CHARACTERIZATION OF BALANCED FRACTIONAL 2^m FACTORIAL DESIGNS OF RESOLUTION R^*({1}|3) AND GA-OPTIMAL DESIGNS

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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.

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<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 A-optimality criterion for 6 ≤ <i>m</i> ≤ 8 when the number of assemblies is less than the number of non-negligible factorial effects.

Journal

  • JOURNAL OF THE JAPAN STATISTICAL SOCIETY

    JOURNAL OF THE JAPAN STATISTICAL SOCIETY 33(2), 181-201, 2003-12-01

    THE JAPAN STATISTICAL SOCIETY

References:  13

Codes

  • NII Article ID (NAID)
    110003144463
  • NII NACSIS-CAT ID (NCID)
    AA1105098X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    03895602
  • NDL Article ID
    6885717
  • NDL Source Classification
    ZD43(経済--統計)
  • NDL Call No.
    Z3-1003
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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