Skip to main content

Construction of Improved Branching Latin Hypercube Designs

Abstract

In this paper, we propose a new method, called the level-collapsing method, to construct branching Latin hypercube designs (BLHDs). The obtained design has a sliced structure in the third part, that is, the part for the shared factors, which is desirable for the qualitative branching factors. The construction method is easy to implement, and (near) orthogonality can be achieved in the obtained BLHDs. A simulation example is provided to illustrate the effectiveness of the new designs.

This is a preview of subscription content, access via your institution.

References

  1. Hung Y, Joseph V R, Melkote S N. Design and analysis of computer experiments with branching and nested factors. Technometrics, 2009, 51: 354–365

    MathSciNet  Article  Google Scholar 

  2. Taguchi G. System of Experimental Design. New York: Unipub/Kraus International, 1987

    MATH  Google Scholar 

  3. Hedayat A S, Sloane N J A, Stufken J. Orthogonal Arrays: Theory and Applications. New York: Springer, 1999

    Book  Google Scholar 

  4. Phadke M S. Quality Engineering Using Robust Design. Englewood Cliffs: Prentice Hall, 1989

    Google Scholar 

  5. McKay M D, Beckman R J, Conover W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 1979, 21: 239–245

    MathSciNet  MATH  Google Scholar 

  6. Qian P Z G. Sliced Latin hypercube designs. Journal of the American Statistical Association, 2012, 107: 393–399

    MathSciNet  Article  Google Scholar 

  7. Yang J F, Lin C D, Qian P Z G, et al. Construction of sliced orthogonal Latin hypercube designs. Statistica Sinica, 2013, 23: 1117–1130

    MathSciNet  MATH  Google Scholar 

  8. Huang H Z, Yang J F, Liu M Q. Construction of sliced (nearly) orthogonal Latin hypercube designs. Journal of Complexity, 2014, 30: 355–365

    MathSciNet  Article  Google Scholar 

  9. Cao R Y, Liu M Q. Construction of second-order orthogonal sliced Latin hypercube designs. Journal of Complexity, 2015, 31: 762–772

    MathSciNet  Article  Google Scholar 

  10. Yang J Y, Chen H, Lin D K J, et al. Construction of sliced maximin-orthogonal Latin hypercube designs. Statistica Sinica, 2016, 26: 589–603

    MathSciNet  MATH  Google Scholar 

  11. Wang X L, Zhao Y N, Yang J F, et al. Construction of (nearly) orthogonal sliced Latin hypercube designs. Statistics and Probability Letters, 2017, 125: 174–180

    MathSciNet  Article  Google Scholar 

  12. Chen H, Yang J Y, Lin D K J, et al. Sliced Latin hypercube designs with both branching and nested factors. Statistics and Probability Letters, 2019, 146: 124–131

    MathSciNet  Article  Google Scholar 

  13. Yang J Y, Liu M Q. Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs. Statistica Sinica, 2012, 22: 433–442

    MathSciNet  MATH  Google Scholar 

  14. Qian P Z G, Wu H Q, Wu C F J. Gaussian process models for computer experiments with qualitative and quantitative factors. Technometrics, 2008, 50: 383–396

    MathSciNet  Article  Google Scholar 

  15. Santner T J, Williams B J, Notz W I. The Design and Analysis of Computer Experiments. New York: Springer, 2003

    Book  Google Scholar 

  16. Fang K T, Li R, Sudjianto A. Design and Modeling for Computer Experiments. New York: CRC Press, 2006

    MATH  Google Scholar 

  17. Lophaven S N, Nielsen H B, Sondergaard J. A Matlab kriging toolbox DACE. Version 2.5, 2002

  18. Tang B. Orthogonal array-based Latin hypercubes. Journal of the American Statistical Association, 1993, 88: 1392–1397

    MathSciNet  Article  Google Scholar 

  19. Yin Y H, Lin D K J, Liu M Q. Sliced Latin hypercube designs via orthogonal arrays. Journal of Statistical Planning and Inference, 2014, 149: 162–171

    MathSciNet  Article  Google Scholar 

  20. Yang X, Chen H, Liu M Q. Resolvable orthogonal array-based uniform sliced Latin hypercube designs. Statistics and Probability Letters, 2014, 93: 108–115

    MathSciNet  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Min-Qian Liu.

Additional information

This work was supported by the National Natural Science Foundation of China (11601367, 11771219 and 11771220), National Ten Thousand Talents Program, Tianjin Development Program for Innovation and Entrepreneurship, and Tianjin “131” Talents Program

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, H., Yang, J. & Liu, MQ. Construction of Improved Branching Latin Hypercube Designs. Acta Math Sci 41, 1023–1033 (2021). https://doi.org/10.1007/s10473-021-0401-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-021-0401-0

Key words

  • Branching and nested factors
  • computer experiment
  • Gaussian process model
  • orthogonality

2010 MR Subject Classification

  • 62K15
  • 62K20