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Optimum Addition of Information to Computer Experiments in View of Uniformity and Orthogonality

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Abstract

Computer experiments have become ubiquitous across the engineering, physical and chemical sciences. Computer experiments are constructed to emulate the behavior of a physical system. Assume that we perform an experiment using a two-level uniform design. If, after obtaining data, we decide additional runs of the computer simulator are needed, how to add more runs after collecting our data? How to design the experiment to efficiently extract useful information from it? In this paper, we try to answer these questions by providing a new approach for constructing efficient uniform designs by adding new runs to an existing uniform design. The optimization criteria are the uniformity criteria measured by Lee, symmetric, wrap-around, centered and mixture discrepancy and the orthogonality criteria measured by the B-criterion and the O-criterion. We investigate the relationship between orthogonality and uniformity criteria in view of analytical expressions and lower bounds.

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Acknowledgements

The authors greatly appreciate helpful suggestions of the referees and the Editor in Chief Prof. Rosihan M. Ali that significantly improved the paper. This work was partially supported by the UIC Grants (Nos. R201409 and R201712), the Zhuhai Premier Discipline Grant and the National Natural Science Foundation of China (Nos. 11271147, 11471135, 11471136).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    A. M. Elsawah

  2. Division of Science and Technology, BNU-HKBU United International College, Zhuhai, 519085, China

    A. M. Elsawah, Kai-Tai Fang & Ping He

  3. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Hong Qin

  4. The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing, China

    Kai-Tai Fang

Authors
  1. A. M. Elsawah
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  2. Kai-Tai Fang
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  3. Ping He
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  4. Hong Qin
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Corresponding author

Correspondence to A. M. Elsawah.

Additional information

Communicated by See Keong Lee.

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Elsawah, A.M., Fang, KT., He, P. et al. Optimum Addition of Information to Computer Experiments in View of Uniformity and Orthogonality. Bull. Malays. Math. Sci. Soc. 42, 803–826 (2019). https://doi.org/10.1007/s40840-017-0513-9

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  • DOI: https://doi.org/10.1007/s40840-017-0513-9

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