Journal of Statistical Theory and Practice

, Volume 6, Issue 1, pp 190–203 | Cite as

Characterization of Balanced Second-Order Designs for 3m Factorials

  • Hiromu Yumiba
  • Yoshifumi Hyodo
  • Masahide KuwadaEmail author


We consider a fractional 3m factorial design for the second-order model derived from a simple array (SA), where m ≥ 4. In this article, we give a necessary and sufficient condition for an SA to be a balanced second-order design for 3m factorials. Such a design is characterized by the suffixes of the index of an SA.

AMS Subject Classification

62K15 05B30 


BSO design Factorial effect MDR algebra Quadratic equation Row rank SA Second-order model 


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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  • Hiromu Yumiba
    • 1
  • Yoshifumi Hyodo
    • 1
    • 2
  • Masahide Kuwada
    • 1
    • 3
    Email author
  1. 1.International Institute for Natural SciencesKurashikiJapan
  2. 2.Graduate School of InformaticsOkayama University of ScienceOkayamaJapan
  3. 3.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan

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