IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v83y2020i5d10.1007_s00184-019-00741-6.html
   My bibliography  Save this article

Quadrupling: construction of uniform designs with large run sizes

Author

Listed:
  • Hongyi Li

    (Jishou University)

  • Hong Qin

    (Zhongnan University of Economics and Law
    Central China Normal University)

Abstract

Fractional factorial designs are widely used because of their various merits. Foldover or level permutation are usually used to construct optimal fractional factorial designs. In this paper, a novel method via foldover and level permutation, called quadrupling, is proposed to construct uniform four-level designs with large run sizes. The relationship of uniformity between the initial design and the design obtained by quadrupling is investigated, and new lower bounds of wrap-around $$L_2$$L2-discrepancy for such designs are obtained. These results provide a theoretical basis for constructing uniform four-level designs with large run sizes by quadrupling successively. Furthermore, the analytic connection between the initial design and the design obtained by quadrupling is presented under generalized minimum aberration criterion.

Suggested Citation

  • Hongyi Li & Hong Qin, 2020. "Quadrupling: construction of uniform designs with large run sizes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 527-544, July.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:5:d:10.1007_s00184-019-00741-6
    DOI: 10.1007/s00184-019-00741-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-019-00741-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-019-00741-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yu Tang & Hongquan Xu, 2014. "Permuting regular fractional factorial designs for screening quantitative factors," Biometrika, Biometrika Trust, vol. 101(2), pages 333-350.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. A. M. Elsawah, 2021. "Multiple doubling: a simple effective construction technique for optimal two-level experimental designs," Statistical Papers, Springer, vol. 62(6), pages 2923-2967, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    3. Zujun Ou & Hong Qin & Hongyi Li, 2015. "Some lower bounds of centered $$L_2$$ L 2 -discrepancy of $$2^{s-k}$$ 2 s - k designs and their complementary designs," Statistical Papers, Springer, vol. 56(4), pages 969-979, November.
    4. A. M. Elsawah & Kai-Tai Fang & Xiao Ke, 2021. "New recommended designs for screening either qualitative or quantitative factors," Statistical Papers, Springer, vol. 62(1), pages 267-307, February.
    5. Liuqing Yang & Yongdao Zhou & Min-Qian Liu, 2021. "Maximin distance designs based on densest packings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 615-634, July.
    6. Yuxuan Lin & Kai-Tai Fang, 2019. "The main effect confounding pattern for saturated orthogonal designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 843-861, October.
    7. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    8. Li, Hongyi & Qin, Hong, 2018. "Some new results on Triple designs," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 1-9.
    9. Narayanaswamy Balakrishnan & Hong Qin & Kashinath Chatterjee, 2016. "Generalized projection discrepancy and its applications in experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 19-35, January.
    10. Yong-Dao Zhou & Hongquan Xu, 2017. "Composite Designs Based on Orthogonal Arrays and Definitive Screening Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1675-1683, October.
    11. Lin Wang & Hongquan Xu & Min-Qian Liu, 2023. "Fractional factorial designs for Fourier-cosine models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 373-390, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:83:y:2020:i:5:d:10.1007_s00184-019-00741-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.