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Two-level Supersaturated Designs: A Review

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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(s 2), 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.

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References

  • Booth, K.H.V., Cox, D.R., 1962. Some systematic supersaturated designs. Technometrics, 4, 489–495.

    MathSciNet  MATH  Google Scholar 

  • Bulutoglu, D.A., 2007. Cyclically constructed E(s 2)-optimal supersaturated designs. J. Statist. Plann. Inf., 137, 2413–2428.

    MathSciNet  MATH  Google Scholar 

  • Bulutoglu, D.A., Cheng, C.S., 2004. Construction of E(s 2)-optimal supersaturated designs. Ann. Statist., 32, 1662–1678.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • Cheng, C.S. (1995). Some projection properties of orthogonal arrays. Ann. Statist. 23, 1223–1233.

    MathSciNet  MATH  Google Scholar 

  • Cheng, C.S., Tang, B., 2001. Upper bounds on the number of columns in supersaturated designs. Biometrika, 88, 1169–1174.

    MathSciNet  MATH  Google Scholar 

  • Das A., Dey, A., Chan, L.Y., Chatterjee, K., 2008. E(s 2)-optimal supersaturated designs. J. Statist. Plann. Inf., 138, 3749–3757.

    MathSciNet  MATH  Google Scholar 

  • Deng, L.Y., Lin, D.K.J., Wang, J., 1996. Marginally oversaturated designs. Commun. Statist.-Theory Meth., 25, 2557–2573.

    MathSciNet  MATH  Google Scholar 

  • Deng, L.Y., Lin, D.K.J., Wang, J., 1999. A resolution rank criterion for supersaturated designs. Statist. Sinica, 9, 605–610.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • Ghosh, S., 1979. On single and multistage factor screening procedures. J. Combinatorics, Information and System Sciences, 4, 275–284.

    MathSciNet  MATH  Google Scholar 

  • Ghosh, S., Avila, D., 1985. Some new factor screening designs using the search linear model. J. Statist. Plann. Inf., 2, 259–266.

    MathSciNet  MATH  Google Scholar 

  • Gupta, S., Chatterjee, K., 1998. Supersaturated designs: A review. J. Combinatorics, Information and System Sciences, 23, 475–488.

    MathSciNet  MATH  Google Scholar 

  • Gupta, S., Kohli, P., 2008. Analysis of supersaturated designs: A review. J. Ind. Soc. Agril. Statist., 62, 156–168.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • Li, W.W., Wu, C.F.J., 1997. Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics, 39, 171–179.

    MathSciNet  MATH  Google Scholar 

  • Lin, D.K.J., 1993a. A new class of supersaturated designs. Technometrics, 35, 28–31.

    Google Scholar 

  • Lin, D.K.J., 1993b. Another look at first-order saturated designs: The p-efficient designs. Technometrics, 35, 284–292.

    MathSciNet  MATH  Google Scholar 

  • Lin, D.K.J., 1995. Generating systematic supersaturated designs. Technometrics, 37, 213–225.

    MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • Liu, M., Zhang, R., 2000. Construction of E(s 2) optimal supersaturated designs using cyclic BIBDs. J. Statist. Plann. Inf., 91, 139–150.

    MathSciNet  MATH  Google Scholar 

  • Lu, X., Meng, Y., 2000. A new method in the construction of two-level supersaturated designs. J. Statist. Plann. Inf., 86, 229–238.

    MathSciNet  MATH  Google Scholar 

  • Ma, C.X., Fang, K.T., 2001. A note on generalized aberration in factorial designs. Metrika, 53, 85–93.

    MathSciNet  MATH  Google Scholar 

  • Müller, M., 1993. Supersaturated designs for one or two effective factors. J. Statist. Plann. Inf., 37, 237–244.

    MathSciNet  MATH  Google Scholar 

  • Nguyen, N.K., 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.

    MATH  Google Scholar 

  • Nguyen, N.K., Cheng, C.S., 2008. New E(s 2)-optimal supersaturated designs constructed from incomplete block designs. Technometrics, 50, 26–31.

    MathSciNet  Google Scholar 

  • Plackett, R.L., Burman, J.P., 1946. The design of optimum multi-factorial experiments. Biometrika, 33, 111–137.

    Google Scholar 

  • Ryan, K.J., Bulutoglu, D.A., 2007. E(s 2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inf., 137, 2250–2262.

    MathSciNet  MATH  Google Scholar 

  • Satterwaite, F., 1959. Random balance experimentation. Technometrics, 1, 111–137.

    MathSciNet  Google Scholar 

  • 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 

  • Suen, C.S., Das, A., 2010. E(s 2)-optimal supersaturated designs with odd number of runs. J. Statist. Plann. Inf., 140, 1398–1409.

    MathSciNet  MATH  Google Scholar 

  • Tang, B., Deng, L.Y., 1999. Minimum G 2-aberration for non-regular fractional factorial designs. Ann. Statist., 27, 1914–1926.

    MathSciNet  MATH  Google Scholar 

  • 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 

  • 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.

    MathSciNet  Google Scholar 

  • Watson, G.S., 1961. A study of the group screening method. Technometrics, 3, 371–388.

    MathSciNet  MATH  Google Scholar 

  • Wu, C.F.J., 1993. Construction of supersaturated designs through partially aliased interactions. Biometrika, 80, 661–669.

    MathSciNet  MATH  Google Scholar 

  • Xu, H., 2003. Minimum moment aberration for non-regular designs and supersaturated designs. Statistica Sinica, 13, 691–708.

    MathSciNet  MATH  Google Scholar 

  • Xu, H., Wu, C.F.J., 2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist., 29, 1066–1077.

    MathSciNet  MATH  Google Scholar 

  • 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 

  • Yamada, S., Lin, D.K.J., 1997. Supersaturated designs including an orthogonal base. Canad. J. Statist., 25, 203–213.

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

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  1. Library Avenue, Indian Agricultural Statistics Research Institute, Pusa, New Delhi, 110012, India

    Basudev Kole, Jyoti Gangwani, V. K. Gupta & Rajender Parsad

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  1. Basudev Kole
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  2. Jyoti Gangwani
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  3. V. K. Gupta
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  4. Rajender Parsad
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Correspondence to Basudev Kole.

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Kole, B., Gangwani, J., Gupta, V.K. et al. Two-level Supersaturated Designs: A Review. J Stat Theory Pract 4, 589–608 (2010). https://doi.org/10.1080/15598608.2010.10412006

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  • DOI: https://doi.org/10.1080/15598608.2010.10412006

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