A survey and evaluation of methods for determination of combinatorial equivalence of factorial designs

Journal of Statistical Planning and Inference

Volumn 138, Issue 1, 2008, Pages 245-258

  Katsaounis, T I ^a   Dean, A M ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

Combinatorial equivalence; Deseq algorithm; Design isomorphism; Factorial experiment; Hamming distance; Hamming weight; Indicator function; J characteristic

Indexed keywords

EID: 34548860637     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.05.008     Document Type: Article

References (55)

1. Block, R.M., 2003. Theory and construction methods for large regular resolution IV designs. Ph.D. dissertation, University of Tennessee 〈http://www.etd.utk.edu/2003/BlockRobert.pdf〉.
2. Block R.M., and Mee R.W. Resolution IV designs with 128 runs. J. Quality Techn. 37 (2005) 282-293
3. Booth K., and Cox D.R. Some systematic supersaturated designs. Technometrics 4 (1962) 489-495
4. Chatterjee K., Fang K.T., and Qin H. Uniformity in factorial designs with mixed levels. J. Statist. Plann. Inference 128 (2005) 593-607
5. n - k fractional factorial designs and search for minimum aberration designs. Ann. Statist. 20 (1992) 2124-2141
6. Chen H., and Cheng C.-S. Uniqueness of some resolution IV two-level regular fractional factorial designs. SIAM J. Discrete. Math. 13 (2000) 571-575
7. Chen H.H., and Cheng C.-S. Aberration, estimation capacity and estimation index. Statist. Sin. 14 (2004) 203-215
8. k - p designs. J. Statist. Plann. Inference 28 (1991) 95-98
9. Chen J., Sun D.X., and Wu C.F.J. A catalogue of two-level and three-level fractional factorial designs with small runs. Internat. Statist. Rev. 61 (1993) 131-145
10. Cheng S.W., and Wu C.F.J. Factor screening and response surface exploration. Statist. Sin. 11 (2001) 553-604
11. Cheng S.W., and Ye K. Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. Ann. Statist. 32 (2004) 2168-2185
12. Clark J.B., and Dean A.M. Equivalence of fractional factorial designs. Statist. Sin. 11 (2001) 537-547
13. Deng L.Y., and Tang B. Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs. Statist. Sin. 9 (1999) 1071-1082
14. Deng L.Y., and Tang B. Design selection and classification for Hadamard matrices using generalized minimum aberration criteria. Technometrics 44 (2002) 173-184
15. k - p designs. Ann. Math. Statist. 38 (1967) 1110-1126
16. Draper N.R., and Mitchell T.J. Construction of the set of 256-run designs of resolution ≥ 5 and the set of even 512-run designs of resolution ≥ 6 with special reference to the unique saturated designs. Ann. Math. Statist. 39 (1968) 246-255
17. Draper N.R., and Mitchell T.J. Construction of a set of 512-run designs of resolution ≥ 5 and the set of even 1024-run designs of resolution ≥ 6. Ann. Math. Statist. 41 (1970) 876-887
18. Eskridge K.M., Gilmour S.G., Mead R., Butler N., and Travnicek D.A. Large supersaturated designs. J. Statist. Comput. Simulation 74 (2004) 525-542
19. Evangelaras H., Koukouvinos C., Dean A.M., and Dingus C.A. Projection properties of certain three level orthogonal arrays. Metrika 62 (2005) 241-257
20. Fang K.T., and Ge G. A sensitive algorithm for detecting the inequivalence of Hadamard matrices. Math. Comput. 73 (2003) 843-851
21. Fang K.T., and Mukerjee R. A connection between uniformity and aberration in regular fractions of two level factorials. Biometrika 87 (2000) 193-198
22. Fang K.T., and Wang Y. Number-theoretic Methods in Statistics (1994), Chapman & Hall, New York
23. Fontana R., Pistone G., and Rogantin M.P. Classification of two-level factorial designs. J. Statist. Plann. Inference 87 (2000) 149-172
24. Hedayat A.S., Sloane N.J.A., and Stufken J. Orthogonal Arrays (1999), Springer, New York
