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Journal of Systems Science and Complexity

, Volume 31, Issue 5, pp 1391–1404 | Cite as

Efficient Asymmetrical Extended Designs Under Wrap-Around L2-Discrepancy

  • Tingxun Gou
  • Hong Qin
  • Kashinath Chatterjee
Article

Abstract

The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two-and three-level design. A formulation of wrap-around L2-discrepancy for the extended designs is developed. As a benchmark of obtaining (nearly) uniform asymmetrical extended designs, a lower bound to the wrap-around L2-discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.

Keywords

Asymmetrical extended design follow-up experiment lower bound wrap-around L2-discrepancy 

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References

  1. [1]
    Fang K T, Li R, and Sudjianto A, Design and Modeling for Computer Experiments, CRC Press, New York, 2005.CrossRefzbMATHGoogle Scholar
  2. [2]
    Bernardo M C, Buck R, Liu L, et al., Integrated circuit design optimization using a sequential strategy, IEEE Transactions on Computer-Aided Design, 1992, 11(3): 361–372.CrossRefGoogle Scholar
  3. [3]
    Sacks J, Welch W J, Mitchell T J, et al., Design and analysis of computer experiments, Statistical Science, 1989, 4(4): 409–423.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Welch W J and Sacks J, A system for quality improvement via computer experiments, Communications in Statistics — Theory and Methods, 1991, 20(2): 477–495.CrossRefGoogle Scholar
  5. [5]
    Welch W J, Buck R J, Sacks J, et al., Screening, predicting, and computer experiments, Technometrics, 1992, 34(1): 15–25.Google Scholar
  6. [6]
    Durrieu G and Briollais L, Sequential design for microarray experiments, Journal of the American Statistical Association, 2009, 104(486): 650–660.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Xiong S F, Qian P Z G, and Wu C F J, Sequential design and analysis of high-accuracy and low-accuracy computer codes, Technometrics, 2013, 55(1): 37–46.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Jala M, Lévy-Leduc C, Moulines ´E, et al., Sequential design of computer experiments for the assessment of fetus exposure to electromagnetic fields, Technometrics, 2016, 58(1): 30–42.Google Scholar
  9. [9]
    Ji Y B, Alaerts G, Xu C J, et al., Sequential uniform designs for fingerprints development of Ginkgo biloba extracts by capillary electrophoresis, Journal of Chromatography A, 2006, 1128(1): 273–281.CrossRefGoogle Scholar
  10. [10]
    Wu C F J and Hamada M S, Experiments: Planning, Analysis, and Optimization, John Wiley & Sons, New Jersey, 2011.zbMATHGoogle Scholar
  11. [11]
    Butler N A and Ramos V M, Optimal additions to and deletions from two-level orthogonal arrays, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2007, 69(1): 51–61.MathSciNetGoogle Scholar
  12. [12]
    Gupta V K, Singh P, Kole B, et al., Addition of runs to a two-level supersaturated design, Journal of Statistical Planning and Inference, 2010, 140(9): 2531–2535.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Qin H, Gou T, and Chatterjee K, A new class of two-level optimal extended designs, Journal of the Korean Statistical Society, 2016, 45(2): 168–175.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Gou T, Qin H, and Chatterjee K, A new extension strategy on three-level factorials under wraparound L2-discrepancy, Communications in Statistics — Theory and Methods, 2017, 46(18): 1–12.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Yang F, Zhou Y D, and Zhang X R, Augmented uniform designs, Journal of Statistical Planning and Inference, 2017, 182: 61–73.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Jones B and Majumdar D, Optimal supersaturated designs, Journal of the American Statistical Association, 2014, 109(508): 1592–1600.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Zhang R and Mukerjee R, Minimum aberration designs for two-level factorials in N = 1 (mod 4) runs, Statistica Sinica, 2013, 23: 853–872.MathSciNetzbMATHGoogle Scholar
  18. [18]
    Hickernell F, A generalized discrepancy and quadrature error bound, Mathematics of Computation, 1998, 67(221): 299–322.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Chatterjee K, Fang K T, and Qin H, Uniformity in factorial designs with mixed levels, Journal of Statistical Planning and Inference, 2005, 128(2): 593–607.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Zhang Q, Wang Z H, Hu J, et al., A new lower bound for wrap-around L2-discrepancy on two and three mixed level factorials, Statistics & Probability Letters, 2015, 96: 133–140.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsCentral China Normal UniversityWuhanChina
  2. 2.Department of StatisticsVisva-Bharati UniversitySantiniketanIndia

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