[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2006.13.3.777

On the Geometric Equivalence of Asymmetric Factorial Designs

Park, Dong-Kwon (Department of Informations and Statistics, Yonsei University)
Park, Eun-Hye (Department of Applied Statistics, Yonsei University)

Publication Information

Communications for Statistical Applications and Methods / v.13, no.3, 2006 , pp. 777-786 More about this Journal

Abstract

Two factorial designs with quantitative factors are called geometrically equivalent if the design matrix of one can be transformed into the design matrix of the other by row and column permutations, and reversal of symbol order in one or more columns. Clark and Dean (2001) gave a sufficient and necessary condition (which we call the 'gCD condition') for two symmetric factorial designs with quantitative factors to be geometrically equivalent. This condition is based on the absolute value of the Euclidean(or Hamming) distance between pairs of design points. In this paper we extend the gCD condition to asymmetric designs. In addition, a modified algorithm is applied for checking the equivalence of two designs.

Keywords

Asymmetric; geometrically equivalent; quantitative;

Citations & Related Records

Reference

1	Draper, N.R. and Mitchell, T.J. (1968). Construction of the set of 256-run designs of resolution ${\geq}$ 5 and the set of even 512-run designs of resolution ${\geq}$ 6 with special reference to the unique saturated designs. Annals of Mathematical Statistics, Vol. 39, 246-255 DOI
2	Cheng, S.W. and Ye, K.Q. (2004). Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. The Annals of Statistics, Vol. 32, 2168-2185 DOI
3	Draper, N.R. and Mitchell, T.J. (1967). The construction of saturated $2^{k-p}_{R}$ designs. Annals of Mathematical Statistics, Vol. 38, 1110-1128 DOI
4	Draper, N.R. and Mitchell, T.J. (1970). Construction of the set of 512-run designs of resolution ${\geq}$ 5 and the set of even 1024-run designs of resolution ${\geq}$ 6. Annals of Mathematical Statistics, Vol. 41, 876-887 DOI
5	Chen, J. and Lin, D.K.J. (1991). On the identity relationship of $2^{k-p}$ designs. Journal of Statistical Planning and Inference, Vol. 28, 95-98 DOI ScienceOn
6	Xu, H. (2005). A catalogue of three-level regular fractional factorial designs. Metrika, Vol. 62, 259--281 DOI ScienceOn
7	Cheng, S.W. and Wu, C.F.J. (2001). Factor screening and response surface exploration (with discussion). Statistica Sinica, Vol. 11, 553-604
8	Clark, J.B. and Dean A.M. (2001). Equivalence of fractional factorial designs. Statistica Sinica, Vol. 11, 537-547