CONSTRUCTION OF IMPROVED BRANCHING LATIN HYPERCUBE DESIGNS

doi:10.1007/s10473-021-0401-0

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (4): 1023-1033.doi: 10.1007/s10473-021-0401-0

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CONSTRUCTION OF IMPROVED BRANCHING LATIN HYPERCUBE DESIGNS

Hao CHEN¹, Jinyu YANG², Min-Qian LIU²

1. School of Statistics, Tianjin University of Finance and Economics, Tianjin 300222, China;
2. School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China

Received:2019-05-24 Revised:2020-05-19 Online:2021-08-25 Published:2021-09-01
Contact: Min-Qian LIU E-mail:mqliu@nankai.edu.cn
Supported by:
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. The first two authors contributed equally to this work.

Abstract

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.

Key words: Branching and nested factors, computer experiment, Gaussian process model, orthogonality

CLC Number:

62K15

Hao CHEN, Jinyu YANG, Min-Qian LIU. CONSTRUCTION OF IMPROVED BRANCHING LATIN HYPERCUBE DESIGNS[J].Acta mathematica scientia,Series B, 2021, 41(4): 1023-1033.

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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
[2] Taguchi G. System of Experimental Design. New York:Unipub/Kraus International, 1987
[3] Hedayat A S, Sloane N J A, Stufken J. Orthogonal Arrays:Theory and Applications. New York:Springer, 1999
[4] Phadke M S. Quality Engineering Using Robust Design. Englewood Cliffs:Prentice Hall, 1989
[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
[6] Qian P Z G. Sliced Latin hypercube designs. Journal of the American Statistical Association, 2012, 107:393-399
[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
[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
[9] Cao R Y, Liu M Q. Construction of second-order orthogonal sliced Latin hypercube designs. Journal of Complexity, 2015, 31:762-772
[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
[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
[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
[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
[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
[15] Santner T J, Williams B J, Notz W I. The Design and Analysis of Computer Experiments. New York:Springer, 2003
[16] Fang K T, Li R, Sudjianto A. Design and Modeling for Computer Experiments. New York:CRC Press, 2006
[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
[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
[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

CONSTRUCTION OF IMPROVED BRANCHING LATIN HYPERCUBE DESIGNS

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