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
Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes
TL;DR: This article introduces a collection of strength-3 nonregular designs with large run sizes that, to the best of the knowledge, have not been explored before in the design literature and outperform many comparably sized benchmark designs in terms of the aliasing among the two-factor interactions.
Journal ArticleDOI
Using Individual Factor Information in Fractional Factorial Designs
William Li,Robert W. Mee,Qi Zhou +2 more
TL;DR: The individual generalized word length pattern (iGWLP) is proposed, a criterion for choosing best designs when the focus is on a small set of important factors, for which the aliasing of effects involving these factors is minimized.
Journal ArticleDOI
OApackage: A Python package for generation and analysis of orthogonal arrays, optimal designs and conference designs
Pieter Eendebak,Alan R. Vazquez +1 more
Dissertation
Optimal factorial designs with robust properties
TL;DR: In this article, the authors introduce the concept of partially clear interactions which leads to a richer class of robust designs when specific interactions are known to be negligible a priori, and develop several methods to construct designs that allow for additional factors to be studied in comparison to designs with clear two-factor interactions.
Journal ArticleDOI
Interaction balance for symmetrical factorial designs with generalized minimum aberration
Mingyao Ai,Shuyuan He +1 more
TL;DR: This paper showed that the generalized wordlength pattern exactly measures the balance pattern of interaction columns of a symmetrical design ground on the orthogonal components system, and thus an alternative angle to look at the generalized minimum aberration criterion is given.
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.