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Orthogonal Arrays Robust to a Specified Set of Nonnegligible Effects

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Abstract

This paper considers experimental situations where the interested effects have to be orthogonal to a set of nonnegligible effects. It is shown that various types of orthogonal arrays with mixed strength are A-optimal for estimating the parameters in ANOVA high dimension model representation. Both cases including interactions or not are considered in the model. In particularly, the estimations of all main effects are A-optimal in a mixed strength (2, 2)3 orthogonal array and the estimations of all main effects and two-factor interactions in G 1×G 2 are A-optimal in a mixed strength (2, 2)4 orthogonal array. The properties are also illustrated through a simulation study.

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References

  1. Wu C F J and Zhu Y, Optimal selection of single arrays for parameter design experiments, Statistica Sinica, 2003, 13(4): 1179–1199.

    MathSciNet  MATH  Google Scholar 

  2. Zhu Y, Zeng P, and Jennings K, Optimal compound orthogonal arrays and single arrays for robust parameter design experiments, Technometrics, 2007, 49(4): 440–453.

    Article  MathSciNet  Google Scholar 

  3. Yang J F, Zhang R C, and Liu M Q, Construction of optimal blocking schemes for robust parameter designs, Acta Mathematica Scientia, 2013, 33(5): 1431–1438.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ke W, Tang B, and Wu H, Compromise plans with clear two-factor interactions, Statistica Sinica, 2005, 15(3): 709–715.

    MathSciNet  MATH  Google Scholar 

  5. Tang B, Orthogonal arrays robust to nonnegligible two-factor interactions, Biometrika, 2006, 93(1): 137–146.

    Article  MathSciNet  MATH  Google Scholar 

  6. Lekivetz R and Tang B, Robust designs through partially clear two-factor interactions, Biometrika, 2011, 98(3): 733–739.

    Article  MathSciNet  MATH  Google Scholar 

  7. Tang B and Zhou J, D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions, Metrika, 2013, 76(3): 325–337.

    Article  MathSciNet  MATH  Google Scholar 

  8. Efron B and Stein C, The Jackknife estimate of variance, The Annals of Statistics, 1981, 9(3): 586–596.

    Article  MathSciNet  MATH  Google Scholar 

  9. Sobol I M, Sensitivity analysis for nonlinear mathematical models, Mathematical Modeling and Computational Experiments, 1993, 1(4): 407–414.

    MathSciNet  MATH  Google Scholar 

  10. Wang X D, Tang Y C, and Zhang Y S, Orthogonal arrays for estimating global sensitivity indices of non-parametric models based on ANOVA high-dimensional model representation, Journal of Statistical Planning and Inference, 2012, 142(7): 1801–1810.

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhang Y S, Lu Y Q, and Pang S Q, Orthogonal arrays obtained by orthogonal decomposition of projection matrices, Statistica Sinica, 1999, 9(2): 595–604.

    MathSciNet  MATH  Google Scholar 

  12. Zhang Y S, Pang S Q, and Wang Y P, Orthogonal arrays obtained by generalized Hadamard product, Discrete Mathematics, 2001, 238(1): 151–170.

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang Y S, Li W G, Mao S S, and Zheng Z G, A simple method for constructing orthogonal arrays by the Kronecker sum, Journal of Systems Science and Complexity, 2006, 19(2): 266–273.

    Article  MathSciNet  MATH  Google Scholar 

  14. Pang S Q, Liu S Y, and Zhang Y S, A note on orthogonal arrays obtained by orthogonal decomposition of projection matrices, Statistics and Probability Letters, 2003, 63(4): 411–416.

    Article  MathSciNet  MATH  Google Scholar 

  15. Pang S Q, Zhang Y S, and Liu S Y, Further results on the orthogonal arrays obtained by generalized Hadamard product, Statistics and Probability Letters, 2004, 68(1): 17–25.

    Article  MathSciNet  MATH  Google Scholar 

  16. Wu C F J and Hamada M, Experiments: Planning, Analysis, and Optimization Second Edition, John Wiley & Sons, Inc. Hoboken, New Jersey, 2009.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 211189, China

    Xueping Chen & Jinguan Lin

  2. Department of Mathematics, Jiangsu University of Technology, Changzhou, 213001, China

    Xueping Chen

Authors
  1. Xueping Chen
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  2. Jinguan Lin
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Corresponding author

Correspondence to Jinguan Lin.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11171065, 11301073, the Natural Science Foundation of Jiangsu under Grant No. BK20141326, the Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20120092110021, and Scientific Research Foundation of Graduate School of Southeast University under Grant No. YBJJ1444.

This paper was recommended for publication by Editor SUN Liuquan.

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Chen, X., Lin, J. Orthogonal Arrays Robust to a Specified Set of Nonnegligible Effects. J Syst Sci Complex 29, 531–541 (2016). https://doi.org/10.1007/s11424-015-3275-1

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  • DOI: https://doi.org/10.1007/s11424-015-3275-1

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