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Construction of Optimal Mixed-Level Uniform Designs

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Abstract

The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments. The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design. In this paper, the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound. These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms. Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods. Moreover, the resulting designs are also Χ2-optimal and minimum moment aberration designs.

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Author information

Authors and Affiliations

  1. Department of Population Health Sciences, Division of Biostatistics and Data Science, Augusta University, Augusta, GA, 30912, USA

    Kashinath Chatterjee

  2. NITFID, LPMC & KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin, 300071, China

    Min-Qian Liu & Liuqing Yang

  3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Hong Qin

Authors
  1. Kashinath Chatterjee
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  2. Min-Qian Liu
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  3. Hong Qin
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  4. Liuqing Yang
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Corresponding author

Correspondence to Min-Qian Liu.

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The authors declare no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12131001, 12226343, 12371260, and 12371261, National Ten Thousand Talents Program of China, and the 111 Project under Grant No. B20016.

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Chatterjee, K., Liu, MQ., Qin, H. et al. Construction of Optimal Mixed-Level Uniform Designs. J Syst Sci Complex 37, 841–862 (2024). https://doi.org/10.1007/s11424-024-2379-x

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  • DOI: https://doi.org/10.1007/s11424-024-2379-x

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