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Two-level orthogonal designs in 24 and 28 runs

Author

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  • SCHOEN, Eric D.
  • VO-THANH, Nha
  • GOOS, Peter

Abstract

Due to incomplete previous approaches it is largely unclear which are the best 24-run and 28-run two-level designs in terms of any of the criteria currently in use to evaluate designs. In the present paper, we address this issue. First, we study the complete catalog of non-isomorphic orthogonal two-level 24-run designs involving 3-23 factors and we identify the best few designs in terms of aliasing between main effects and two-factor interaction effects and, subject to this, in terms of aliasing among two-factor interaction effects. Next, by modifying an existing enumeration algorithm, we identify the best few 28-run designs involving 3-14 factors. Based on a complete catalog of 7570 designs with 28 runs and 27 factors, we also seek good designs with more than 14 factors. To demonstrate the added value of our work, we provide a detailed comparison of our designs to the alternatives available in the literature.

Suggested Citation

  • SCHOEN, Eric D. & VO-THANH, Nha & GOOS, Peter, 2015. "Two-level orthogonal designs in 24 and 28 runs," Working Papers 2015016, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2015016
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    File URL: https://repository.uantwerpen.be/docman/irua/1d5004/a6323294.pdf
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    References listed on IDEAS

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    1. Lin, Dennis K. J. & Draper, Norman R., 1993. "Generating alias relationships for two-level Plackett and Burman designs," Computational Statistics & Data Analysis, Elsevier, vol. 15(2), pages 147-157, February.
    2. P. Angelopoulos & H. Evangelaras & C. Koukouvinos & E. Lappas, 2007. "An effective step-down algorithm for the construction and the identification of nonisomorphic orthogonal arrays," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 139-149, September.
    3. Eric D. Schoen & Robert W. Mee, 2012. "Two‐level designs of strength 3 and up to 48 runs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(1), pages 163-174, January.
    4. H. Evangelaras & S. Georgiou & C. Koukouvinos, 2004. "Evaluation of inequivalent projections of Hadamard matrices of order 24," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 51-73, February.
    5. SCHOEN, Eric D. & MEE, Robert W., 2012. "Two-level designs of strength 3 and up to 48 runs," Working Papers 2012005, University of Antwerp, Faculty of Business and Economics.
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    Cited by:

    1. VÁZQUEZ-ALCOCER, Alan & GOOS, Peter & SCHOEN, Eric D., 2016. "Two-level designs constructed by concatenating orthogonal arrays of strenght three," Working Papers 2016011, University of Antwerp, Faculty of Business and Economics.
    2. SCHOEN, Eric D. & VO-THANH, Nha & GOOS, Peter, 2016. "Orthogonal blocking arrangements for 24-run and 28-run two-level designs," Working Papers 2016002, University of Antwerp, Faculty of Business and Economics.

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