2n-l designs with weak minimum aberration
Hegang Chen,A. S. Hedayat +1 more
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In this paper, the concept of weak minimum aberration was introduced and several families of fractional factorial designs of resolution III and IV with minimal aberration were obtained. But they did not show the usefulness of this new design concept.Abstract:
Since not all $2^{n-1}$ fractional factorial designs with maximum resolution are equally good, Fries and Hunter introduced the minimum aberration criterion for selecting good $2^{n-1}$ fractional factorial designs with the same resolution. We modify the concept of minimum aberration and define weak minimum aberration and show the usefulness of this new design concept. Using some techniques from finite geometry, we construct $2^{n-1}$ fractional factorial designs of resolution III with weak minimum aberration. Further, several families of $2^{n-1}$ fractional factorial designs of resolution III and IV with minimum aberration are obtained.read more
Citations
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Generalized minimum aberration for asymmetrical fractional factorial designs
Hongquan Xu,C. F. J. Wu +1 more
TL;DR: In this paper, a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs is proposed, which is independent of the choice of treatment contrasts and thus model-free.
Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs
Lih-Yuan Deng,Boxin Tang +1 more
TL;DR: In this paper, a generalized resolution criterion is defined and used for assessing non-regular fractional factorials, notably Plackett-Burman designs, which is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order fractional fractional factors under the assumption that higher order effects are negligible.
Minimum moment aberration for nonregular designs and supersaturated designs
TL;DR: In this paper, a new combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs, which is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2).
Journal ArticleDOI
Design Selection and Classification for Hadamard Matrices Using Generalized Minimum Aberration Criteria
Lih-Yuan Deng,Boxin Tang +1 more
TL;DR: This article considers the problem of classifying and ranking designs that are based on Hadamard matrices and finds that generalized aberration performs quite well under these familiar criteria.
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Theory of optimal blocking of $2^{n-m}$ designs
Hegang Chen,Ching-Shui Cheng +1 more
TL;DR: In this paper, the authors define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment-defining words and blockdefining word, and establish general rules for identifying minimum aberration blocked $2 n-m} designs in terms of their blocked residual designs.
References
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Journal ArticleDOI
Designs for two-level factorial experiments with linear models containing main effects and selected two-factor interactions
A. S. Hedayat,H. Pesotan +1 more
TL;DR: In this paper, methods of constructing g-matrices are studied since such constructions are equivalent to the construction of g-designs, and some bounds on the absolute value of a determinant of a g -matrix are given.