25. Hickernell F.J. A generalized discrepancy and quadrature error bound. Math. Comput. 67 (1998) 299-322
26. Hickernell F.J. Goodness-of-fit statistics, discrepancies and robust designs. Statist. Probab. Lett. 44 (1999) 73-78
27. Hickernell F.J., and Liu M.Q. Uniform designs limit aliasing. Biometrika 89 (2002) 893-904
28. Katsaounis, T.I., 2006. Equivalence of symmetric factorial designs and characterization and ranking of two-level split-plot designs. Ph.D. dissertation, The Ohio State University.
29. Katsaounis, T.I., Dingus, C.A., Dean, A.M., 2007. On the geometric equivalence and non-equivalence of symmetric factorial designs. J. Statist. Theory Pract. 1, 101-115.
30. Leon J.S. An algorithm for computing the automorphism group of a Hadamard matrix. J. Combin. Theory A 27 (1979) 289-306
31. Lin D.K.J. A new class of supersaturated designs. Technometrics 35 (1993) 28-31
32. Lin, C.D., Sitter, R.R., 2007. An isomorphism check for two-level fractional factorial designs. J. Statist. Plann. Inference, in press, doi:10.1016/j.jspi.2007.05.036.
33. Lin C., Wallis W.D., and Zhu L. Generalized 4-profiles of Hadamard matrices. J. Combinatorics 18 (1993) 397-400
34. Liu Y.-F., and Dean A.M. k-circulant supersaturated designs. Technometrics 46 (2004) 32-43
35. 2 efficient supersaturated designs. J. Statist. Plann. Inference 137, 1516-1529.
36. Ma C.X., and Fang K.T. A note on generalized aberration in factorial designs. Metrika 53 (2001) 85-93
37. Ma C.X., Fang K.T., and Lin D.K.J. On the isomorphism of fractional factorial designs. J. Complexity 17 (2001) 86-97
38. Ma C.X., Fang K.T., and Lin D.K.J. A note on uniformity and orthogonality. J. Statist. Plann. Inference 113 (2003) 323-334
39. McKay B.D. Hadamard equivalence via graph isomorphism. Discrete Math. 27 (1979) 213-214
40. Pistone G., and Wynn H.P. Generalised confounding with Grobner bases. Biometrika 83 (1996) 653-666
41. Qin H., and Fang K.T. Discrete discrepancy in factorial designs. Metrika 60 (2004) 59-72
42. Srivastava, J.N., 1975. Designs for searching non-negligible effects. Survey of Statistical Design and Linear Models. North-Holland, Amsterdam.
43. Srivastava J.N., Raktoe B.L., and Pesotan H. On invariance and randomization in fractional replication. Ann. Statist. 4 (1976) 423-430
44. Stufken, J., Tang, B., 2007. Complete enumeration of two-level orthogonal arrays of strength d with d + 2 constraints. Ann. Statist. 35(2) 〈http://www/imstat.org/aos/issue_35_2.html〉.
45. Sun, D., Li, W., Ye, K.Q., 2002. An algorithm for sequentially constructing non-isomorphic orthogonal designs and its applications. Technical Report, Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, SUNYSB-AMS-01-13 〈http://www.ams.sunysb.edu/papers/papers02.html〉.
46. 2-aberration. Biometrika 88 (2001) 401-407
47. 2-aberration for nonregular fractional factorial designs. Ann. Statist. 27 (1999) 1914-1926
48. Tsai P.W., Gilmour S.G., and Mead R. Projective three-level main effects designs robust to model uncertainty. Biometrika 87 (2000) 467-475
49. Wu C.F.J. Construction of supersaturated designs through partially aliased interactions. Biometrika 80 (1993) 661-669
50. Wu C.F.J., and Hamada M. Experiments, Planning, Analysis, and Parameter Design Optimization (2000), Wiley, New York
51. Xu H. Minimum moment aberration for nonregular designs and supersaturated designs. Statist. Sin. 13 (2003) 691-708
52. Xu H. A catalogue of three-level regular fractional factorial designs. Metrika 62 (2005) 259-281
53. Xu H., and Deng L.Y. Moment aberration projection for nonregular fractional factorial designs. Technometrics 47 (2005) 121-131
54. Xu H., and Wu C.F.J. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist. 29 (2001) 1066-1077
55. Ye K. Indicator function and its application in two level factorial designs. Ann. Statist. 31 (2003) 984-994