CHARACTERIZATION OF BALANCED FRACTIONAL 2^m FACTORIAL DESIGNS OF RESOLUTION R^*({1}3) AND GAOPTIMAL DESIGNS
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In this paper, based on the assumption that the fourfactor and higherorder 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 Aoptimality criterion for 6 ≤ m ≤ 8 when the number of assemblies is less than the number of nonnegligible factorial effects.
In this paper, based on the assumption that the fourfactor and higherorder interactions are to be negligible, we consider a balanced fractional 2<sup><i>m</i></sup> factorial design derived from a simple array such that all the main effects are estimable, i.e., resolution R<sup>*</sup>({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 Aoptimality criterion for 6 ≤ <i>m</i> ≤ 8 when the number of assemblies is less than the number of nonnegligible factorial effects.
Journal

 JOURNAL OF THE JAPAN STATISTICAL SOCIETY

JOURNAL OF THE JAPAN STATISTICAL SOCIETY 33(2), 181201, 20031201
THE JAPAN STATISTICAL SOCIETY