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.
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Hung Y, Joseph V R, Melkote S N. Design and analysis of computer experiments with branching and nested factors. Technometrics, 2009, 51: 354–365
Taguchi G. System of Experimental Design. New York: Unipub/Kraus International, 1987
Hedayat A S, Sloane N J A, Stufken J. Orthogonal Arrays: Theory and Applications. New York: Springer, 1999
Phadke M S. Quality Engineering Using Robust Design. Englewood Cliffs: Prentice Hall, 1989
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
Qian P Z G. Sliced Latin hypercube designs. Journal of the American Statistical Association, 2012, 107: 393–399
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
Huang H Z, Yang J F, Liu M Q. Construction of sliced (nearly) orthogonal Latin hypercube designs. Journal of Complexity, 2014, 30: 355–365
Cao R Y, Liu M Q. Construction of second-order orthogonal sliced Latin hypercube designs. Journal of Complexity, 2015, 31: 762–772
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
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
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
Yang J Y, Liu M Q. Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs. Statistica Sinica, 2012, 22: 433–442
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
Santner T J, Williams B J, Notz W I. The Design and Analysis of Computer Experiments. New York: Springer, 2003
Fang K T, Li R, Sudjianto A. Design and Modeling for Computer Experiments. New York: CRC Press, 2006
Lophaven S N, Nielsen H B, Sondergaard J. A Matlab kriging toolbox DACE. Version 2.5, 2002
Tang B. Orthogonal array-based Latin hypercubes. Journal of the American Statistical Association, 1993, 88: 1392–1397
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
Yang X, Chen H, Liu M Q. Resolvable orthogonal array-based uniform sliced Latin hypercube designs. Statistics and Probability Letters, 2014, 93: 108–115
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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
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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
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DOI: https://doi.org/10.1007/s10473-021-0401-0