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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
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Dissertation
A new algorithm for obtaining mixed-level orthogonal and nearly-orthogonal arrays
TL;DR: This project will introduce a new algorithm for the construction of orthogonal arrays and nearly-orthogonal array with desirable statistical properties, and compare the new algorithm to a pre-existing algorithm.
Journal Article
Identifying Minimum G Aberration Designs for Hadamard Matrices of Order 28
Journal ArticleDOI
Generalized variable resolution designs
TL;DR: In this paper, the concept of generalized variable resolution is proposed for designs with nonnegligible interactions between groups, and the conditions for the existence of GVR designs are discussed.
Dissertation
A-optimal Minimax Design Criterion for Two-level Fractional Factorial Designs
TL;DR: An A-optimal minimax design criterion for two-level fractional factorial designs is introduced, which can be used to estimate a linear model with main effects and some interactions, and many interesting examples are presented in the thesis.
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.