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Construction of four-level and mixed-level designs with zero Lee discrepancy

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Listed:
  • Liuping Hu

    (Jishou University)

  • Zujun Ou

    (Jishou University)

  • Hongyi Li

    (Jishou University)

Abstract

The uniformity criterion under Lee discrepancy favors designs with the smallest Lee discrepancy value. Based on quaternary codes, the present paper explores the construction of four-level and mixed two- and four-level fractional factorial designs with zero Lee discrepancy. A general construction method is provided, and our theoretic results show that designs with zero Lee discrepancy can be obtained from two-level full factorial designs. When measuring uniformity by Lee discrepancy, designs with a value of zero apparently are optimal. In particular, an additional lower bound on Lee discrepancy is not required.

Suggested Citation

  • Liuping Hu & Zujun Ou & Hongyi Li, 2020. "Construction of four-level and mixed-level designs with zero Lee discrepancy," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 129-139, January.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:1:d:10.1007_s00184-019-00720-x
    DOI: 10.1007/s00184-019-00720-x
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    References listed on IDEAS

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    1. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    2. Hong Qin & Kai-Tai Fang, 2004. "Discrete discrepancy in factorial designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(1), pages 59-72, July.
    3. Zou, Na & Ren, Ping & Qin, Hong, 2009. "A note on Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 496-500, February.
    4. 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.
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