IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i5d10.1007_s00362-017-0892-x.html
   My bibliography  Save this article

Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy

Author

Listed:
  • Zujun Ou

    (Jishou University)

  • Hong Qin

    (Central China Normal University)

Abstract

Literatures reveal that foldover is a useful technique in construction of factorial designs. The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around $$L_2$$ L 2 -discrepancy to assess the optimal foldover plans for asymmetric fractional factorials. A general foldover strategy and combined design under a foldover plan are developed for asymmetric fractional factorials, some theoretical properties on the equivalence between the defined foldover plan and its complementary foldover plan are discussed. A new lower bound for the wrap-around $$L_2$$ L 2 -discrepancy of combined designs is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.

Suggested Citation

  • Zujun Ou & Hong Qin, 2019. "Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy," Statistical Papers, Springer, vol. 60(5), pages 1699-1716, October.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0892-x
    DOI: 10.1007/s00362-017-0892-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0892-x
    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/s00362-017-0892-x?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. Kashinath Chatterjee & Kai-Tai Fang & Hong Qin, 2006. "A Lower Bound for the Centered L 2 -Discrepancy on Asymmetric Factorials and its Application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 243-255, April.
    2. Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2005. "Choice of optimal initial designs in sequential experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 127-135, April.
    3. Fasheng Sun & Jie Chen & Min-Qian Liu, 2011. "Connections between uniformity and aberration in general multi-level factorials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 305-315, May.
    4. Fang, Kai-Tai & Lin, Dennis K. J. & Qin, Hong, 2003. "A note on optimal foldover design," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 245-250, April.
    5. Zujun Ou & Kashinath Chatterjee & Hong Qin, 2011. "Lower bounds of various discrepancies on combined designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 109-119, July.
    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. Zujun Ou & Hongyi Li, 2021. "A new foldover strategy and optimal foldover plans for three-level design," Statistical Papers, Springer, vol. 62(5), pages 2433-2451, October.
    2. Zongyi Hu & Jiaqi Liu & Yi Li & Hongyi Li, 2021. "Uniform augmented q-level designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 969-995, October.

    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. Elsawah, A.M. & Qin, Hong, 2015. "Lee discrepancy on symmetric three-level combined designs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 273-280.
    2. Zujun Ou & Hongyi Li, 2021. "A new foldover strategy and optimal foldover plans for three-level design," Statistical Papers, Springer, vol. 62(5), pages 2433-2451, October.
    3. Elsawah, A.M. & Qin, Hong, 2015. "A new strategy for optimal foldover two-level designs," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 116-126.
    4. A. M. Elsawah, 2018. "Choice of optimal second stage designs in two-stage experiments," Computational Statistics, Springer, vol. 33(2), pages 933-965, June.
    5. 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.
    6. Tu, Min & Huang, Hui & Liu, Ze-Hua & Chen, Huan-Xin & Ren, Cheng-Qin & Chen, Guo-Jie & Hu, Yan, 2017. "Factor analysis and optimization of operational parameters in a liquid desiccant air-conditioning system," Energy, Elsevier, vol. 139(C), pages 767-781.
    7. Liuping Hu & Kashinath Chatterjee & Jiaqi Liu & Zujun Ou, 2020. "New lower bound for Lee discrepancy of asymmetrical factorials," Statistical Papers, Springer, vol. 61(4), pages 1763-1772, August.
    8. Ai, Mingyao & Hickernell, Fred J. & Lin, Dennis K.J., 2008. "Optimal foldover plans for regular s-level fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 896-903, May.
    9. Yang, Xue & Yang, Gui-Jun & Su, Ya-Juan, 2018. "Uniform minimum moment aberration designs," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 26-33.
    10. Zujun Ou & Kashinath Chatterjee & Hong Qin, 2011. "Lower bounds of various discrepancies on combined designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 109-119, July.
    11. Zou, Na & Gou, Tingxun & Qin, Hong & Chatterjee, Kashinath, 2020. "Generalized foldover method for high-level designs," Statistics & Probability Letters, Elsevier, vol. 164(C).
    12. A. M. Elsawah & Kai-Tai Fang, 2020. "New foundations for designing U-optimal follow-up experiments with flexible levels," Statistical Papers, Springer, vol. 61(2), pages 823-849, April.
    13. A. M. Elsawah & Hong Qin, 2017. "Optimum mechanism for breaking the confounding effects of mixed-level designs," Computational Statistics, Springer, vol. 32(2), pages 781-802, June.
    14. Stelios Georgiou & Christos Koukouvinos & Min-Qian Liu, 2014. "U-type and column-orthogonal designs for computer experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 1057-1073, November.
    15. Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2007. "2 m 4 1 designs with minimum aberration or weak minimum aberration," Statistical Papers, Springer, vol. 48(2), pages 235-248, April.
    16. Elsawah, A.M., 2016. "Constructing optimal asymmetric combined designs via Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 24-31.
    17. Caporale, Diana & De Lucia, Caterina, 2015. "Social acceptance of on-shore wind energy in Apulia Region (Southern Italy)," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 1378-1390.
    18. Kashinath Chatterjee & Kai-Tai Fang & Hong Qin, 2006. "A Lower Bound for the Centered L 2 -Discrepancy on Asymmetric Factorials and its Application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 243-255, April.
    19. Chatterjee, Kashinath & Li, Zhaohai & Qin, Hong, 2012. "Some new lower bounds to centered and wrap-round L2-discrepancies," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1367-1373.

    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:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0892-x. 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.