Journal ArticleDOI
A note on connections among criteria for asymmetrical factorials
Fang Pang,Min-Qian Liu +1 more
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TLDR
In this article, the equivalence of the generalized minimum aberration and the minimum χ 2 criteria is reported, which not only provides another justification for each other but also develops some theoretical results for designs with generalized minimum abnormality and some lower bounds for the generalized wordlength pattern.Abstract:
Various optimal criteria have been proposed to rank asymmetrical frac- tional factorial designs. Among them, the generalized minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention. Recently, Liu et al. (Stat Sin 16:1285-1297, 2006) proposed the mini- mum χ 2 criterion in terms of level-combinations. In this paper, the equivalency of the generalized minimum aberration and the minimum χ 2 criteria is reported, which not only provides another justification for each other but also develops some theoretical results for designs with generalized minimum aberration and some lower bounds for the generalized wordlength pattern. Besides, an analytic relationship between gener- alized minimum aberration and minimum moment aberration is obtained for asym- metrical fractional factorial designs.read more
Citations
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Journal ArticleDOI
Building some bridges among various experimental designs
A. M. Elsawah,A. M. Elsawah +1 more
TL;DR: In this article, the authors tried to answer the interesting questions by building some bridges among these designs, which can be used to select a suitable criterion for studying some hard problems effectively, such as detection of (combinatorial/geometrical) non-isomorphism among designs and construction of optimal designs.
Journal ArticleDOI
A generalized general minimum lower order confounding criterion for nonregular designs
TL;DR: In this paper, the generalized aliasing effect number pattern (G2-AENP) and generalized general minimum lower order confounding (G 2-GMC) were proposed for non-regular designs.
References
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Book
Experiments: Planning, Analysis, and Parameter Design Optimization
C. F. Jeff Wu,Michael S. Hamada +1 more
TL;DR: This book discusses Factorial and Fractional Factorial Experiments at Three Levels, Robust Parameter Design for Signal-Response Systems, and other Design and Analysis Techniques for Experiments for Improving Reliability.
Book
Orthogonal Arrays: Theory and Applications
TL;DR: The Rao Inequalities for Mixed Orthogonal Arrays., 9.2 The Rao InEqualities for mixed Orthogonic Arrays.- 9.4 Construction X4.- 10.1 Constructions Inspired by Coding Theory.
Journal ArticleDOI
Minimum Aberration 2 k–p Designs
Arthur Fries,William G. Hunter +1 more
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Minimum Aberration 2k-p Designs
Arthur Fries,William G. Hunter +1 more
TL;DR: The concept of resolution was introduced by Box and Hunter as discussed by the authors, who defined the resolution of a two-level fractional factorial design as the length of the shortest word in the defining relation.
Journal ArticleDOI
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.