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Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs
Lih-Yuan Deng,Boxin Tang +1 more
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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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Complete Enumeration of Pure-Level and Mixed-Level Orthogonal Arrays
TL;DR: In this paper, the authors present an algorithm to enumerate a minimum complete set of combinatorially non-isomorphic orthogonal arrays of given strength t, run-size N, and level-numbers of the factors.
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.
Factor screening and response surface exploration
Shao-Wei Cheng,Chien-Fu Wu +1 more
TL;DR: In this paper, a two-stage anal- ysis that employs factor screening, projection and response surface exploration is proposed to achieve the two objectives on the same experiment, based on one design.
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Optimal Foldover Plans for Two-Level Nonregular Orthogonal Designs
TL;DR: It is proved that the full-foldover plan that reverses the signs of all factors is optimal for all 12-run and 20-run orthogonal designs.
Journal ArticleDOI
Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration
TL;DR: In this article, it was shown that a factorial design is uniquely determined by its J-characteristics, just as a regular factorial is uniquely defined by its defining relation, and the projection justification of minimum G 2 -aberration is established.
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.