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Some new results on Triple designs

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  • Li, Hongyi
  • Qin, Hong

Abstract

The method of doubling has been used to construct two-level fractional factorial designs. Zhang (2016) extended the method of doubling to the method of tripling, which has been used to construct three-level fractional factorial designs. Various popular screening criteria, such as E(fNOD) criterion, generalized minimum aberration (GMA), minimum moment aberration (MMA), B criterion and uniformity criterion, have been proposed from different viewpoints to compare and construct designs. In this paper, the analytic connections between Triple designs constructed by tripling and initial designs under the above screening criteria are considered. These connections are suitable to general original three-level fractional factorial designs, whether regular or nonregular. Furthermore, the connections provide theoretical basis for constructing a kind of optimal three-level designs with large sizes by tripling successively.

Suggested Citation

  • Li, Hongyi & Qin, Hong, 2018. "Some new results on Triple designs," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 1-9.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:1-9
    DOI: 10.1016/j.spl.2018.03.003
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    References listed on IDEAS

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    1. Ou, Zujun & Qin, Hong, 2010. "Some applications of indicator function in two-level factorial designs," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 19-25, January.
    2. Yamada, Shu & Lin, Dennis K. J., 1999. "Three-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 31-39, October.
    3. 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.
    4. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 279-291, December.
    5. Zhang, Qionghui & Wang, Zhenghong & Hu, Jianwei & Qin, Hong, 2015. "A new lower bound for wrap-around L2-discrepancy on two and three mixed level factorials," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 133-140.
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    Cited by:

    1. Zujun Ou & Minghui Zhang & Hongyi Li, 2023. "Triple Designs: A Closer Look from Indicator Function," Mathematics, MDPI, vol. 11(3), pages 1-12, February.
    2. Hongyi Li & Xingyou Huang & Huili Xue & Hong Qin, 2021. "A novel method for constructing mixed two- and three-level uniform factorials with large run sizes," Statistical Papers, Springer, vol. 62(6), pages 2907-2921, December.

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