Abstract
In this paper we present a new method for constructing multi-level supersaturated designs with n rows, m columns and the equal occurrence property. We investigate the existence of multi-level supersaturated designs using a single generator vector and its k-cyclic permutations as rows. We find the conditions needed, in order this vector to generate a balanced supersaturated design. These conditions are simplified for the case of three level supersaturated designs. By using the proposed method three level supersaturated designs are constructed and explored. Moreover, many new, optimal and near optimal, multi-level supersaturated designs are provided as well.
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
Box GEP, Meyer RD (1986) An analysis for unreplicated fractional factorials. Technometrics 28:11–18
Butler N, Mead R, Eskridge KM, Gilmour SG (2001) A general method of constructing E(s 2)-optimal supersaturated designs. J R Stat Soc B 63:621–632
Cheng CS (1997) E(s 2)-optimal supersaturated designs. Stat Sin 7:929–939
Fang KT, Ge G, Liu MQ (2002) Uniform supersaturated design and its construction. Sci China 45:1080–1088
Fang KT, Lin DKJ, Liu MQ (2003) Optimal mixed-level supersaturated design. Metrika 58:279–291
Fang KT, Lin DKJ, Ma CX (2000) On the construction of multi-level supersaturated designs. J Stat Plan Inference 86:239–252
Li WW, Wu CFJ (1997) Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics 39:171–179
Liu YF, Dean AM (2004) k-circulant supersaturated designs. Technometrics 46:32–43
Lin DKJ (1993) A new class of supersaturated designs. Technometrics 35:28–31
Lin DKJ (1995) Generating systematic supersaturated designs. Technometrics 37:213–225
Liu M, Zhang R (2000) Construction of E(s 2) optimal supersaturated designs using cyclic BIBDs. J Stat Plan Inference 91:139–150
Lu X, Meng Y (2000) A new method in the construction of two-level supersaturated designs. J Stat Plan Inference 86:229–238
Lu X, Sun Y (2001) Supersaturated design with more than two levels. Chin Ann Math 22B(2):183–194
Lu X, Hu W, Zheng Y (2003) A systematic procedure in the construction of multi-level supersaturated design. J Stat Plan Inference 115:287–310
Nguyen NK (1996) An algorithmic approach to constructing supersaturated designs. Technometrics 38:69–73
Satterthwaite FE (1959) Random balance experimentation (with discussions). Technometrics 1:111–137
Tang B, Wu CFJ (1997) A method for constructing supersaturated designs and its Es 2-optimality. Can J Stat 25:191–201
Yamada S, Lin DKJ (1997) Supersaturated designs including an orthogonal base. Can J Stat 25:203–213
Yamada S, Ikebe YT, Hashiguchi H, Niki N (1999) Construction of three-level supersaturated design. J Stat Plan Inference 81:183–193
Yamada S, Lin DKJ (1999) Three-level supersaturated designs. Stat Probab Lett 45:31–39
Yamada S, Matsui T (2002) Optimality of mixed-level supersaturated designs. J Stat Plan Inference 104:459–468
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Georgiou, S., Koukouvinos, C. Multi-level k-circulant Supersaturated Designs. Metrika 64, 209–220 (2006). https://doi.org/10.1007/s00184-006-0045-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0045-z