Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Mutual Information as a Criterion for Evaluating the Degree of the Orthogonality of Nearly Orthogonal Arrays

근사직교배열의 직교성을 평가하기 위한 측도로서의 상호정보

  • Jang, Dae-Heung (Division of Mathematical Sciences, Pukyong National University)
  • 장대흥 (부경대학교 수리과학부 통계학)
  • Published : 2008.09.30
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Abstract

The orthogonality is an important property in the experimental designs. When we use nearly orthogonal arrays(for example, supersaturated designs), we need evaluate the degree of the orthogonality of given nearly orthogonal arrays. We can use the mutual information as a new criterion for evaluating and testing the degree of the orthogonality of given nearly orthogonal arrays.

Keywords

References

  1. 장대흥(2004), '근사직교배열의 직교성의 정도를 평가하기 위한 그래픽방법', 한국품질경영학회지, 32권 4호, 220-228
  2. Booth, K. H. V. and Cox, D. R.(1962), 'Some Systematic Supersaturated Designs', Technometrics, Vol. 4, 489-495 https://doi.org/10.2307/1266285
  3. Brillinger, D. R. and Guha, A.(2007), 'Mutual Information in the Frequency Domain', Journal of Statistical Planning and Inference, Vol. 137, 1076-1084 https://doi.org/10.1016/j.jspi.2006.06.026
  4. Bulutoglu, D. A. and Ryan, K. J.(2008), $E_(s^{2})$'-optimal Supersaturated Designs with Good Minimax Properties when is Odd', Journal of Statistical Planning and Inference, Vol. 138, 1754-1762 https://doi.org/10.1016/j.jspi.2007.06.026
  5. Butler, N. A.(2008), 'Two-Level Supersaturated Designs for $2^k$ Runs and Other Cases', Journal of Statistical Planning and Inference, to appear
  6. Chatterjee, K., Sarkar, A. and Lin, D. K. J.(2008), 'Supersaturated Designs with High Searching Probability', Journal of Statistical Planning and Inference, Vol. 138, 272-277 https://doi.org/10.1016/j.jspi.2007.05.006
  7. Chen, J. and Liu, M. Q.(2008), 'Optimal Mixed-level Supersaturated Design with General Number of Runs', Statistics and Probability Letters, to appear
  8. Chen, J. and Liu, M. Q.(2008), 'Optimal Mixed-level k-circulant Supersaturated Designs', Journal of Statistical Planning and Inference, Vol. 138, 4151-4157 https://doi.org/10.1016/j.jspi.2008.03.025
  9. Das, A., Dey, A., Chan, L. Y. and Chatterjee, K.(2008), 'On $E_(s^{2})$-optimal Supersaturated Designs', Journal of Statistical Planning and Inference, Vol. 138, 3749-3757 https://doi.org/10.1016/j.jspi.2007.12.014
  10. Dionisio, A., Menezes, R. and Mendes, D. A.(2004), 'Mutual Information: A Measure of Dependency for Nonlinear Time Series', Physica A, Vol. 344, 326-329 https://doi.org/10.1016/j.physa.2004.06.144
  11. Fang, K. T., Lin, D. K. J. and Liu, M.(2003), 'Optimal Mixed-level Supersaturated Design', Metrika, Vol. 58, 279-291 https://doi.org/10.1007/s001840300266
  12. Fang, K. T., Lin, D. K. J., Winker, P., and Zhang, Y.(2000), 'Uniform Design: Theory and Application', Technometrics, Vol. 42, 237-248
  13. Fang, K. T., Tang, Y. and Yin, J.(2008), 'Lower Bounds of Various Criteria in Experimental Designs', Journal of Statistical Planning and Inference, Vol. 138, 184-195 https://doi.org/10.1016/j.jspi.2007.05.013
  14. Jang, D. H.(2002), 'Measures for Evaluating Non-orthogonality of Experimental Designs', Communications in Statistics-Theory and Methods, Vol. 31, 249-260 https://doi.org/10.1081/STA-120002649
  15. Jones, B. A., Lin, D. K. J. and Nachtsheim, C. J.(2008), 'Bayesian D-optimal Supersaturated Designs', Journal of Statistical Planning and Inference, Vol. 138, 86-92 https://doi.org/10.1016/j.jspi.2007.05.021
  16. Jones, B. A., Li, W., Nachtsheim, C. J. and Ye, K. Q.(2008), 'Model-Robust Supersaturated and Partially-Supersaturated Designs', Journal of Statistical Planning and Inference, to appear
  17. Koukouvinos, C., Mylona, K.(2008), 'A Method for Analyzing Supersaturated Designs with a Block Orthogonal Structure', Communications in Statistics-Simulation and Computation, Vol. 37, 290-300 https://doi.org/10.1080/03610910701790376
  18. Koukouvinos, C., Mylona, K. and Simos, D. E. (2008), 'A Hybrid SAGA Algorithm for the Construction of $E_(s^{2})$-optimal Cyclic Supersaturated Designs', Journal of Statistical Planning and Inference, to appear
  19. Koukouvinos, C., Mylona, K. and Simos, D. E. (2008), '$E_(s^{2})$-optimal and Minimaxoptimal Cyclic Supersaturated Designs via Multi-objective Simulated Annealing', Journal of Statistical Planning and Inference, Vol. 138, 1639-1646 https://doi.org/10.1016/j.jspi.2007.05.044
  20. Ma, C., Fang, K. T., and Liski, E.(2000), 'A New Approach in Constructing Orthogonal and Nearly Orthogonal Arrays', Metrika, Vol. 50, 255-268 https://doi.org/10.1007/s001840050049
  21. Nguyen, N. K. and Cheng, C. S.(2008), 'New $E_(s^{2})$-optimal Supersaturated Designs Constructed from Incomplete Block Designs', Technometrics, Vol. 50, 26-31 https://doi.org/10.1198/004017007000000452
  22. Plackett, R. L. and Burman, J. P.(1946), 'The Design of Optimum Multifactorial Experiments', Biometrika, Vol. 33, 305-325 https://doi.org/10.1093/biomet/33.4.305
  23. Siomina, I. and Ahlinder, S.(2008), 'Lean Optimization Using Supersaturated Experimental Design', Applied Numerical Mathematics, Vol. 58, 1-15 https://doi.org/10.1016/j.apnum.2006.10.007
  24. Wang, J. C. and Wu, C. F. J.(1992), 'Nearly Orthogonal Arrays with Mixed Levels and Small Runs', Technometrics, Vol. 34, 409-422 https://doi.org/10.2307/1268940
  25. Yamada, S. and Lin, D. K. J.(1999), 'Three-level Supersaturated Designs', Statistics and Probability Letters, Vol. 45, 31-39 https://doi.org/10.1016/S0167-7152(99)00038-3
  26. Zhang, Q. Z., Zhang, R. C. and Liu, M. Q.(2006), 'A Method for Screening Active Effects in Supersaturated Designs', Journal of Statistical Planning and Inference, Vol. 137, 2068-2079 https://doi.org/10.1016/j.jspi.2006.06.038