Advertisement

Journal of Statistical Theory and Practice

, Volume 4, Issue 4, pp 589–608 | Cite as

Two-level Supersaturated Designs: A Review

  • Basudev KoleEmail author
  • Jyoti Gangwani
  • V. K. Gupta
  • Rajender Parsad
Article

Abstract

Supersaturated Designs (SSDs) are fractional factorial designs in which the run size is not enough to estimate the main effects of all the factors in the experiment. Two-level SSDs have been studied extensively in the literature. The thrust of research has been on obtaining lower bounds to the value of E(s2), a measure of departure from orthogonality, and constructing designs that attain these lower bounds. The focus of this paper is to review the literature on two-level SSDs.

Key-words

SSD Optimality criteria Supersaturated design 

AMS Subject Classification

62K15 62K05 62K99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Booth, K.H.V., Cox, D.R., 1962. Some systematic supersaturated designs. Technometrics, 4, 489–495.MathSciNetzbMATHGoogle Scholar
  2. Bulutoglu, D.A., 2007. Cyclically constructed E(s 2)-optimal supersaturated designs. J. Statist. Plann. Inf., 137, 2413–2428.MathSciNetzbMATHGoogle Scholar
  3. Bulutoglu, D.A., Cheng, C.S., 2004. Construction of E(s 2)-optimal supersaturated designs. Ann. Statist., 32, 1662–1678.MathSciNetzbMATHGoogle Scholar
  4. Bulutoglu, D.A., Ryan, K.J., 2008. E(s 2)-optimal supersaturated designs with good minimax properties when N is odd. J. Statist. Plann. Inf., 138, 1754–1762.MathSciNetzbMATHGoogle Scholar
  5. Butler, N., Mead, R., Eskridge, K.M., Gilmour, S.G., 2001. A general method of constructing E(s 2)-optimal supersaturated designs. J. Royal Statist. Soc., B 63, 621–632.MathSciNetzbMATHGoogle Scholar
  6. Cheng, C.S. (1995). Some projection properties of orthogonal arrays. Ann. Statist. 23, 1223–1233.MathSciNetzbMATHGoogle Scholar
  7. Cheng, C.S., Tang, B., 2001. Upper bounds on the number of columns in supersaturated designs. Biometrika, 88, 1169–1174.MathSciNetzbMATHGoogle Scholar
  8. Das A., Dey, A., Chan, L.Y., Chatterjee, K., 2008. E(s 2)-optimal supersaturated designs. J. Statist. Plann. Inf., 138, 3749–3757.MathSciNetzbMATHGoogle Scholar
  9. Deng, L.Y., Lin, D.K.J., Wang, J., 1996. Marginally oversaturated designs. Commun. Statist.-Theory Meth., 25, 2557–2573.MathSciNetzbMATHGoogle Scholar
  10. Deng, L.Y., Lin, D.K.J., Wang, J., 1999. A resolution rank criterion for supersaturated designs. Statist. Sinica, 9, 605–610.MathSciNetzbMATHGoogle Scholar
  11. Deng, L.Y., Tang, B., 1999. Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs. Statist. Sinica, 9, 1071–1082.MathSciNetzbMATHGoogle Scholar
  12. 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.MathSciNetzbMATHGoogle Scholar
  13. Ghosh, S., 1979. On single and multistage factor screening procedures. J. Combinatorics, Information and System Sciences, 4, 275–284.MathSciNetzbMATHGoogle Scholar
  14. Ghosh, S., Avila, D., 1985. Some new factor screening designs using the search linear model. J. Statist. Plann. Inf., 2, 259–266.MathSciNetzbMATHGoogle Scholar
  15. Gupta, S., Chatterjee, K., 1998. Supersaturated designs: A review. J. Combinatorics, Information and System Sciences, 23, 475–488.MathSciNetzbMATHGoogle Scholar
  16. Gupta, S., Kohli, P., 2008. Analysis of supersaturated designs: A review. J. Ind. Soc. Agril. Statist., 62, 156–168.MathSciNetzbMATHGoogle Scholar
  17. Gupta, V.K., Parsad, R., Kole, B., Bhar, L.M., 2008. Computer-aided construction of efficient two level supersaturated designs. J. Ind. Soc. Agril. Statist., 62, 183–194.zbMATHGoogle Scholar
  18. Gupta V.K., Singh, P., Kole, B., Parsad, R., 2010. Addition of runs to a two-level supersaturated design. J. Statist. Plann. Inf., 140, 2531–2535.MathSciNetzbMATHGoogle Scholar
  19. Lejeune, M.A., 2003. A coordinate-columnwise exchange algorithm for construction of supersaturated, saturated and non-saturated experimental designs. American Journal of Mathematical and Management Sciences, 23, 109–142.MathSciNetGoogle Scholar
  20. Li, W.W., Wu, C.F.J., 1997. Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics, 39, 171–179.MathSciNetzbMATHGoogle Scholar
