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: In this paper, Phoa et al. explored the properties and uses of quaternary codes towards the construction of quarter-fraction nonregular designs and obtained the results regarding the aliasing structure of such designs.
Abstract: Submitted QUARTER-FRACTION FACTORIAL DESIGNS CONSTRUCTED VIA QUATERNARY CODES ∗ By Frederick K. H. Phoa and Hongquan Xu University of California, Los Angeles The research of developing a general methodology for the con- struction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong (2007) suggested a new class of nonregular designs constructed from quaternary codes. This paper explores the properties and uses of quaternary codes towards the construction of quarter-fraction nonregular designs. Some theo- retical results are obtained regarding the aliasing structure of such designs. Optimal designs are constructed under the maximum resolu- tion, minimum aberration and maximum projectivity criteria. These designs often have larger generalized resolution and larger projectiv- ity than regular designs of the same size. It is further shown that some of these designs have generalized minimum aberration and maximum projectivity among all possible designs. 1. Introduction. In many scientific researches and investigations, the interests lie in the study of effects of many factors simultaneously. Frac- tional factorial designs, especially two-level fractional factorial designs, are the most commonly used experimental plans for this type of investigations. Designs that can be constructed through defining relations among factors are called regular designs. Any two factorial effects in a regular design are Supported in part by NSF Grant DMS-05-05728. AMS 2000 subject classifications: Primary 62K15. Keywords and phrases: Aliasing index, fractional factorial design, generalized minimum aberration, generalized resolution, nonregular design, projectivity.
21 citations
21 citations
TL;DR: In this paper, a generalized minimum aberration criterion for comparing and selecting general fractional factorial designs is defined using a set of χ ≥ 1 (D) values, called J-characteristics by Xu and Wu.
Abstract: Recently, Xu and Wu (2001) presented generalized minimum aberration criterion for comparing and selecting general fractional factorial designs. This criterion is defined using a set of χ
u
(D) values, called J-characteristics by us. In this paper, we find a set of linear equations that relate the set of design points to that of J-characteristics, which implies that a factorial design is uniquely determined by its J-characteristics once the orthonormal contrasts are designated. Thereto, a projection justification of generalized minimum aberration is established. All of these conclusions generalize the results for two-level symmetrical factorial designs in Tang (2001).
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TL;DR: In this article, it was shown that two 2k−p designs with the same word length pattern can be different and the difference was detected via a letter pattern comparison test, and that two designs with equivalent letter pattern matrices are indeed equivalent designs.
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TL;DR: The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details, and provides a unified framework for a wide range of factorial designs.
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Cites background from "Minimum Aberration 2 k–p Designs"
...More discriminating criteria such as minimum aberration (Fries and Hunter, 1980) or maximum estimation capacity (Cheng and Mukerjee, 1998) have been developed....
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471 citations
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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.
311 citations
09 Jun 1976
271 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