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Two-Level Orthogonal Screening Designs With 24, 28, 32, and 36 Runs

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  • Eric D. Schoen
  • Nha Vo-Thanh
  • Peter Goos

Abstract

The potential of two-level orthogonal designs to fit models with main effects and two-factor interaction effects is commonly assessed through the correlation between contrast vectors involving these effects. We study the complete catalog of nonisomorphic orthogonal two-level 24-run designs involving 3–23 factors and we identify the best few designs in terms of these correlations. By modifying an existing enumeration algorithm, we identify the best few 28-run designs involving 3–14 factors and the best few 36-run designs in 3–18 factors as well. Based on a complete catalog of 7570 designs with 28 runs and 27 factors, we also seek good 28-run designs with more than 14 factors. Finally, starting from a unique 31-factor design in 32 runs that minimizes the maximum correlation among the contrast vectors for main effects and two-factor interactions, we obtain 32-run designs that have low values for this correlation. To demonstrate the added value of our work, we provide a detailed comparison of our designs to the alternatives available in the literature. Supplementary materials for this article are available online.

Suggested Citation

  • Eric D. Schoen & Nha Vo-Thanh & Peter Goos, 2017. "Two-Level Orthogonal Screening Designs With 24, 28, 32, and 36 Runs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1354-1369, July.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:519:p:1354-1369
    DOI: 10.1080/01621459.2017.1279547
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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. 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.
    3. Angelopoulos, P. & Koukouvinos, C., 2007. "Maximum estimation capacity projection designs from Hadamard matrices with 32, 36 and 40 runs," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 220-229, January.
    4. H. Evangelaras & C. Koukouvinos & K. Mylona, 2006. "Projection Properties of Hadamard Matrices of Order 36 Obtained from Paley’s Constructions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(3), pages 351-359, December.
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    Cited by:

    1. Emanuele Borgonovo & Elmar Plischke & Giovanni Rabitti, 2022. "Interactions and computer experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1274-1303, September.
    2. Singh, Rakhi & Stufken, John, 2024. "Factor selection in screening experiments by aggregation over random models," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    3. VÁZQUEZ-ALCOCER, Alan & SCHOEN, Eric D. & GOOS, Peter, 2018. "A mixed integer optimization approach for model selection in screening experiments," Working Papers 2018007, University of Antwerp, Faculty of Business and Economics.
    4. Eendebak, Pieter T. & Schoen, Eric D. & Vazquez, Alan R. & Goos, Peter, 2023. "Systematic enumeration of two-level even-odd designs of strength 3," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).

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