IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v85y2022i6d10.1007_s00184-021-00843-0.html
   My bibliography  Save this article

Construction of group strong orthogonal arrays of strength two plus

Author

Listed:
  • Mengmeng Liu

    (Nankai University)

  • Min-Qian Liu

    (Nankai University)

  • Jinyu Yang

    (Nankai University)

Abstract

Strong orthogonal arrays (SOAs) have received more and more attention recently since they enjoy more desirable space-filling properties than ordinary orthogonal arrays. Among them, the SOAs of strength $$2+$$ 2 + are the most advisable as they satisfy the same two-dimensional space-filling property as SOAs of strength 3 while having more columns for given run sizes. In addition, column-orthogonality is also a desirable property for designs of computer experiments. Existing column-orthogonal SOAs of strength $$2+$$ 2 + have limited columns. In this paper, we propose a new class of space-filling designs, called group SOAs of strength $$2+$$ 2 + , and provide construction methods for such designs. The proposed designs can accommodate more columns than column-orthogonal SOAs of strength $$2+$$ 2 + for given run sizes while satisfying similar stratifications and retaining a high proportion of column-orthogonal columns. Orthogonal arrays and difference schemes play important roles in the construction. The construction procedures are easy to implement and a large amount of group SOAs with $$s^2$$ s 2 levels are constructed where $$s \ge 2$$ s ≥ 2 is a prime power. In addition, the run sizes of the constructed designs are s times the ones of the orthogonal arrays used in the construction procedure. Thus they are relatively flexible.

Suggested Citation

  • Mengmeng Liu & Min-Qian Liu & Jinyu Yang, 2022. "Construction of group strong orthogonal arrays of strength two plus," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 657-674, August.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:6:d:10.1007_s00184-021-00843-0
    DOI: 10.1007/s00184-021-00843-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-021-00843-0
    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/s00184-021-00843-0?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. Yongdao Zhou & Boxin Tang, 2019. "Column-orthogonal strong orthogonal arrays of strength two plus and three minus," Biometrika, Biometrika Trust, vol. 106(4), pages 997-1004.
    2. Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    3. Derek Bingham & Randy R. Sitter & Boxin Tang, 2009. "Orthogonal and nearly orthogonal designs for computer experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 51-65.
    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. Grömping, Ulrike, 2023. "A unifying implementation of stratum (aka strong) orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).

    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. Wenlong Li & Min-Qian Liu & Jian-Feng Yang, 2022. "Construction of column-orthogonal strong orthogonal arrays," Statistical Papers, Springer, vol. 63(2), pages 515-530, April.
    2. Grömping, Ulrike, 2023. "A unifying implementation of stratum (aka strong) orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    3. Song-Nan Liu & Min-Qian Liu & Jin-Yu Yang, 2023. "Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    4. Jiang, Bochuan & Wang, Zuzheng & Wang, Yaping, 2021. "Strong orthogonal arrays of strength two-plus based on the Addelman–Kempthorne method," Statistics & Probability Letters, Elsevier, vol. 175(C).
    5. 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.
    6. Li Gu & Jian-Feng Yang, 2013. "Construction of nearly orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 819-830, August.
    7. Ifigenia Efthimiou & Stelios Georgiou & Min-Qian Liu, 2015. "Construction of nearly orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 45-57, January.
    8. Mandal, B.N. & Dash, Sukanta & Parui, Shyamsundar & Parsad, Rajender, 2016. "Orthogonal Latin hypercube designs with special reference to four factors," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 181-185.
    9. Fasheng Sun & Boxin Tang, 2017. "A Method of Constructing Space-Filling Orthogonal Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 683-689, April.
    10. Li, Hui & Yang, Liuqing & Liu, Min-Qian, 2022. "Construction of space-filling orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 180(C).
    11. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    12. Zujun Ou & Minghui Zhang & Hongyi Li, 2023. "Triple Designs: A Closer Look from Indicator Function," Mathematics, MDPI, vol. 11(3), pages 1-12, February.
    13. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    14. Ru Yuan & Bing Guo & Min-Qian Liu, 2021. "Flexible sliced Latin hypercube designs with slices of different sizes," Statistical Papers, Springer, vol. 62(3), pages 1117-1134, June.

    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:85:y:2022:i:6:d:10.1007_s00184-021-00843-0. 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.