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Construction of three-level factorial designs with general minimum lower-order confounding via resolution IV designs

Author

Listed:
  • Tian-fang Zhang

    (Jiangxi Normal University)

  • Yingxing Duan

    (No. 3 Middle School of Jiujiang City)

  • Shengli Zhao

    (Qufu Normal University)

  • Zhiming Li

    (Xinjiang University)

Abstract

The general minimum lower order confounding (GMC) is a criterion for selecting designs when the experimenter has prior information about the order of the importance of the factors. The paper considers the construction of $$3^{n-m}$$ 3 n - m designs under the GMC criterion. Based on some theoretical results, it proves that some large GMC $$3^{n-m}$$ 3 n - m designs can be obtained by combining some small resolution IV designs T. All the results for $$4\le \#\{T\} \le 20$$ 4 ≤ # { T } ≤ 20 are tabulated in the table, where $$\#$$ # means the cardinality of a set.

Suggested Citation

  • Tian-fang Zhang & Yingxing Duan & Shengli Zhao & Zhiming Li, 2025. "Construction of three-level factorial designs with general minimum lower-order confounding via resolution IV designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(5), pages 679-687, July.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:5:d:10.1007_s00184-024-00972-2
    DOI: 10.1007/s00184-024-00972-2
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    References listed on IDEAS

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    1. Hongquan Xu, 2005. "A catalogue of three-level regular fractional factorial designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(2), pages 259-281, November.
    2. Zhiming Li & Zhidong Teng & Tianfang Zhang & Runchu Zhang, 2016. "Analysis on $$s^{n-m}$$ s n - m designs with general minimum lower-order confounding," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(2), pages 207-222, April.
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