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New recommended designs for screening either qualitative or quantitative factors

Author

Listed:
  • A. M. Elsawah

    (Zagazig University
    BNU-HKBU United International College)

  • Kai-Tai Fang

    (BNU-HKBU United International College
    The Chinese Academy of Sciences)

  • Xiao Ke

    (Southern University of Science and Technology
    Hong Kong Baptist University)

Abstract

By the affine resolvable design theory, there are 68 non-isomorphic classes of symmetric orthogonal designs involving 13 factors with 3 levels and 27 runs. This paper gives a comprehensive study of all these 68 non-isomorphic classes from the viewpoint of the uniformity criteria, generalized word-length pattern and Hamming distance pattern, which provides some interesting projection and level permutation behaviors of these classes. Selecting best projected level permuted subdesigns with $$3\le k\le 13$$ 3 ≤ k ≤ 13 factors from all these 68 non-isomorphic classes is discussed via these three criteria with catalogues of best values. New recommended uniform minimum aberration and minimum Hamming distance designs are given for investigating either qualitative or quantitative $$4\le k\le 13$$ 4 ≤ k ≤ 13 factors, which perform better than the existing recommended designs in literature and the existing uniform designs. A new efficient technique for detecting non-isomorphic designs is given via these three criteria. By using this new approach, in all projections into $$1\le k\le 13$$ 1 ≤ k ≤ 13 factors we classify each class from these 68 classes to non-isomorphic subclasses and give the number of isomorphic designs in each subclass. Close relationships among these three criteria and lower bounds of the average uniformity criteria are given as benchmarks for selecting best designs.

Suggested Citation

  • A. M. Elsawah & Kai-Tai Fang & Xiao Ke, 2021. "New recommended designs for screening either qualitative or quantitative factors," Statistical Papers, Springer, vol. 62(1), pages 267-307, February.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01089-9
    DOI: 10.1007/s00362-019-01089-9
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    References listed on IDEAS

    as
    1. Yu Tang & Hongquan Xu, 2014. "Permuting regular fractional factorial designs for screening quantitative factors," Biometrika, Biometrika Trust, vol. 101(2), pages 333-350.
    2. A. M. Elsawah, 2018. "Choice of optimal second stage designs in two-stage experiments," Computational Statistics, Springer, vol. 33(2), pages 933-965, June.
    3. A. M. Elsawah & Hong Qin, 2016. "Asymmetric uniform designs based on mixture discrepancy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2280-2294, September.
    4. H. Evangelaras & C. Koukouvinos & A. M. Dean & C. A. Dingus, 2005. "Projection properties of certain three level orthogonal arrays," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(2), pages 241-257, November.
    5. Chen, Wen & Qi, Zong-Feng & Zhou, Yong-Dao, 2015. "Constructing uniform designs under mixture discrepancy," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 76-82.
    6. H. Evangelaras & C. Koukouvinos & E. Lappas, 2007. "18-run nonisomorphic three level orthogonal arrays," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(1), pages 31-37, July.
    7. Yong-Dao Zhou & Hongquan Xu, 2014. "Space-Filling Fractional Factorial Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1134-1144, September.
    8. P. Angelopoulos & H. Evangelaras & C. Koukouvinos, 2009. "Model identification using 27 runs three level orthogonal arrays," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(1), pages 33-38.
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    Cited by:

    1. Lin-Chen Weng & Kai-Tai Fang & A. M. Elsawah, 2023. "Degree of isomorphism: a novel criterion for identifying and classifying orthogonal designs," Statistical Papers, Springer, vol. 64(1), pages 93-116, February.

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