Characterization of Balanced Fractional 2m Factorial Designs of Resolution R*({1}|3) and GA-optimal Designs

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  • Kuwada Masahide
    Faculty of Integrated Arts and Sciences, Hiroshima University
  • Hyodo Yoshifumi
    Department of Applied Mathematics, Faculty of Science, Okayama University of Science Now at Department of Information Science, Graduate School of Informatics, Okayama University of Science
  • Han Dong
    Graduate School of Engineering, Hiroshima University

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  • Characterization of Balanced Fractional 2<sup><i>m</i></sup> Factorial Designs of Resolution R<sup>*</sup>({1}|3) and GA-optimal Designs

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In this paper, based on the assumption that the four-factor and higher-order interactions are to be negligible, we consider a balanced fractional 2m 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.

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