance under each fixed level of another factor.This paper investigates the gener...The factorial design within a conditional model is utilized when the effects of one factor in a factorial experiment hold greater significance under each fixed level of another factor.This paper investigates the generalized minimum aberration(N,sp)-design,where each factor is s-level,with s being any prime or prime power.Via utilizing the method of complementary designs,the authors explore the design with a pair of conditional and conditioning factors.The proposed approach applies not only to regular designs but also to nonregular designs.Additionally,the findings can be extrapolated to encompass designs under the two pairs conditional model.The findings presented in this paper not only strengthen but also generalize the existing knowledge in this field.展开更多
The objective of this paper is to study the issue of design efficiency for minimum projection uniformity designs. The results show that for orthogonal arrays with strength two, the minimum projection uniformity criter...The objective of this paper is to study the issue of design efficiency for minimum projection uniformity designs. The results show that for orthogonal arrays with strength two, the minimum projection uniformity criterion is a good surrogate for the design efficiency criterion proposed by Cheng, Deng and Tang （2002）.展开更多
Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study m...Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.展开更多
Space-filling designs are widely used in various fields because of their nice space-filling properties.Uniform designs are one of space-filling designs,which desires the experimental points to scatter uniformly over t...Space-filling designs are widely used in various fields because of their nice space-filling properties.Uniform designs are one of space-filling designs,which desires the experimental points to scatter uniformly over the experimental area.For practical need,the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper.Firstly,the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the Type-I code mapping and tripling technique.Secondly,the algorithm of constructing nine-level uniform designs is presented from a three-level base design by the Type-II code mapping and generalized orthogonal arrays.Moreover,relative properties are discussed based on the two code mappings.Finally,some numerical examples are given out for supporting our theoretical results.展开更多
A fundamental and practical question for fractional factorial designs is the issue of optimal factor assignment. Recently, some new criteria, such as generalized minimum aberration, WV-criterion, NB-criterion and unif...A fundamental and practical question for fractional factorial designs is the issue of optimal factor assignment. Recently, some new criteria, such as generalized minimum aberration, WV-criterion, NB-criterion and uniformity criterion are proposed for comparing and selecting fractions. In this paper, we indicate that these criteria agree quite well for symmetrical fraction factorial designs.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12301318 and 12101357Beijing Institute of Technology Research Fund Program for Young Scholars and Natural Science Foundation of Shandong under Grant No.ZR2021QA080。
文摘The factorial design within a conditional model is utilized when the effects of one factor in a factorial experiment hold greater significance under each fixed level of another factor.This paper investigates the generalized minimum aberration(N,sp)-design,where each factor is s-level,with s being any prime or prime power.Via utilizing the method of complementary designs,the authors explore the design with a pair of conditional and conditioning factors.The proposed approach applies not only to regular designs but also to nonregular designs.Additionally,the findings can be extrapolated to encompass designs under the two pairs conditional model.The findings presented in this paper not only strengthen but also generalize the existing knowledge in this field.
基金supported bythe National Natural Science Foundation of China under Grant No.10671080NCET under Grant No.06-672+1 种基金SRFDP under Grant No.20090144110002the Innovation Program Funded by Central China Normal University
文摘The objective of this paper is to study the issue of design efficiency for minimum projection uniformity designs. The results show that for orthogonal arrays with strength two, the minimum projection uniformity criterion is a good surrogate for the design efficiency criterion proposed by Cheng, Deng and Tang （2002）.
基金supported by National Natural Science Foundation of China(Nos.11601195,11601538,11571073)Natural Science Foundation of Jiangsu Province of China(No.BK20160289)+1 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.16KJB110005)Jiangsu Qing Lan Project
文摘Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.
基金supported by the National Natural Science Foundation of China(Nos.12161040,119610271,1701213,11871237)Natural Science Foundation of Hunan Province(Nos.2020JJ4497,2021JJ30550)+2 种基金Scientific Research Plan Item of Hunan Provincial Department of Education(No.19A403)Graduate Scientific Research Innovation Item of Hunan Province(No.CX20211504)the Scientific Research Item of Jishou University(No.Jdy20057)。
文摘Space-filling designs are widely used in various fields because of their nice space-filling properties.Uniform designs are one of space-filling designs,which desires the experimental points to scatter uniformly over the experimental area.For practical need,the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper.Firstly,the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the Type-I code mapping and tripling technique.Secondly,the algorithm of constructing nine-level uniform designs is presented from a three-level base design by the Type-II code mapping and generalized orthogonal arrays.Moreover,relative properties are discussed based on the two code mappings.Finally,some numerical examples are given out for supporting our theoretical results.
基金Supported by the National Natural Science Foundation of China （No.i0441001）, the Key Project of Chinese Ministry of Education （No. i05119）, SRF for R0CS（SEM） （No.[2004]176） and the Nature Science Foundation of Hubei Province. Acknowledgements. The authors cordially thank the referees and Editor for their valuable comments.
文摘A fundamental and practical question for fractional factorial designs is the issue of optimal factor assignment. Recently, some new criteria, such as generalized minimum aberration, WV-criterion, NB-criterion and uniformity criterion are proposed for comparing and selecting fractions. In this paper, we indicate that these criteria agree quite well for symmetrical fraction factorial designs.
