The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Measures for Evaluating the Orthogonal Array of Strength 3

강도 3의 직교대열을 평가하기 위한 측도

  • Jang Dae-Heung (Division of Mathematical Sciences, Pukyong National University)
  • 장대흥 (부경대학교 수리과학부 통계학)
  • Published : 2005.11.01
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Abstract

We usually use orthogonal designs-orthogonal array of strength 2 as orthogonal arrays. It was shown that fractional factorial plaits represented by orthogonal arrays of strength 3 are universally optimal under the additive motels that includes the mean, all main effects and all two-factor interactions. Therefore, we need the measure for evaluating the orthogonal array of strength 3. We can extend this measure as the measure for evaluating the orthogonal array of strength t($\ge$ 2).

우리는 직교배열로서 직교계획, 즉 강도(strength)가 2인 직교배열을 주로 이용한다. 그러나, 강도 3인 직교배열은 주효과들과 2인자교호작용이 포함되는 가법모형 하에서 전체최적화(universal optimality)하다는 것이 밝혀져 있다. 그러므로 임의의 배열이 강도 3인 직교배열인가를 평가하는 측도가 필요하다. 이를 확장하면 임의의 배열이 강도 t($\ge$ 2)인 직교배열인가를 평가하는 측도를 제안할 수 있다.

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References

  1. Bisgaard, S. and Gertsbakh, I.(2000). $2^{K-P}$Experiments with binary responses: Inverse binomial sampling, Journal of Quality Technology, 32, 148-156
  2. Chan, L., Ma, C., and Goh, T. N.(2003). Orthogonal arrays for experiments with Lean designs, Journal of Quality Technology, 35, 123-138
  3. Chateauneuf, M. A., Colbourn, C. J., and Kreher, D. L.(1999). Covering arrays of strength 3, Design Cades and Cryptography, 16, 235-242 https://doi.org/10.1023/A:1008379710317
  4. Chateauneuf, M. A. and Kreher, D. L.(2002). On the state of strength-three covering arrays, the Journal of Combinatorial Designs, 10, 217-238 https://doi.org/10.1002/jcd.10002
  5. Cheng, C. and Mukerjee, R.(2001). Blocked regular fractional factorial designs with maximum estimation capacity, Annals of Statistics, 29, 530-548 https://doi.org/10.1214/aos/1009210551
  6. Crosier, R. B. (2000). Some new two-level saturated designs, Journal of Quality Technology, 32, 103-110
  7. Das, A., Dey, A. and Midha, C. K.(2003). On a property of orthogonal arrays and optimal blocking of fractional factorial plans, Metrika, 57, 127-135 https://doi.org/10.1007/s001840200204
  8. Dey, A.(2002). Asymmetric orthogonal arrays, Design Workshop Lecture Nates, 97-115
  9. Druilhet, P.(2004). Conditions for optimality in experimental designs, Linear Algebra and Its Applications, to appear
  10. Druilhet, P.(2004). Conditions for optimality in experimental designs, Linear Algebra and Its Applications, to appear
  11. Fang, K, Lin, D. K. J., and Ma, C.(2000). On the construction of multi-level supersaturated designs, Journal of Statistical Planning and Inference, 86, 239-252 https://doi.org/10.1016/S0378-3758(99)00163-9
  12. Fang, K., Lin, D. K. J., Winker, P., and Zhang, Y.(2000). Uniform design: Theory and application, Technometrics, 42, 237-248 https://doi.org/10.2307/1271079
  13. Jang, D. H.(2002). Measures for evaluating non-orthogonality of experimental designs, Communications in Statistics - Theory and Methods, 31, 249-260 https://doi.org/10.1081/STA-120002649
  14. Kreher, C.. J. (1996). Orthogonal arrays of strength 3, the Journal of Combinatorial Designs, 4, 67-69 https://doi.org/10.1002/(SICI)1520-6610(1996)4:1<67::AID-JCD7>3.0.CO;2-Y
  15. Li, W. W. and Wu, C. F. J.(1997). Columnwise-pairwise algorithms with applications to the construction of supersaturated designs, Technometrics, 39, 171-179 https://doi.org/10.2307/1270905
  16. Liao, C. T. and Lyer, H. K.(2000). Optimal $2^{n-p}$fractional factorial designs for dispersion effects under a location-dispersion model, Communications in Statistics - Theory and Methods, 29, 823-835 https://doi.org/10.1080/03610920008832517
  17. Lin, D. K. J.(1993). A new class of supersaturated designs, Technometrics, 35, 28-31 https://doi.org/10.2307/1269286
  18. Lin, D. K. J.(1995). Generating systematic supersaturated designs, Technometrics, 37, 213-225 https://doi.org/10.2307/1269622
  19. Ma, C., Fang, K., and Lin, D. K. J.(2001). On the isomorphism of fractional factorial designs, Journal of Complexity, 17, 86-97 https://doi.org/10.1006/jcom.2000.0569
  20. Ma, C., Fang, K, and Liski, E.(2000). A new approach in constructing orthogonal and nearly orthogonal arrays, Metrika, 50, 255-268 https://doi.org/10.1007/s001840050049
  21. Markiewicz, A.(1997). Properties of information matrices for linear models and universal optimality of experimental designs, Journal of Statistical Planning and Inference, 59, 127-137 https://doi.org/10.1016/S0378-3758(96)00106-1
  22. Mukerjee, R. and Wu, C. F. J.(1999). Blocking in regular fractional factorials: A projective geometric approach, Annals of Statistics, 27, 1256-1271 https://doi.org/10.1214/aos/1017938925
  23. Pielou, E. C. (1966). The measurement of diversity in different types of biological collections, Journal of Theoretical Biology, 33, 305-32
  24. Suen, C. and Chen, H.(2000). A family of regular fractional factorial designs with maximum resolution, Journal of Statistical Computing and Simulation, 66, 67-78 https://doi.org/10.1080/00949650008812012
  25. Xu, H.(1999). Universally optimal designs for computer experiments, Statistica Sinica, 9, 1083-1088
  26. Zhang, R. and Park, D.(2000). Optimal blocking of two level fractional factorial designs, Journal of Statistical Planning and Inference, 91, 107-121 https://doi.org/10.1016/S0378-3758(00)00133-6