scispace - formally typeset
Search or ask a question

Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs

Lih-Yuan Deng, Boxin Tang
01 Jan 1999-
TL;DR: 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.

Content maybe subject to copyright    Report

Citations
More filters
Journal Article•DOI•
Construction of minimum generalized aberration designs

[...]

Kai-Tai Fang1, Gennian Ge2, Min-Qian Liu3, Hong Qin4, Hong Qin1 •
Hong Kong Baptist University1, Soochow University (Suzhou)2, Nankai University3, Central China Normal University4
01 Feb 2003-Metrika
TL;DR: In this article, the minimum generalized aberration (MGA) criterion was used for comparing non-regular symmetrical designs for evaluating supersaturated designs, and a new construction method for MGA symmetrical supersaturated design via resolvable balanced incomplete block designs was proposed, along with the investigation of properties of the resulting designs.
Abstract: Supersaturated designs have become increasingly popular in recent years because of their potential in saving run size and the technical novelty In this paper, the minimum generalized aberration (MGA) criterion proposed by Ma and Fang (2001) (and another two equivalent criteria proposed by Xu and Wu (2001) and Xu (2001b) respectively) for comparing non-regular symmetrical designs is used for evaluating supersaturated designs A new construction method for MGA symmetrical supersaturated designs via resolvable balanced incomplete block designs is proposed, and some infinite classes for the existence of such MGA designs are obtained simultaneously, along with the investigation of properties of the resulting designs The construction method shows a strong connection between these two different kinds of designs

43 citations

Cites background or methods from "Generalized resolution and minimum ..."

  • ...For assessing non-regular 2-level factorials, Deng and Tang (1999) introduced a minimum G-aberration criterion which is very stringent, while Tang and Deng (1999) proposed a relaxed variant of minimum G-aberration, called minimum G2-aberration....

    [...]

  • ...Furthermore, if the equality of (9) holds, then the design has MGA....

    [...]

  • ...The equality of (9) holds if and only if the number of coincidences between any pair of distinct rows is a constant d 1⁄4 mðn qÞ=1⁄2qðn 1ނ....

    [...]

Journal Article•DOI•
Incorporating Prior Information in Optimal Design for Model Selection

[...]

Derek Bingham1, Hugh A. Chipman•
Simon Fraser University1
01 May 2007-Technometrics
TL;DR: This article goes further than identification of effects, introducing a design criterion that seeks to maximize the ability to discriminate between models, based on the Hellinger distance between predictive distributions under competing models.
Abstract: An important use of experimental designs is in screening, in which experimenters seek to identify significant effects (both main effects and potentially interactions) from a large set of candidate effects. This article goes further than identification of effects, introducing a design criterion that seeks to maximize the ability to discriminate between models. Motivated by the work of Meyer, Steinberg, and Box, the Bayesian criterion is based on the Hellinger distance between predictive distributions under competing models. A bound for the criterion is obtained, greatly improving interpretability. The set of all possible models to compare is huge, and not all models are equally plausible. This challenge is addressed through prior distributions on the space of models that indicate preference for intuitively appealing models, such as those with few effects, more low-order than high-order effects, and inheritance structure between active main effects and interactions. Techniques for evaluating the criterion a...

42 citations

Cites background from "Generalized resolution and minimum ..."

  • ...The belief that estimation of some models is more important than others is not easy to incorporate into such criteria as MA and its generalizations (Deng and Tang 1999; Tang and Deng 2000) and EC in some practical applications....

    [...]

  • ...…(EC) criterion (Sun 1997; Cheng and Mukerjee 1998; Cheng, Steinberg, and Sun 1999), which computes the proportion of models containing all main effects and a fixed number of 2fi’s that are estimable, and generalizations of the minimum aberration criterion (Deng and Tang 1999; Tang and Deng 2000)....

    [...]

Moment Aberration Projection for Nonregular Fractional Factorial Designs

[...]

Hongquan Xu1, Lih-Yuan Deng2•
University of California, Los Angeles1, University of Memphis2
01 Jan 2002
TL;DR: A novel criterion, called moment aberration projection, is proposed to rank and classify nonregular designs, which measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs.
Abstract: Nonregular fractional factorial designs such as Plackett-Burman designs are widely used in industrial experiments for run size economy and flexibility. A novel criterion, called moment aberration pro jection, is proposed to rank and classify nonregular designs. It measures the goodness of a design through moments of the number of coincidences between the rows of its pro jection designs. The new criterion is applied to rank and classify designs of 16, 20 and 27 runs. Examples are given to illustrate that the ranking of designs is supported by other design criteria.

40 citations

Book•
Total Quality Management And Six Sigma

[...]