  21. Lin, D.K.J., 1993a. A new class of supersaturated designs. Technometrics, 35, 28–31.Google Scholar
  22. Lin, D.K.J., 1993b. Another look at first-order saturated designs: The p-efficient designs. Technometrics, 35, 284–292.MathSciNetzbMATHGoogle Scholar
  23. Lin, D.K.J., 1995. Generating systematic supersaturated designs. Technometrics, 37, 213–225.zbMATHGoogle Scholar
  24. Liu, Y., Ruan, S., Dean, A.M., 2007. Construction and analysis of E(s 2) efficient supersaturated designs. J. Statist. Plann. Inf., 137, 1516–1529.MathSciNetzbMATHGoogle Scholar
  25. Liu, M., Zhang, R., 2000. Construction of E(s 2) optimal supersaturated designs using cyclic BIBDs. J. Statist. Plann. Inf., 91, 139–150.MathSciNetzbMATHGoogle Scholar
  26. Lu, X., Meng, Y., 2000. A new method in the construction of two-level supersaturated designs. J. Statist. Plann. Inf., 86, 229–238.MathSciNetzbMATHGoogle Scholar
  27. Ma, C.X., Fang, K.T., 2001. A note on generalized aberration in factorial designs. Metrika, 53, 85–93.MathSciNetzbMATHGoogle Scholar
  28. Müller, M., 1993. Supersaturated designs for one or two effective factors. J. Statist. Plann. Inf., 37, 237–244.MathSciNetzbMATHGoogle Scholar
  29. Nguyen, N.K., 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.zbMATHGoogle Scholar
  30. Nguyen, N.K., Cheng, C.S., 2008. New E(s 2)-optimal supersaturated designs constructed from incomplete block designs. Technometrics, 50, 26–31.MathSciNetGoogle Scholar
  31. Plackett, R.L., Burman, J.P., 1946. The design of optimum multi-factorial experiments. Biometrika, 33, 111–137.Google Scholar
  32. Ryan, K.J., Bulutoglu, D.A., 2007. E(s 2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inf., 137, 2250–2262.MathSciNetzbMATHGoogle Scholar
  33. Satterwaite, F., 1959. Random balance experimentation. Technometrics, 1, 111–137.MathSciNetGoogle Scholar
  34. Srivastava, J.N., 1975. Designs for searching non-negligible effects. A Survey of Statistical Designs and Linear Models. North Holland, Amsterdam, 507–519.Google Scholar
  35. Suen, C.S., Das, A., 2010. E(s 2)-optimal supersaturated designs with odd number of runs. J. Statist. Plann. Inf., 140, 1398–1409.MathSciNetzbMATHGoogle Scholar
  36. Tang, B., Deng, L.Y., 1999. Minimum G 2-aberration for non-regular fractional factorial designs. Ann. Statist., 27, 1914–1926.MathSciNetzbMATHGoogle Scholar
  37. Tang, B., Wu, C.F.J., 1993. A method for constructing supersaturated designs and its E(s 2)-optimality. IIQP Research Report, RR-93-05, University of Waterloo.Google Scholar
  38. Tang, B., Wu, C.F.J., 1997. A method for constructing supersaturated designs and its E(s 2) optimality. Canad. J. Statist., 25, 191–201.MathSciNetGoogle Scholar
  39. Watson, G.S., 1961. A study of the group screening method. Technometrics, 3, 371–388.MathSciNetzbMATHGoogle Scholar
  40. Wu, C.F.J., 1993. Construction of supersaturated designs through partially aliased interactions. Biometrika, 80, 661–669.MathSciNetzbMATHGoogle Scholar
  41. Xu, H., 2003. Minimum moment aberration for non-regular designs and supersaturated designs. Statistica Sinica, 13, 691–708.MathSciNetzbMATHGoogle Scholar
  42. Xu, H., Wu, C.F.J., 2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist., 29, 1066–1077.MathSciNetzbMATHGoogle Scholar
  43. Xu, H., Wu, C.F.J., 2003. Construction of optimal multi-level supersaturated designs. UCLA, Department of Statistics, Electronic Publication. (http://repositories.cdlib.orgluclastat)Google Scholar
  44. Yamada, S., Lin, D.K.J., 1997. Supersaturated designs including an orthogonal base. Canad. J. Statist., 25, 203–213.MathSciNetzbMATHGoogle Scholar
  45. Zhang, Q.Z., Zhang, R.C., Liu, M.Q., 2007. A method for screening active effects in supersaturated designs. J. Statist. Plann. Inf., 137, 2068–2079.MathSciNetzbMATHGoogle Scholar

Copyright information

© Grace Scientific Publishing 2010

Authors and Affiliations

  • Basudev Kole
    • 1
    Email author
  • Jyoti Gangwani
    • 1
  • V. K. Gupta
    • 1
  • Rajender Parsad
    • 1
  1. 1.Library AvenueIndian Agricultural Statistics Research InstitutePusa, New DelhiIndia

Personalised recommendations