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A Modern Theory of Factorial DesignsMinimum Aberration Designs for Mixed Factorials

A Modern Theory of Factorial Designs: Minimum Aberration Designs for Mixed Factorials [Extension of the ideas in Chapters 3 and 4 to designs with factors at different numbers of levels is the focus of this chapter. The important special case of mixed two- and four-level designs is first discussed. An extension of the minimum aberration criterion is considered. More generally, designs with one factor at sr levels and n factors at s levels, or one factor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ s^{r_1 }$$\end{document} levels, a second factor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ s^{r_2 }$$\end{document} levels, and n factors at s levels, where s is a prime or prime power, are considered. These designs can be conveniently described and their properties obtained using finite projective geometry. The method of complementary sets is again seen to provide a general approach for finding minimum aberration designs in such settings.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Modern Theory of Factorial DesignsMinimum Aberration Designs for Mixed Factorials

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Publisher
Springer New York
Copyright
© Springer Science+Business Media, Inc. 2006
ISBN
978-0-387-31991-9
Pages
125 –150
DOI
10.1007/0-387-37344-6_6
Publisher site
See Chapter on Publisher Site

Abstract

[Extension of the ideas in Chapters 3 and 4 to designs with factors at different numbers of levels is the focus of this chapter. The important special case of mixed two- and four-level designs is first discussed. An extension of the minimum aberration criterion is considered. More generally, designs with one factor at sr levels and n factors at s levels, or one factor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ s^{r_1 }$$\end{document} levels, a second factor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ s^{r_2 }$$\end{document} levels, and n factors at s levels, where s is a prime or prime power, are considered. These designs can be conveniently described and their properties obtained using finite projective geometry. The method of complementary sets is again seen to provide a general approach for finding minimum aberration designs in such settings.]

Published: Jan 1, 2006

Keywords: Orthogonal Array; Minimum Aberration; Mixed Factorial; Nonsingular Transformation; Regular Fraction

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