Some theory for constructing minimum aberration fractional factorial designs

Butler, Neil A.

doi:10.1093/biomet/90.1.233

Cited by 39 publications

(22 citation statements)

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“…It is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row (i.e., treatment combination) without zeros. Sufficient conditions are given for constructing MA blocked 3 designs from unblocked MA designs. Some technical lemmas are presented in Section 3 and the main results are given in Section 4.…”

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confidence: 99%

Blocked regular fractional factorial designs with minimum aberration

Xu¹

2006

Ann. Statist.

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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 [Statist. Sinica 13 (2003) 691--708] 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.Comment: Published at http://dx.doi.org/10.1214/009053606000000777 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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confidence: 99%

Blocked regular fractional factorial designs with minimum aberration

Xu¹

2006

Ann. Statist.

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“…However, this is not true for n = 31, which agrees with the theoretical result of Xu and Cheng (2007). For 40 < n ≤ 64, MA designs can be obtained via deleting the MA complementary even designs from the unique even 2 64−57 design; see Butler (2003) and Block and Mee (2005) for details. Again, this can be achieved by enumerating a set of good even designs.…”

Section: Tables Of Designsmentioning

confidence: 58%

The distribution of Voronoi cells generated by Southern California earthquake epicenters

2008

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Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed from its minimum aberration projection in the sequential build-up process.To efficiently identify nonisomorphic designs, designs are divided into different categories according to their moment projection patterns. A fast isomorphism check procedure is developed by matching the factors using their delete-one-factor projections. A method is proposed for constructing minimum aberration designs using only a partial catalog of some good designs.

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“…When 0 < m < 3N/16, the complement (in the unique R = 4, N run, N/2 factor regular design) of an MA even 2 m−p design X is an MA 2 m c −p c design X c , where m c = N/2 − m and p c = N/2 − 2m + p (see Butler 2003). Each 2 m−p design X with R ≥ 4 is even when 5N/16 < m ≤ N/2.…”

Section: A Large Number Of Factorsmentioning

confidence: 99%

Minimum Aberration Fractional Factorial Designs With LargeN

Ryan

Bulutoglu²

2010

Technometrics

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Xu has cataloged 165 minimum aberration (MA) regular fractional factorial (FF) designs with 2-levels and large run sizes N = 128 (m = 8-64 factors), N = 256 (m = 9-28, 109-119), N = 512 (m = 10-25, 238-246), N = 1024 (m = 11-24, 488-501), N = 2048 (m = 12-23), and N = 4096 (m = 13-24). Such an extensive catalog was produced because of an improved algorithm. We extend the catalog by 36 MA, 2level regular FF designs: N = 256 (m = 29-36, 100-108), N = 512 (m = 26-29), N = 1024 (m = 25-28), N = 2048 (m = 24-32), and N = 4096 (m = 25-26). Although such enumeration problems are notoriously difficult with increased N and/or m, we brought the newly solved problems within computational reach by changing the vital isomorphism check component of Xu's algorithm. Here we present a new, compact graph for solving regular design isomorphism problems and use the nauty program to solve the corresponding graph isomorphism problems. Supplemental appendices are available online. KEY WORDS: Bipartite undirected graph; Graph theory; Word-length pattern.

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Some theory for constructing minimum aberration fractional factorial designs

Cited by 39 publications

References 17 publications

Blocked regular fractional factorial designs with minimum aberration

Blocked regular fractional factorial designs with minimum aberration

The distribution of Voronoi cells generated by Southern California earthquake epicenters

Minimum Aberration Fractional Factorial Designs With LargeN

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