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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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An approach to constructing "good" two-level orthogonal factorial designs with large run sizes
TL;DR: In this paper, the authors proposed an approach to construct a "good" factorial with a large run size using two small minimum G2-aberration designs and derived the word length pattern of the large design to be obtained from those of the two small designs.
Journal ArticleDOI
Complete enumeration of two-Level orthogonal arrays of strength $d$ with $d+2$ constraints
John Stufken,Boxin Tang +1 more
TL;DR: In this article, the authors provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength two, three, and four with constraints on the number of parameters and the run size.
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Some orthogonal arrays with 32 runs and their projection properties
TL;DR: In this paper, the authors presented 15 inequivalent Hadamard matrices of order n = 32 constructed from circulant cores and studied their projection properties using several well-known statistical criteria.
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A simple method for dealing with aliasing in experimental design
TL;DR: In this paper, a simple and unified method for generating the aliasing pattern of two-and three-level fractional factorial designs be they regular or non-regular is proposed.
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Families of search designs for simultaneous detection of the active main and 2-factor interaction effects
Fahimeh Barati,Hooshang Talebi +1 more
TL;DR: In this paper, the problem of searching for and estimating k 1 and k 2 non-zero main and 2-factor interaction effects, respectively, that are not known a priori, is considered.
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.