Abstract
Supersaturated designs (SSDs) constitute an important class of fractional factorial designs that could be extremely useful in factor screening experiments. Most of the existing studies have focused on balanced designs. This paper provides a new lower bound for the \(E(f_{NOD})\)-optimality measure of SSDs with general run sizes. This bound is a generalization of existing bounds since it is applicable to both balanced and unbalanced designs. Optimal multi and mixed-level, balanced and nearly balanced SSDs are constructed by applying a k-circulant type methodology. Necessary and sufficient conditions are introduced for the generator vectors, in order to pre-ensure the optimality of the constructed k-circulant SSDs. The provided lower bounds were used to measure the efficiency of the generated designs. The presented methodology leads to a number of new families of improved SSDs, providing tools for directly constructing optimal or nearly-optimal k-circulant designs by just checking the corresponding generator vector.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aggarwal ML, Gupta S (2004) A new method of construction of multi-level supersaturated designs. J Stat Plan Inference 121:127–134
Booth KHV, Cox DR (1962) Some systematic supersaturated designs. Technometrics 4:489–495
Bulutoglu DA, Cheng CS (2004) Construction of \(E(s^2)\)-optimal supersaturated designs. Ann Stat 32:1662–1678
Bulutoglu DA, Ryan KJ (2008) \(E(s^2)\)-optimal supersaturated designs with good minimax properties when N is odd. J Stat Plan Inference 138:1754–1762
Chai FS, Chatterjee K, Das A, Midha C (2012) Optimal supersaturated designs for \(s^m\) factorials in \(N\lnot \equiv 0 (mod s)\) runs. J Stat Theory Pract 6:1170–7177
Chen J, Liu M-Q (2008a) Optimal mixed-level supersaturated designs with general number of runs. Stat Probab Lett 78:2496–2502
Chen J, Liu M-Q (2008b) Optimal mixed-level k-circulant supersaturated designs. J Stat Plan Inference 138:4151–4157
Fang KT, Lin DKJ, Liu MQ (2003) Optimal mixed-level supersaturated design. Metrika 58:279–291
Georgiou SD (2014) Supersaturated designs: a review of their construction and analysis. J Stat Plan Inference 144:92–109
Georgiou S, Koukouvinos C (2006) Multi-level k-circulant supersaturated designs. Metrika 64:209–220
Gupta VK, Singh P, Kole B, Parsad R (2009) Construction of efficient unbalanced mixed-level supersaturated designs. Stat Probab Lett 79:2359–2366
Jones B, Majumdar D (2014) Optimal supersaturated designs. J Am Stat Assoc 109:1592–1600
Liu YF, Dean AM (2004) k-circulant supersaturated designs. Technometrics 46:32–43
Liu Y, Liu MQ (2012) Construction of equidistant and weak equidistant supersaturated designs. Metrika 75:33–53
Nguyen NK, Cheng C-S (2008) New \(E(s^2)\)-optimal supersaturated designs constructed from incomplete block designs. Technometrics 50:26–31
Parker PA, Kowalski SM, Vining GG (2007) Unbalanced and minimal point equivalent estimation second-order split-plot designs. J Qual Technol 39:376–388
Satterthwaite F (1959) Random balance experimentation (with discussion). Technometrics 1:111–137
Suen CS, Das A (2010) \(E(s^2)\)-optimal supersaturated designs with odd number of runs. J Stat Plan Inference 140:1398–1409
Sun FS, Lin DKJ, Liu MQ (2011) On construction of optimal mixed-level supersaturated designs. Ann Stat 39:1310–1333
Tang B, Deng LY (1999) Minimum \(G_2\)-aberration for nonregular fractional factorial designs. Ann Stat 27:1914–1926
Wu CFJ (1993) Construction of supersaturated designs through partially aliased interactions. Biometrika 80:661–669
Xu H (2003) Minimum moment aberration for nonregular designs and supersaturated designs. Stat Sinica 13:691–708
Xu H, Wu CFJ (2001) Generalized minimum aberration for asymmetrical fractional factorial designs. Ann Stat 29:1066–1077
Xu H, Wu CFJ (2005) Construction of optimal multi-level supersaturated designs. Ann Stat 33:2811–2836
Acknowledgements
The authors would like to thank the Editor, an Associate Editor and the two Referees for their insightful comments that led to the improvement of the quality of this paper. The research of the second author (K.D.) was financially supported by a scholarship awarded by the Secretariat of the Research Committee of National Technical.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Chatterjee, K., Drosou, K., Georgiou, S.D. et al. Multi-level and mixed-level k-circulant supersaturated designs. Metrika 81, 337–355 (2018). https://doi.org/10.1007/s00184-018-0645-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-018-0645-4