Open Access
Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs
Lih-Yuan Deng,Boxin Tang +1 more
TLDR
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.Abstract:
Resolution has been the most widely used criterion for comparing regular fractional factorials since it was introduced in 1961 by Box and Hunter. In this pa- per, we examine how a generalized resolution criterion can be defined and used for assessing nonregular fractional factorials, notably Plackett-Burman designs. Our generalization is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order ef- fects under the assumption that higher order effects are negligible. Our generalized resolution provides a fruitful criterion for ranking different designs while Webb's resolution is mainly useful as a classification rule. An additional advantage of our approach is that the idea leads to a natural generalization of minimum aberration. Examples are given to illustrate the usefulness of the new criteria.read more
Citations
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Three‐level designs: Evaluation and comparison for screening purposes
Journal ArticleDOI
Some optimal criteria of model-robustness for two-level non-regular fractional factorial designs
TL;DR: Some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs are presented and can be expressed as linear combinations of Bs(d) characteristic, which is used to characterize the generalized minimum aberration.
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A Note on Foldover of 2k − p Designs With Column Permutations
William Li,Dennis K.J. Lin +1 more
TL;DR: In this paper, the permutation of columns in foldover has been considered and the authors show that almost all designs are better than existing results with respect to the minimum aberration criterion.
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Orthogonal blocking arrangements for 24-run and 28-run two-level designs
TL;DR: In this paper, the authors presented the best arrangements of 24-run and 28-run two-level screening algorithms in 3, 4, and 6 blocks and the best arrangement of 28 run in 7 blocks, respectively.
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Generalized Wordtype Pattern for Nonregular Factorial Designs with Multiple Groups of Factors
Mingyao Ai,Shuyuan He +1 more
TL;DR: In this article, the generalized word type pattern of a non-regular fractional factorial design was introduced and its connection with the distance distribution was considered. And the corresponding relationship between a fractional factororial design and a code was developed.
References
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Journal ArticleDOI
The design of optimum multifactorial experiments
R. L. Plackett,J. P. Burman +1 more
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A Basis for the Selection of a Response Surface Design
TL;DR: In this paper, the problem of choosing a design such that the polynomial f(ξ) = f (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function over some region of interest R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R, is considered.
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The 2 k-p fractional factorial designs part I
George E. P. Box,J. S. Hunter +1 more
TL;DR: The 2 k-p Fractional Factorial Designs Part I. as discussed by the authors is a collection of fractional fractional factorial designs with a focus on the construction of the construction.
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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.