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Construction of space-filling orthogonal Latin hypercube designs

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  • Li, Hui
  • Yang, Liuqing
  • Liu, Min-Qian

Abstract

Latin hypercube designs (LHDs) play an important role in computer experiments, because they can achieve the maximum stratification when projected onto any one dimension. The orthogonal LHD (OLHD), as a special kind of LHDs, has been widely studied and used. OLHDs ensure that the estimates of main effects in linear models are uncorrelated. Also, it is crucial to use a design with good stratifications in order to explore the experimental region efficiently and build a high-quality metamodel. This paper first proposes a method to construct OLHDs with sd runs and d⌊(sd−1)/(d(s−1))⌋/2 factors, which achieve a stratification on an s2×s or s×s2 grid when projected onto any two dimensions. Moreover, most column pairs achieve stratifications on s2×s2 grids. Another method is further provided to construct OLHDs with more factors, which achieve the aforementioned stratifications in each sub-design. The resulting OLHDs are more space-filling than existing OLHDs.

Suggested Citation

  • Li, Hui & Yang, Liuqing & Liu, Min-Qian, 2022. "Construction of space-filling orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221002078
    DOI: 10.1016/j.spl.2021.109245
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    References listed on IDEAS

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    1. Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    2. Fasheng Sun & Min-Qian Liu & Dennis K. J. Lin, 2009. "Construction of orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 971-974.
    3. 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.
    4. Fasheng Sun & Boxin Tang, 2017. "A general rotation method for orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 104(2), pages 465-472.
    5. 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.
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    Cited by:

    1. 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.

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