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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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Uniform fractional factorial designs
TL;DR: In this article, uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion, and optimal designs with 27 and 81 runs are obtained for practical use.
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Bacteriocin-producing lactic acid bacteria isolated from mangrove forests in southern Thailand as potential bio-control agents in food: Isolation, screening and optimization
TL;DR: In this paper, a total of 386 isolates of lactic acid bacteria isolated from mangrove forests (soil, water, leaf, twig and fruit) in southern Thailand were screened for bacteriocin production.
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Moment aberration projection for nonregular fractional factorial designs
Hongquan Xu,Lih-Yuan Deng +1 more
TL;DR: In this article, a novel criterion, called moment aberration projection, is proposed to rank and classify non-regular fractional factorial designs, which measures the goodness of a design through moments of the number of coincidences between rows of its projection designs.
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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, a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d + 2 constraints for any d and any run size n = λ 2 d was provided.
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R Package FrF2 for Creating and Analyzing Fractional Factorial 2-Level Designs
TL;DR: The R package FrF2 offers both regular and non-regular fractional factorial 2-level designs, in the regular case with blocking and split plot facilities and algorithms for ensuring estimability of certain two-factor interactions.
References
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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.