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Journal ArticleDOI

Minimum Aberration 2 k–p Designs

01 Nov 1980-Technometrics (Taylor & Francis Group)-Vol. 22, Iss: 4, pp 601-608
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.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors derived a general and explicit relationship between the wordlength pattern of any even design and that of its complement in the maximal even design, and used these identities to identify some (weak) minimum aberration designs of resolution IV and the structures of their complementary designs.
Abstract: It is known that all resolution IV regular $2^{n-m}$ designs of run size $N=2^{n-m}$ where $5N/16

7 citations


Cites background from "Minimum Aberration 2 k–p Designs"

  • ...Minimum aberration (MA), introduced by Fries and Hunter (1980), has become the most popular criterion for selecting fractional factorial designs....

    [...]

Journal ArticleDOI
TL;DR: In this article, the optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity, and a general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.
Abstract: The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.

6 citations

Journal ArticleDOI
01 Nov 2004-Metrika
TL;DR: In this paper, the authors proposed an algorithm to sequentially examine designs obtained from Hadamard matrices under estimation capacity (EC) and provide designs with maximum or high EC for various combinations of run-size and number-of-factors.
Abstract: Deng and Tang (1999) proposed the generalized minimum aberration (GMA) criterion to assess fractional factorial designs, and a design with GMA is often regarded as the best. However, there exist situations where some other designs may suit practical needs better. In this article, we propose an algorithm to sequentially examine designs obtained from Hadamard matrices under estimation capacity (EC) and provide designs with maximum or high EC for various combinations of run-size and number-of-factors. The usefulness of maximum or high EC designs is discussed.

6 citations

01 Jan 2006
TL;DR: In this paper, the problems of combinatorial and geometric equivalence of symmetric factorial experiments, as well as characterization and ranking of two-level Split-plot and Split-lot designs are considered.
Abstract: The problems of combinatorial and geometric equivalence of symmetric factorial experiments, as well as characterization and ranking of two-level Split-plot and Splitlot designs are considered. Two fractional factorial symmetric designs with qualitative factors are said to be combinatorially equivalent if one can be obtained from the other by reordering the runs, relabeling the factors and relabeling factor levels. If the only permissible relabeling of factors levels is reversal of symbols, geometric equivalence is obtained. Existing criteria for detecting combinatorial and geometric equivalence or non-equivalence of symmetric factorial designs are described and evaluated via computer algorithms. Some new necessary and sufficient criteria for both types of equivalence are presented. All results generalize to designs with factors having different number of levels. A characterization method for two-level Split-plot and Split-lot designs based on nonregular fractional factorial designs is given. As an application, a new ranking method is proposed for general two-level Split-plot and Split-lot designs which suggests that existing ranking criteria overlook some aspects of the designs.

6 citations

Journal ArticleDOI
TL;DR: In this paper, a unified numerical method based on the double coincidence distribution for identifying clear or strongly clear main effects or two-factor interactions in a blocked regular fractional factorial design is presented.

6 citations

References
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Book
01 Jan 1978

5,151 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.

311 citations

Journal ArticleDOI
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