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

  • A. M. ElsawahEmail author
  • Kai-Tai Fang
  • Ping He
  • Hong Qin


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.


Computer experiment Uniform design Uniformity criteria Orthogonality criteria Added design Extended design 

Mathematics Subject Classification

62K05 62K15 



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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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt
  2. 2.Division of Science and TechnologyBNU-HKBU United International CollegeZhuhaiChina
  3. 3.Faculty of Mathematics and StatisticsCentral China Normal UniversityWuhanChina
  4. 4.The Key Lab of Random Complex Structures and Data AnalysisThe Chinese Academy of SciencesBeijingChina

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