Advertisement

Journal of Statistical Theory and Practice

, Volume 7, Issue 4, pp 703–712 | Cite as

Finding MDS-Optimal Supersaturated Designs Using Computer Searches

  • Arden Miller
  • Boxin Tang
Article

Abstract

Supersaturated designs can be evaluated using the minimal dependent sets (MDSs) of columns in the design matrix. This article describes an extensive computer search of balanced two-level supersaturated designs to find those that are MDS-optimal.

Keywords

Aberration Hadamard matrix Nonorthogonal design Nonregular design Screening design 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Booth, E. H., and D. R. Cox. 1962. Some systematic supersaturated designs. Technometrics, 4, 489–495.MathSciNetCrossRefGoogle Scholar
  2. Bulutoglu, D. A., and C. S. Cheng. 2004. Construction of E(s 2)-optimal supersaturated designs. Ann. Stat., 32, 1662–1678.MathSciNetCrossRefGoogle Scholar
  3. Butler, N. A., R. Mead, K. M. Eskridge, and S. G. Gilmour. 2001. A general method of constructing E(s 2)-optimal supersaturated designs. J. R. Stat. Soc. B, 63, 621–632.MathSciNetCrossRefGoogle Scholar
  4. Cheng, C. S. 1997. E(s 2)-optimal supersaturated designs. Stat. Sin., 7, 929–939.MathSciNetMATHGoogle Scholar
  5. Cheng, C. S., D. M. Steinberg, and D. X. Sun. 1999. Minimum aberration and model robustness for two level fractional factorial designs. J. R. Stat. Soc. Ser. B, 61, 85–93.MathSciNetCrossRefGoogle Scholar
  6. Deng, L. Y., D. K. J. Lin, and J. Wang. 1996. Marginally oversaturated designs. Commun. Stat. Theory Methods, 25(11), 2557–2573.MathSciNetCrossRefGoogle Scholar
  7. Deng, L. Y., D. K. J. Lin, and J. Wang. 1999. A resolution rank criteria for supersaturated designs. Stat. Sin., 9, 605–610.MATHGoogle Scholar
  8. Lin, C. D., A. E. Miller, and R. R. Sitter. 2008. Folded over non-orthogonal designs. J. Stat. Plan. Inference, 134, 3107–3124.MathSciNetCrossRefGoogle Scholar
  9. Lin, D. K. J. 1993. A new class of supersaturated designs. Technometrics, 35, 28–31.CrossRefGoogle Scholar
  10. Miller, A. E. and R. R. Sitter. 2004. Choosing columns from the 12-run Plackett-Burman design. Stat. Probability Lett., 67, 193–201.MathSciNetCrossRefGoogle Scholar
  11. Miller, A. E., and R. R. Sitter. 2005. Using folded over non-orthogonal designs. Technometrics, 47, 502–513.MathSciNetCrossRefGoogle Scholar
  12. Miller, A. E., and B. Tang. 2012. Using minimal dependent sets to evaluate supersaturated designs. Stat. Sin., 22, 1273–1285.MATHGoogle Scholar
  13. Nguyen, N. K. 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.CrossRefGoogle Scholar
  14. Srivastava, J. N. 1975. Designs for searching non-negligible effects. In A survey of statistical design and linear models. Amsterdam, The Netherlands, North-Holland.Google Scholar
  15. Tang, B., and C. F. J. Wu. 1997. A method for constructing supersaturated designs and its E(s 2)-optimality. Can. J. Stat., 25, 191–201.CrossRefGoogle Scholar
  16. Wu, C. F. J. 1993. Construction of supersaturated designs through partially aliased interactions. Biometrika, 80, 661–669.MathSciNetCrossRefGoogle Scholar
  17. Yamada, S., and D. K. J. Lin. 1997. Supersaturated design including an orthogonal base. Can. J. Stat., 25, 203–213.MathSciNetCrossRefGoogle Scholar
  18. Xu, H., and C. F. J. Wu. 2005. Construction of optimal multi-level supersaturated designs. Ann. Stat., 33, 2811–2836.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.Department of StatisticsThe University of AucklandAucklandNew Zealand
  2. 2.Simon Fraser UniversityBurnabyCanada

Personalised recommendations