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Design Efficiency of the Asymmetric Minimum Projection Uniform Designs

Author

Listed:
  • Qiming Bai

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, China)

  • Hongyi Li

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, China)

  • Shixian Zhang

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, China)

  • Jiezhong Tian

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, China)

Abstract

Highly efficient designs and uniform designs are widely applied in many fields because of their good properties. The purpose of this paper is to study the issue of design efficiency for asymmetric minimum projection uniform designs. Based on the centered L 2 discrepancy, the uniformity of the designs with mixed levels is defined, which is used to measure the projection uniformity of the designs. The analytical relationship between the uniformity pattern and the design efficiency is established for mixed-level orthogonal arrays with a strength of two. Moreover, a tight lower bound of the uniformity pattern is presented. The research is relevant in the field of experimental design by providing a theoretical basis for constructing the minimum number of projection uniform designs with a high design efficiency under a certain condition. These conclusions are verified by some numerical examples, which illustrate the theoretical results obtained in this paper.

Suggested Citation

  • Qiming Bai & Hongyi Li & Shixian Zhang & Jiezhong Tian, 2023. "Design Efficiency of the Asymmetric Minimum Projection Uniform Designs," Mathematics, MDPI, vol. 11(3), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:765-:d:1056282
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    References listed on IDEAS

    as
    1. C.‐S. Cheng & D. M. Steinberg & D. X. Sun, 1999. "Minimum aberration and model robustness for two‐level fractional factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 85-93.
    2. Kang Wang & Zujun Ou & Jiaqi Liu & Hongyi Li, 2021. "Uniformity pattern of q-level factorials under mixture discrepancy," Statistical Papers, Springer, vol. 62(4), pages 1777-1793, August.
    3. Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, vol. 89(4), pages 893-904, December.
    4. Liuping Hu & Kashinath Chatterjee & Jiaqi Liu & Zujun Ou, 2020. "New lower bound for Lee discrepancy of asymmetrical factorials," Statistical Papers, Springer, vol. 61(4), pages 1763-1772, August.
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