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Group strong orthogonal arrays and their construction methods

Author

Listed:
  • Pengnan Li

    (Changchun University of Technology)

  • Chunjie Wang

    (Changchun University of Technology)

  • Bochuan Jiang

    (Beijing Jiaotong University)

Abstract

In practical applications, group structures may exist between response variables and input factors in certain computer experiments. The interactions of interest occur exclusively within factors within several disjoint groups. In such experiments, an ideal design ensures superior space-filling properties for each group compared to the overall design, which itself exhibits commendable space-filling characteristics. Inspired by this idea, we introduce the concept of group strong orthogonal arrays, which can be partitioned into distinct groups. Both the overall design and each individual group constitute strong orthogonal arrays, with the strength of each group exceeding that of the entire design. Addressing different strengths and levels, we present the construction methods for three distinct types of such designs, among which two types are column-orthogonal. Orthogonal arrays, difference matrices, and rotation matrices play pivotal roles in the construction process.

Suggested Citation

  • Pengnan Li & Chunjie Wang & Bochuan Jiang, 2025. "Group strong orthogonal arrays and their construction methods," Statistical Papers, Springer, vol. 66(3), pages 1-30, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01674-1
    DOI: 10.1007/s00362-025-01674-1
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    References listed on IDEAS

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    1. Kleijnen, J.P.C., 2017. "Design and Analysis of simulation experiments : Tutorial," Other publications TiSEM c7ad6b68-dcd6-4485-9ee2-0, Tilburg University, School of Economics and Management.
    2. 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.
    3. V. Roshan Joseph & Evren Gul & Shan Ba, 2015. "Maximum projection designs for computer experiments," Biometrika, Biometrika Trust, vol. 102(2), pages 371-380.
    4. Cheng-Yu Sun & Boxin Tang, 2023. "Uniform Projection Designs and Strong Orthogonal Arrays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 417-423, January.
    5. Xu He, 2021. "Lattice-based designs with quasi-optimal separation distance on all projections [A framework for controlling sources of inaccuracy in Gaussian process emulation of deterministic computer experiment," Biometrika, Biometrika Trust, vol. 108(2), pages 443-454.
    6. Yongdao Zhou & Hongquan Xu, 2015. "Space-filling properties of good lattice point sets," Biometrika, Biometrika Trust, vol. 102(4), pages 959-966.
    7. 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.
    8. Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    9. Wenlong Li & Min-Qian Liu & Boxin Tang, 2021. "A method of constructing maximin distance designs [Interleaved lattice-based maximin distance designs]," Biometrika, Biometrika Trust, vol. 108(4), pages 845-855.
    10. David M. Steinberg & Dennis K. J. Lin, 2006. "A construction method for orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 93(2), pages 279-288, June.
    11. C. Devon Lin & Rahul Mukerjee & Boxin Tang, 2009. "Construction of orthogonal and nearly orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 96(1), pages 243-247.
    12. Yaping Wang & Jianfeng Yang & Hongquan Xu, 2018. "On the connection between maximin distance designs and orthogonal designs," Biometrika, Biometrika Trust, vol. 105(2), pages 471-477.
    13. 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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