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A novel method for constructing mixed two- and three-level uniform factorials with large run sizes

Author

Listed:
  • Hongyi Li

    (Jishou University)

  • Xingyou Huang

    (Jishou University)

  • Huili Xue

    (Jishou University)

  • Hong Qin

    (Zhongnan University of Economics and Law)

Abstract

The methods of doubling and tripling have been used to construct two-level and three-level symmetrical fractional factorial designs with optimal properties. In this paper, the construction of symmetrical designs is generalized to an asymmetrical case, a novel construction method by amplifying is presented for constructing mixed two- and three-level uniform designs with large run sizes. The analytic relationship between the squared wrap-around $$L_2$$ L 2 - discrepancy value of the amplified design constructed by amplifying and the wordlength pattern of the initial design is built. Furthermore, the relationships of uniformity and aberration between the amplified design and the corresponding initial design are respectively considered. These results provide a theoretical basis for constructing mixed two- and three-level uniform designs with large run sizes. Finally, some numerical results are provided to support our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01219-8
    DOI: 10.1007/s00362-020-01219-8
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    References listed on IDEAS

    as
    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. Zujun Ou & Hong Qin, 2017. "Analytic connections between a double design and its original design in terms of different optimality criteria," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7630-7641, August.
    3. Li, Hongyi & Qin, Hong, 2018. "Some new results on Triple designs," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 1-9.
    Full references (including those not matched with items on IDEAS)

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