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Construction of group strong orthogonal arrays of strength two plus

Author

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Grömping, Ulrike, 2023. "A unifying implementation of stratum (aka strong) orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).

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