Minimum Aberration 2 k–p Designs
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.
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TL;DR: Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning.
Abstract: Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.
963 citations
TL;DR: A group of practitioners and researchers discuss the role of parameter design and Taguchi's methodology for implementing it and the importance of parameter-design principles with well-established statistical techniques.
Abstract: It is more than a decade since Genichi Taguchi's ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchi's methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchi's methodology for implementing it. The topics covered include the importance of vari...
633 citations
Cites methods from "Minimum Aberration 2 k–p Designs"
...Maximum resolution (Box and Hunter 1961) and minimum aberration (Fries and Hunter 1980) are often used as criteria for planning fractional factorial experiments....
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TL;DR: In this paper, a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs is proposed, which is independent of the choice of treatment contrasts and thus model-free.
Abstract: By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for regular designs and the minimum G 2 -aberration criterion for two-level nonregular designs. In addition, by exploring the connection between factorial design theory and coding theory, we develop a complementary design theory for general symmetrical designs, which covers many existing results as special cases.
282 citations
Cites methods from "Minimum Aberration 2 k–p Designs"
...For regular designs, the minimum aberration criterion proposed by Fries and Hunter (1980) has become the standard criterion for optimal factor assignment....
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TL;DR: In this article, the authors review major developments in the design of experiments, offer their thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design.
Abstract: We review major developments in the design of experiments, offer our thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design, practitioners of experimental design, and researchers jointly exploring new frontiers. Specific topics covered are optimal design, computer-aided design, robust design, response surface design, mixture design, factorial design, block design, and designs for nonlinear models.
282 citations
TL;DR: In this paper, the algebraic structure of fractional factorial (FF) designs with minimum aberration is explored and an algorithm for constructing complete sets of FF designs is proposed.
Abstract: Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for 'best' designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.
252 citations
References
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457 citations
Book•
23 Jun 1976
TL;DR: In conclusion, the size of Industrial Experiments, Fractional Replication--Elementary, and Incomplete Factorials are found to be about the same as that of conventional comparison experiments.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
310 citations
09 Jun 1976
266 citations
TL;DR: Incomplete Factorials, Fractional Replication, Intermediate Factorial, and Nested Designs as discussed by the authors are some of the examples of incomplete Factorial Experiments and incomplete fractional replicates.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
252 citations