Uniformity pattern and related criteria for two-level factorials

Science in China, Series A: Mathematics

Volumn 48, Issue 1, 2005, Pages 1-11

  Fang, Kaitai ^a   Qin, Hong ^a,b  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b CENTRAL CHINA NORMAL UNIVERSITY   (China)

Author keywords

Discrepancy; Generalized minimum aberration; Minimum projection uniformity; Orthogonality; Uniformity pattern; Uniformity resolution

Indexed keywords

EID: 15044352226     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1360/03ys0155     Document Type: Article

References (33)

1. Box, G. E. P., Hunter, W. G., Hunter, J. S., Statistics for Experimenters, New York: Wiley, 1978.
2. k-p designs, Technometrics, 1980, 22(4): 601-608.
3. 2-aberration for nonregular fractional designs, Ann. Statist., 1999, 27(6): 1914-1926.
4. Ma, C. X., Fang, K. T., A note on generalized aberration factorial designs, Metrika, 2001, 53(1): 85-93.
5. Xu, H., Wu, C. F. J., Generalized minimum aberration for asymmetrical fractional factorial designs, Ann. Statist., 2001, 29(2): 549-560.
6. Lin, D. K. J., Draper, N. R., Projection properties of Plackett and Burman designs, Technometrics, 1992, 34(3): 423-428.
7. Lin, D. K. J., Draper, N. R., Generating alias relationship for two-level Plackett and Burman designs, Computational Statistics and Data Analysis, 1993, 15(1): 147-157.
8. Box, G. E. P., Bisgaard, S., What can you find out from 12 experimental runs? Quality Engineering, 1993, 5: 663-668.
9. Wang, J. C., Wu, C. F. J., A hidden projection property of Plackett-Burman and related designs, Statistica Sinica, 1995, 5(1): 235-250.
10. Cheng, C. S., Some projection properties of orthogonal arrays, Ann. Statist., 1995, 23(4): 1223-1233.
11. Cheng, C. S., Projectivity and resolving power, Journal of Combinatorics, Information & System Sciences, 1998, 23(1): 47-58.
12. Box, G. E. P., Tyssedal, J., Projective properties of certain orthogonal arrays, Biometrika, 1996, 83(4): 950-955.
13. Chen, H., Some projective properties of fractional factorial designs, Statist. Prob. Lett., 1998, 40(2): 185-188.
14. Deng, L. Y., Tang, B., Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs, Statist Sinica, 1999, 9(4): 1071-1082.
15. Deng, L. Y., Tang, B., Design selection and classification for Hadamard matrices using generalized minimum aberration criteria, Technometrics, 2002, 44(2): 173-184.
16. 2-aberration, Biometrika, 2001, 88(2): 401-407.
17. Wang, Y., Fang, K. T., A note on uniform distribution and experimental design, Chin. Sci. Bull., 1981, 26(3): 485-489.
18. Fang, K. T., Wang, Y., Number-Theoretic Methods in Statistics, London: Chapmanand Hall, 1994.
19. Fang, K. T., Lin, D. K. J., Winker, P. et al., Uniform design: Theory and applications, Technometrics, 2000, 42(3): 237-248.
20. Hickernell, F. J., A generalized discrepancy and quadrature error bound, Math. Comp., 1998, 67(221): 299-322.
21. Ma, C. X., Fang, K. T., Lin, D. K. J., On isomorphism of factorial designs, J. Complexity, 2001, 17(1): 86-97.
22. Ma, C. X., Fang, K. T., Lin, D. K. J., A note on uniformity and orthogonality, J. Statist. Planning and Inference, 2003, 113(1): 323-334.
23. Fang, K. T., Ge, G. N., A sensitive algorithm for detecting the inequivalence of Hadamard matrices, Math. Computation, 2004, 73(246): 843-851.
24. Hickernell, F. J., Liu, M. Q., Uniform designs limit aliasing, Biometrika, 2002, 89(4): 893-904.
25. 2)-optimality and minimum discrepancy in 2-level supersaturated designs, Statist. Sinica, 2002, 12(3): 931-939.
26. Fang, K. T., Mukerjee, R., Connection between uniformity and aberration in regular fractions of two-level factorials, Biometrika, 2000, 87(1): 173-198.
27. Fang, K. T., Ma, C. X., Mukerjee, R., Uniformity in fractional factorials, in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (eds. Fang, K. T., Hickernell, F. J., Niederreiter, H.), Berlin: Springer, 2002, 232-241.
28. Fang, K. T., Some Applications of Quasi-Monte Carlo Methods in Statistics, in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (eds. Fang, K. T., Hickernell, F. J., Niederreiter, H.), Berlin: Springer, 2002, 10-26.
29. Fang, K. T., Lin, D. K. J., Uniform experimental designs and their applications in industry, in Handbook of Statistics (eds. Khattree, R., Rao, C. R.), Vol. 22, North-Holland: Elsevier, 131-170.
30. Cheng, C. S., Steinberg, D. M., Sun, D. X., Minimum aberration and model robustness for two-level fractional factorial designs, J. R. Statist. Soc. B, 1999, 61(1): 85-93.
31. Cheng, C. S., Deng, L. Y., Tang, B., Generalized minimum aberration and design efficiency for nonregular fractional factorial designs, Statist Sinica, 2002, 12(4): 991-1000.
32. Hickernell, F. J., Lattice rules: How well do they measure up? in Random and Quasi-Random Point Sets (eds. Hellekalek, P., Larcher, G.), Lecture Notes in Statistics, Vol. 138, New York: Springer, 1998, 109-166.
33. MacWilliams, F. J., Sloane, N. J. A., The Theory of Error-Correcting Codes, Amsterdam: North-Holland, 1977.