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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
01 Jul 2004-Metrika
TL;DR: In this article, the authors give linkages among uniformity measured by the discrete discrepancy, generalized minimum aberration, minimum moment aberration and uniformity measure by the centered L2-discrepancy/the wrap-around L2 discrepancy.
Abstract: Discrepancy measure can be utilized as a uniformity measure for comparing factorial designs. A so-called discrete discrepancy has been used to evaluate the uniformity of factorials. In this paper we give linkages among uniformity measured by the discrete discrepancy, generalized minimum aberration, minimum moment aberration and uniformity measured by the centered L2-discrepancy/the wrap-around L2-discrepancy. These close linkages provide a significant justification for the discrete discrepancy used to measure uniformity of factorial designs.

36 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduced minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) criteria for discriminating among rival FFSP designs, which is an improvement and generalization of the related results in (Statist. Sinica 12 (2002) 885).

35 citations

Journal ArticleDOI
TL;DR: In this article, Chen, Sun, and Wu enumerated all possible 2 k-p fractional factorial designs of size 16 and 32 and all resolution four (or higher) fractions of size 64.
Abstract: Chen, Sun, and Wu (1993) enumerated all possible 2 k-p fractional factorial designs of size 16 and 32 and all resolution four (or higher) fractions of size 64. By enumerating all possible designs, they not only provided the minimum aberration design for each value of k but also listed designs attractive for other reasons, e.g., having the most clear two-factor interactions. Here we present the results of an enumeration of n = 128 run resolution IV designs. As in Chen, Sun, and Wu (1993), we constructed new designs by building up, adding one factor at a time. However, rather than determining whether a new candidate design was isomorphic to an existing design based on a complete permutation check, we retained all designs that differed in their projections. Resolution IV designs are tabulated for k = 12, ..., 64 factors.

34 citations

Journal ArticleDOI
TL;DR: In this article, the concept of minimum moment aberration (MA) blocked factorial designs is extended to blocked designs, and sufficient conditions are given for constructing MA blocked designs from unblocked MA designs.
Abstract: This paper considers the construction of minimum aberration (MA) blocked factorial designs. Based on coding theory, the concept of minimum moment aberration due to Xu (2003) for unblocked designs is extended to blocked designs. The coding theory approach studies designs in a row-wise fashion and therefore links blocked designs with nonregular and supersaturated designs. A lower bound on blocked wordlength pattern is established. It is shown that a blocked design has MA if it originates from an unblocked MA design and achieves the lower bound. It is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros. Sufficient conditions are given for constructing MA blocked designs from unblocked MA designs. The theory is then applied to construct MA blocked designs for all 32 runs, 64 runs up to 32 factors, and all 81 runs with respect to four combined wordlength patterns.

33 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose several criteria for measuring the capability of a design for model discrimination and evaluate a class of 18-run orthogonal designs in terms of their model discriminating capabilities.

33 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