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
Efficient arrangements of two-level orthogonal arrays in two and four blocks
H. Evangelaras,C. Peveretos +1 more
TL;DR: In this paper, the nice properties of two-level orthogonal arrays are taken into consideration and an effective method for arranging experimental runs into two and four blocks of the same size is proposed.
Dissertation
Ranking non-regular designs
TL;DR: In this article, the authors focus on non-regular fractional factorial designs and introduce the projection estimation capacity sequence and use this new criterion to select good non-normal designs.
Posted Content
Selection of Non-Regular Fractional Factorial Designs When Some Two-Factor Interactions are Important
Weiming Ke,Rui Yao +1 more
TL;DR: In this article, a new method is proposed for selecting the optimal non-regular fractional factorial designs in the situation when some two-factor interactions are potentially important, and search for the best designs according to this method is discussed and some results for the Plackett-Burman design of 12 runs are presented.
Journal ArticleDOI
Constructing 2-level foldover designs with minimal aliasing
TL;DR: An algorithmic approach to constructing 2-level foldover designs using the minimum G2-aberration criterion (Tang & Deng, 1999), which can find designs without fully aliased 2-factor interactions (2FIs).
Journal ArticleDOI
Invariance of generalized wordlength patterns
Jay H. Beder,Jeb F. Willenbring +1 more
TL;DR: This article showed that the GWLP of a design is independent of this choice, but that the J-characteristics are not independent of the choice, and that the definitions carry over with appropriate changes if instead one uses an arbitrary abelian group.
References
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Journal ArticleDOI
The design of optimum multifactorial experiments
R. L. Plackett,J. P. Burman +1 more
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.