Advertisement

Journal of Statistical Theory and Practice

, Volume 9, Issue 3, pp 537–543 | Cite as

A Catalog of Orthogonally Blocked Three-Level Second-Order Designs With Run Sizes ≤ 100

Article

Abstract

Box-Behnken designs form a very popular class of three-level second-order designs when the number of factors is small, typically seven or less. For larger number of factors these designs are not as popular because then these designs require a large number of runs. This article provides a catalog of three-level second-order designs for 5–11 factors with run sizes ≤ 100. All the designs reported can be orthogonally blocked and are seen to have high D-efficiencies.

Keywords

D-efficiency Response surface designs Regular graph designs Resolvable incomplete block designs Rotatability measure Q

AMS Subject Classification

62K20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Box, G. E. P., and D. W. Behnken. 1960. Some new three level designs for the study of quantitative variables. Technometrics, 2, 455–475.MathSciNetCrossRefGoogle Scholar
  2. Box, G. E. P., and N. R. Draper. 2007. Response surfaces, mixtures and ridge analyses, 2nd ed. New York, NY: Wiley.CrossRefGoogle Scholar
  3. Box, G. E. P., and K. B. Wilson. 1951. On the experimental attainment of optimum conditions. J. R. Stat. Soc. Ser. B, 13, 1–15.MathSciNetMATHGoogle Scholar
  4. Dey, A. 2009. Orthogonally blocked three-level second order designs. J. Stat. Plan. Inference, 139, 398–3705.MathSciNetCrossRefGoogle Scholar
  5. Dey, A. 2010. Incomplete block designs. Hackensack, NJ: World Scientific.CrossRefGoogle Scholar
  6. Dey, A., and B. Kole. 2013. Small three-level second-order designs with orthogonal blocks. J. Stat. Theor. Pract., 7, 745–752.MathSciNetCrossRefGoogle Scholar
  7. Draper, N. R., and F. Pukelsheim. 1990. Another look at rotatability. Technometrics, 32, 195–202.MathSciNetCrossRefGoogle Scholar
  8. John, J. A., and T. J. Mitchell. 1977. Optimal incomplete block designs. J. R. Stat. Soc. Ser. B, 39, 39–43.MathSciNetMATHGoogle Scholar
  9. Kiefer, J. 1960. Optimum experimental designs V, with applications to systematic and rotatable designs. Proc. Fourth Berkeley Symp., 1, 381–405.Google Scholar
  10. Morris, M. D. 2000. A class of three-level experimental designs for response surface. Technometrics, 42, 111–121.CrossRefGoogle Scholar
  11. Nguyen, N.-K. 1994. Construction of optimal block design by computer. Technometrics, 36, 300–307.MathSciNetCrossRefGoogle Scholar
  12. Nguyen, N.-K., and K. L. Blagoeva. 2010. Incomplete block designs. In International Encyclopedia of Statistical Science, ed. L. Miodrag, 653–655. New York, NY: Springer.Google Scholar
  13. Nguyen, N.-K., and J. J. Borkowski. 2008. New 3-level response surface designs constructed from incomplete block designs. J. Stat. Plan. Inference, 138, 294–305.MathSciNetCrossRefGoogle Scholar
  14. Nguyen, N.-K., and D. K. J. Lin. 2011. A note on small composite designs for sequential experimentation. J. Stat. Theor. Pract., 5, 109–117.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Vietnam Institute for Advanced Study in Mathematics and VNU International SchoolHanoiVietnam
  2. 2.Indian Statistical InstituteNew DelhiIndia

Personalised recommendations