*J. Japan Statist. Soc.,* Vol. 33 (No. 2), pp. 181-201, 2003

## Characterization of Balanced Fractional 2^{m} Factorial Designs of Resolution R^{*}({1}|3) and Ga-Optimal Designs

Masahide Kuwada, Yoshifumi Hyodo and Dong Han

**Abstract. **
In this paper, based on the assumption that the four-factor and higher-order interactions are to be negligible, we consider a balanced fractional 2^{m} factorial design derived from a simple array such that all the main effects are estimable, i.e., resolution R^{*}({1}|3). In this situation, using the algebraic structure of the triangular multidimensional partially balanced association scheme and a matrix equation, we can get designs of four types of resolutions: the first is of resolution R({1}|3), the second is of resolution R({0,1}|3), the third is of resolution R({1,2}|3), i.e., resolution VI, and the last is of resolution R({0,1,2}|3), i.e., resolution VI. This paper gives the characterization of designs mentioned above, and also it gives optimal designs with respect to the generalized A-optimality criterion for 6 ≤ *m* ≤ 8 when the number of assemblies is less than the number of non-negligible factorial effects.

*Key words and phrases*:
Association algebra, BFF designs, estimable parametric functions, GA-optimality criterion, resolution, simple arrays.

[Full text] (PDF 240 KB)