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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Journal ArticleDOI
Projection justification of generalized minimum aberration for asymmetrical fractional factorial designs
TL;DR: In this paper, a generalized minimum aberration criterion for comparing and selecting general fractional factorial designs is defined using a set of χ ≥ 1 (D) values, called J-characteristics by Xu and Wu.
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Generalized minimum aberration two-level split-plot designs
TL;DR: In this article, an approach for constructing minimum aberration orthogonal two-level split-plot designs having 12, 16, 20 and 24 runs is described. But the design scenarios that may be of importance to practitioners are considered, and then the approach for assigning word lengths under these five scenarios is proposed.
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Generalized resolution for orthogonal arrays
Ulrike Grömping,Hongquan Xu +1 more
TL;DR: In this article, the authors derived two versions of generalized resolution for qualitative factors, both of which are generalizations of the generalized resolution by Deng and Tang [Statist. Sinica 9 (1999) 1071-1082] and Tang and Deng [Ann. Statist. 27 (1999] 1914-1926].
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General weighted optimality of designed experiments
TL;DR: In this article, a general theory for weighted optimality, allowing precise design selection according to expressed relative interest in different functions in the estimation space, is developed, and the results are applied to solve the $A$-optimal design problem for baseline factorial effects in unblocked experiments.
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Results for two-level fractional factorial designs of resolution IV or more
TL;DR: The main theorem of as mentioned in this paper states that foldover designs are the only regular two-level factorial designs of resolution IV (strength 3) or more for n runs and n/ 3 ⩽ m⩽ n/ 2 factors.
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.