Journal of Statistical Theory and Practice

, Volume 3, Issue 2, pp 489–504 | Cite as

An Overview of Two-level Supersaturated Designs with Cyclic Structure

  • Stelios D. GeorgiouEmail author
  • Danel Draguljić
  • Angela M. Dean


An overview is given of the link between the k-circulant method of construction of two-level supersaturated designs and construction methods based on cyclic incomplete block designs. It is shown that this link enables a simple formula for the Es2-efficiency of all such designs to be derived. Generators are given for Es2-optimal and near-optimal designs that extend the range of previously known designs or that have a smaller number of highly correlated column pairs.

AMS Subject Classification

Primary: 62K15 Secondary: 62K05 


Circulant design Cyclic design Efficiency Es2 


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  1. Abraham, B., Chipman, H., Vijayan K., 1999. Some risks in the construction and analysis of supersaturated designs. Technometrics, 41 (2), 135–141.CrossRefGoogle Scholar
  2. Beattie, S.D., Fong, D.K.H., Lin, D.K.J., 2002. A two-stage Bayesian model selection strategy for supersaturated designs. Technometrics, 22 (1), 55–63.MathSciNetCrossRefGoogle Scholar
  3. Booth, K.H.V., Cox, D.R., 1962. Some systematic supersaturated designs. Technometrics, 4, 489–495.MathSciNetCrossRefGoogle Scholar
  4. Box, G.E.P., Meyer, R.D., 1986. An analysis for unreplicated fractional factorials. Technometrics, 28, 11–18.MathSciNetCrossRefGoogle Scholar
  5. Bulutoglu, D.A., Cheng, C.S., 2004. Construction of E(s2)-optimal supersaturated designs. Annals of Statistics, 32, 1662–1678.MathSciNetCrossRefGoogle Scholar
  6. Butler, N.A., Mead, R., Eskridge, K.M., Gilmour, S.G., 2001. A general method of constructing E(s2)-optimal supersaturated designs. J. R. Statist. Soc., B, 63, 621–632.CrossRefGoogle Scholar
  7. Chen, J., Lin, D.K.J., 1998. On the identifiability of a supersaturated design. Journal of Statistical Planning and Inference, 72, 99–107.MathSciNetCrossRefGoogle Scholar
  8. Cheng, C.S., 1997. E(s2)-optimal supersaturated designs. Statistica Sinica, 7, 929–939.MathSciNetzbMATHGoogle Scholar
  9. Chipman, H., Hamada, M., Wu, C.F.J., 1997. A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing. Technometrics, 39, 372–381.CrossRefGoogle Scholar
  10. Das, A., Dey, A., Chan, L., Chatterjee, K. (2008). On E(s2)-optimal supersaturated designs. Journal of Statistical Planning and Inference, 138, 3746–3757.CrossRefGoogle Scholar
  11. Eskridge, K.M., Gilmour, S.G., Mead, R., Butler, N.A., Travnicek, D.A., 2004. Large supersaturated designs. J. Stat. Comput. Simul., 74, 525–542.MathSciNetCrossRefGoogle Scholar
  12. Georgiou, S.D., 2008. On the construction of E(s2)-optimal supersaturated designs, Metrika, 68, 189–198.MathSciNetCrossRefGoogle Scholar
  13. Geramita, A.V., Seberry, J., 1979. Orthogonal Designs: Quadratic forms and Hadamard Matrices. Marcel Dekker, New York-Basel.zbMATHGoogle Scholar
  14. Kelly, H.W., III, Voelkel, J.O., 2000. Asymptotic-power problems in the analysis of supersaturated designs. Statistics and Probability Letters, 47, 317–324.CrossRefGoogle Scholar
  15. Li, R., Lin, D.K.J., 2003. Analysis methods for supersaturated design: Some comparisons. Journal of Data Science, 1, 249–260.Google Scholar
  16. Li, W., Wu, C.F.J., 1997. Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics, 39, 171–179.MathSciNetCrossRefGoogle Scholar
  17. Lin, D.K.J., 1993. A new class of supersaturated designs. Technometrics, 35, 28–31.CrossRefGoogle Scholar
  18. Lin, D.K.J., 1995. Generating systematic supersaturated designs. Technometrics, 37, 213–225.CrossRefGoogle Scholar
  19. Liu, Y., Dean, A.M., 2004. k-circulant supersaturated designs. Technometrics, 46, 32–43.MathSciNetCrossRefGoogle Scholar
  20. Liu, Y., Ruan, S., Dean, A.M., 2006. Construction and analysis of Es2 efficient supersaturated designs. Journal of Statistical Planning and Inference, 137, 1516–1529.CrossRefGoogle Scholar
  21. Liu, M., Zhang, R., 2000. Construction of E(s2) optimal supersaturated designs using cyclic BIBDs. Journal of Statistical Planning and Inference, 91, 139–150.MathSciNetCrossRefGoogle Scholar
  22. Meyer, R.D., Wilkinson, R.G., 1998. Bayesian variable assessment. Communications in Statistics: Theory and Methods, 27, 2675–2705.CrossRefGoogle Scholar
  23. Nguyen, N.K., 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.CrossRefGoogle Scholar
  24. Phoa, F., Pan, Y.-H., Xu, H., 2009. Analysis of Supersaturated Designs via Dantzig Selector. Journal of Statical Planning and Inference, 7, 2362–2372.MathSciNetCrossRefGoogle Scholar
  25. Plackett, R.L., Burman, J.P., 1946. The design of optimum multifactorial experiments. Biometrika, 33, 305–325.MathSciNetCrossRefGoogle Scholar
  26. Satterthwaite, F.E., 1959. Random balance experimentation (with discussions). Technometrics, 1, 111–137.MathSciNetCrossRefGoogle Scholar
  27. Ryan, K.J., Bulutoglu, D.A., 2007. Es2-optimal supersaturated designs with good minimax properties. Journal of Statistical Planning and Inference, 137, 2250–2262.MathSciNetCrossRefGoogle Scholar
  28. Street, A.P., Street, D.J., 1987. Combinatorics of Experimental Design. Oxford Science Publications.zbMATHGoogle Scholar
  29. Tang, B., Wu, C.F.J., 1997. A method for constructing supersaturated designs and its Es2 optimality. Canadian Journal of Statistics, 25, 191–201.CrossRefGoogle Scholar
  30. Wallis, W.D., Street, A.P., Seberry, J. Wallis, 1972. Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Lecture Notes in Mathematics, Vol. 292, Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
  31. Westfall, P.H., Young, S.S., Lin, D.K.J., 1998. Forward selection error control in the analysis of supersaturated designs. Statistica Sinica, 8, 101–117.zbMATHGoogle Scholar
  32. Wu, C.F.J., 1993. Construction of supersaturated designs through partially aliased interactions. Biometrika, 80, 661–669.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2009

Authors and Affiliations

  • Stelios D. Georgiou
    • 1
    Email author
  • Danel Draguljić
    • 2
  • Angela M. Dean
    • 2
  1. 1.Department of Statistics and Actuarial-Financial MathematicsUniversity of the AegeanSamosGreece
  2. 2.Department of StatisticsThe Ohio State UniversityColumbusUSA

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