Tauseef Aized
01 Jan 2014
TL;DR: In order to survive in a modern and competitive environment, organizations need to carefully organize their activities regarding quality management as discussed by the authors, and TQM and six sigma are the approaches that have been successful in solving intricate quality problems in products and services.
Abstract: In order to survive in a modern and competitive environment, organizations need to carefully organize their activities regarding quality management. TQM and six sigma are the approaches that have been successful in solving intricate quality problems in products and services. This volume can help those who are interested in the quality management field to understand core ideas along with contemporary efforts done in the field and authored as case studies in this volume. This volume may be useful to students, academics and practitioners across diversified disciplines.

38 citations

Cites background from "Generalized resolution and minimum ..."

  • ...[16] Srdoc A, Sluga A and Bratko I (2005)....

    [...]

  • ...Fires, originated by electrical causes start, general rule, in overloaded circuits, without proper protection and maintenance, and handled by curious laymen covered up by “economic professionals” that seek by “the lowest price” the technical solutions for problems that should have been the cause for specialized diagnosis [16]....

    [...]

  • ...identification of a problem, that has not developed a single expert system that deals with the measurement, evaluation, corrective and preventive action to improve organizational performance and the like [12, 13-16, 10]....

    [...]

Journal Article•DOI•
A quality by design (QbD) case study on enteric- coated pellets: Screening of critical variables and establishment of design space at laboratory scale

[...]

Shuling Kan1, Jing Lu1, Jianping Liu1, Junlin Wang1, Yi Zhao1 •
China Pharmaceutical University1
01 Oct 2014-Asian Journal of Pharmaceutical Sciences
TL;DR: In this article, the authors used failure mode and effect analysis (FMEA) methodology to assess the most important variables affecting enteric-coated pellets characteristics, and a Box-Behnken design was subsequently used for investigating the main, interactive, and quadratic effects of these variables on the response.

38 citations

References
More filters
Journal Article•DOI•
The design of optimum multifactorial experiments

[...]

R. L. Plackett, J. P. Burman
01 Jun 1946-Biometrika

3,546 citations

Journal Article•DOI•
A Basis for the Selection of a Response Surface Design

[...]

George E. P. Box1, Norman R. Draper2•
Princeton University1, University of North Carolina at Chapel Hill2
01 Sep 1959-Journal of the American Statistical Association
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.
Abstract: The general problem is considered of choosing a design such that (a) the polynomial f(ξ) = f(ξ1, ξ2, · · ·, ξ k ) in the k continuous variables ξ' = (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function g(ξ1, ξ2, · · ·, ξ k ) over some “region of interest” R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R; and (b) subject to satisfaction of (a), there is a high chance that inadequacy of f(ξ) to represent g(ξ) will be detected. When the observations are subject to error, discrepancies between the fitted polynomial and the true function occur: i. due to sampling error (called here “variance error”), and ii. due to the inadequacy of the polynomial f(ξ) exactly to represent g(ξ) (called here “bias error”). To meet requirement (a) the design is selected so as to minimize J, the expected mean square error averaged over the region R. J contains two components, one associated entirely with varian...

697 citations

"Generalized resolution and minimum ..." refers result in this paper

  • ...Finally, we note that our argument for minimizing biases is similar to that in Box and Draper (1959)....

    [...]

Journal Article•DOI•
The 2 k — p Fractional Factorial Designs

[...]

George E. P. Box1, J. S. Hunter1•
University of Wisconsin-Madison1
01 Aug 1961-Technometrics

471 citations

"Generalized resolution and minimum ..." refers methods in this paper

  • ...For a detailed discussion on the concept of resolution for regular factorials, we refer to Box and Hunter (1961)....

    [...]

Journal Article•DOI•
The 2 k-p fractional factorial designs part I

[...]

George E. P. Box1, J. S. Hunter1•
University of Wisconsin-Madison1
01 Feb 2000-Technometrics
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.
Abstract: (2000). The 2 k—p Fractional Factorial Designs Part I. Technometrics: Vol. 42, No. 1, pp. 28-47.

449 citations

Journal Article•DOI•
Minimum Aberration 2 k–p Designs

[...]

Arthur Fries, William G. Hunter
01 Nov 1980-Technometrics
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.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.

420 citations

"Generalized resolution and minimum ..." refers methods in this paper

  • ...For results on minimum aberration designs, we refer to Fries and Hunter (1980), Franklin (1984), Chen and Wu (1991), Chen (1992), Tang and Wu (1996), Chen and Hedayat (1996) and Cheng, Steinberg and Sun (1999)....

    [...]

Related Papers (5)
Generalized minimum aberration for asymmetrical fractional factorial designs

[...]

01 Aug 2001-Annals of Statistics
Hongquan Xu, C. F. J. Wu
Experiments: Planning, Analysis, and Parameter Design Optimization

[...]

01 Jan 2000
C. F. Jeff Wu, Michael S. Hamada
Minimum Aberration 2 k–p Designs

[...]

01 Nov 1980-Technometrics
Arthur Fries, William G. Hunter
Minimum Aberration 2k-p Designs

[...]

01 Jan 1980
Arthur Fries, William G. Hunter
Orthogonal Arrays: Theory and Applications

[...]

22 Jun 1999
Lih-Yuan Deng