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Fractional Factorial Plans

25 Mar 1999-
TL;DR: Fractional plans and orthogonal arrays have been extensively studied in the literature, see as discussed by the authors for a survey of some of the most relevant works. But nonexistence of fractional plans has been discussed.
Abstract: Fractional Plans and Orthogonal Arrays. Symmetric Orthogonal Arrays. Asymmetric Orthogonal Arrays. Some Results on Nonexistence. More on Optimal Fractional Plans and Related Topics. Trend-Free Plans and Blocking. Some Further Developments. Appendix. References. Index.

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Journal ArticleDOI
Xinwei Deng1
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.

1,025 citations

Journal ArticleDOI
TL;DR: This paper provides a review of statistical methods that are useful in conducting computer experiments and describes approaches for the two primary tasks of metamodeling: selecting an experimental design and fitting a statistical model.
Abstract: In this paper, we provide a review of statistical methods that are useful in conducting computer experiments. Our focus is on the task of metamodeling, which is driven by the goal of optimizing a complex system via a deterministic simulation model. However, we also mention the case of a stochastic simulation, and examples of both cases are discussed. The organization of our review first presents several engineering applications, it then describes approaches for the two primary tasks of metamodeling: (i) selecting an experimental design; and (ii) fitting a statistical model. Seven statistical modeling methods are included. Both classical and newer experimental designs are discussed. Finally, our own computational study tests the various metamodeling options on two two-dimensional response surfaces and one ten-dimensional surface.

314 citations


Cites background from "Fractional Factorial Plans"

  • ...Dey and Mukerjee (1999) detail the combinatorics of fractional factorials, including OAs....

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Journal ArticleDOI
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.

309 citations


Cites background from "Fractional Factorial Plans"

  • ...It is important to note that XTi Xj 2 is independent of the choice of orthonormal contrasts [see Remark 2.3.1 of Dey and Mukerjee (1999)]....

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Journal ArticleDOI
TL;DR: A comprehensive and state-of-the art survey on common surrogate modeling techniques and surrogate-based optimization methods is given, with an emphasis on models selection and validation, dimensionality reduction, sensitivity analyses, constraints handling or infill and stopping criteria.

174 citations

01 Jan 2001
TL;DR: In this paper, a new combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs, which is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2).
Abstract: Nonregular designs are used widely in experiments due to their run size economy and flexibility. These designs include the Plackett-Burman designs and many other symmetrical and asymmetrical orthogonal arrays. Supersaturated designs have become increasingly popular in recent years because of the potential in saving run size and its technical novelty. In this paper, a novel combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs. The new criterion, which is to sequentially minimize the power moments of the number of coincidence among runs, is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2). In addition, the minimum moment aberration is conceptually simple and convenient for theoretical development. The general theory developed here not only unifies several separate results, but also provides many novel results on nonregular designs and supersaturated designs.

152 citations

References
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TL;DR: In this paper, it was shown that the smallest resolution 4 designs for n factors at two levels must contain at least 2n runs, and that "foldover" designs are available with 2 n runs.
Abstract: Designs of even resolution have the property that a set of parameters, although themselves not estimable, do not appear as aliases of those which are estimable. The most important are designs of resolution 4, which are such that the main effects are estimable with no two-factor interactions as aliases. In this paper it is shown that the smallest resolution 4 designs for n factors at two levels must contain at least 2n runs, and that “foldover” designs are available with 2n runs. It is conjectured that the only minimal resolution 4 designs are foldover designs. The case of resolution 6 designs is also discussed.

67 citations