*J. Japan Statist. Soc.,* Vol. 36 (No. 2), pp. 237-259, 2006

## GA-Optimal Partially Balanced Fractional 2^{m1}+^{m2} Factorial Designs of Resolutions R({00,10,01,20,02} | Ω) and R({00,10,01,20,11} | Ω) with 2 *m*_{1}, *m*_{2} 4

Masahide Kuwada, Shujie Lu, Yoshifumi Hyodo and Eiji Taniguchi

**Abstract. **
Under the assumption that the three-factor and higher-order interactions are negligible, we consider two kinds of partially balanced fractional 2^{m1+m2} factorial designs derived from simple partially balanced arrays, where 2 *m*_{k} for *k* = 1, 2. One is a design such that the general mean, the *m*_{1} + *m*_{2} main effects, the two-factor interactions, the two-factor ones and some linear combinations of the *m*_{1}*m*_{2} two-factor ones are estimable, and the other is a design such that the general mean, the *m*_{1} + *m*_{2} main effects, the two-factor interactions, the *m*_{1}*m*_{2} two-factor ones and some linear combinations of the two-factor ones are estimable. In each kind of designs, we present optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non-negligible factorial effects, where 2 *m*_{1}, *m*_{2} 4.

*Key words and phrases*:
Association algebra, estimable parametric functions, GA-optimality criterion, PBFF designs, resolutions.

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