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Journal of Statistical Theory and Practice

, Volume 1, Issue 3–4, pp 427–464 | Cite as

GA-optimal Partially Balanced Fractional 2m1+m2 Factorial Designs of Resolutions R({10,01} ∪ Ω* | Ω) with 2 ≤ m1, m2 ≤ 4

  • Shujie Lu
  • Eiji Taniguchi
  • Yoshifumi Hyodo
  • Masahide Kuwada
Article

Abstract

We consider a partially balanced fractional 2m1+m2 factorial design derived from a simple partially balanced array such that all the m1 main effects (= θ10, say) and all the m2 ones (= θ01, say) are estimable, and in addition that the general mean (= θ00, say) is at least confounded (or aliased) with the factorial effects of the (2 m1) two-factor interactions (= θ20, say), the (2 m2) ones (= θ02, say) and/or the m1m2 ones ( = θ11, say), where the three-factor and higher-order interactions are assumed to be negligible, and 2 ≤ mk for k = 1,2. Furthermore optimal designs with respect to the generalized A-optimality criterion are presented for 2 ≤ m1,m2 ≤ 4 when the number of assemblies is less than the number of non-negligible factorial effects.

AMS Subject Classification

Primary 62K05 Secondary 05B30 

Keywords

ETMDPB association algebra GA-optimality criterion Parametric functions PBFF designs Resolution SPBA 

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References

  1. Draper, N.R., Lin D.K.J., 1990. Capacity considerations for two-level fractional factorial designs. Journal of Statistical Planning and Inference, 24, 25–35.MathSciNetCrossRefGoogle Scholar
  2. Ghosh, S., Kuwada, M., 2001. Estimable parametric functions for balanced fractional 2m factorial designs. Statistical Research Group, Technical Report 01–7, Hiroshima University.Google Scholar
  3. Kuwada, M., 1986. Optimal partially balanced fractional 2m1+m2 factorial designs of resolution IV. Annals of the Institute of Statistical Mathematics, A38, 343–351.MathSciNetCrossRefGoogle Scholar
  4. Kuwada, M., 1988. A-optimal partially balanced fractional 2m1+m2 factorial designs of resolution V, with 2 ≤ m1 + m2 ≤ 6. Journal of Statistical Planning and Inference, 18, 177–193.MathSciNetCrossRefGoogle Scholar
  5. Kuwada, M., Hyodo, Y., Yumiba, H., 2004. GA-optimal balanced fractional 2m factorial designs of resolution R*(0,1|3). Sankhyā, 66, 343–361.MathSciNetzbMATHGoogle Scholar
  6. Kuwada, M., Lu, S., Hyodo, Y., Taniguchi, E., 2006a. GA-optimal partially balanced fractional 2m1+m2 factorial designs of resolutions R(00,10,01,20,02|Ω) and R(00,10,01,20,11|Ω) with 2 ≤ m1,m2 ≤ 4. Journal of the Japan Statistical Society, 36, 237–259.CrossRefGoogle Scholar
  7. Kuwada, M., Lu, S., Hyodo, Y., Taniguchi, E., 2006b. GA-optimal partially balanced fractional 2m1+m2 factorial designs of resolution R(00,10,01,20|Ω) with 2 ≤ m1,m2 ≤ 4. Communications in Statistics: Theory and Methods, 35(11), 2035–2053.MathSciNetCrossRefGoogle Scholar
  8. Kuwada, M., Matsuura, M., 1984. Further results on partially balanced fractional 2m1+m2 factorial designs of resolution IV. Journal of the Japan Statistical Society, 14, 69–83.zbMATHGoogle Scholar
  9. Lu, S., Taniguchi, E., Hyodo, Y., Kuwada, M., 2007a. GA-optimal partially balanced fractional 2m1+m2 factorial designs of resolution R(00,10,01,11|Ω) with 2 ≤ m1m2 ≤ 4. Scientiae Mathematicae Japonicae, 65, 81–94.MathSciNetzbMATHGoogle Scholar
  10. Lu, S., Taniguchi, E., Kuwada, M., Hyodo, Y., 2007b. GA-optimal partially balanced fractional 2m1+m2 factorial designs of resolution R(00,10,01|Ω) with 2 ≤ m1,m2 ≤ 4. Hiroshima Mathematical Journal, 37, 119–143.MathSciNetzbMATHGoogle Scholar
  11. Margolin, B.H., 1969a. Resolution IV fractional factorial designs. Journal of the Royal Statistical Society, B 31, 514–523.MathSciNetzbMATHGoogle Scholar
  12. Margolin, B.H., 1969b. Results on factorial designs of resolution IV for the 2n and 2n3m series. Technometrics, 11, 431–444.MathSciNetzbMATHGoogle Scholar
  13. Nishii, R., 1981. Balanced fractional rm × sn factorial designs and their analysis. Hiroshima Mathematical Journal, 11, 379–413.MathSciNetzbMATHGoogle Scholar
  14. Webb, S., 1968. Non-orthogonal designs of even resolution. Technometrics, 10, 291–299.MathSciNetCrossRefGoogle Scholar
  15. Yamamoto, S., Hyodo, Y., 1984. Extended concept of resolution and the designs derived from balanced arrays. TRU Mathematics, 20, 341–349.MathSciNetzbMATHGoogle Scholar
  16. Yamamoto, S., Shirakura, T., Kuwada, M., 1976. Characteristic polynomials of the information matrices of balanced fractional 2m factorial designs of higher (2ℓ + 1) resolution. In Ikeda, S. et al. (Eds.), Essays in Probability and Statistics, 73–94, Shinko Tsusho, Tokyo.Google Scholar

Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  • Shujie Lu
    • 1
  • Eiji Taniguchi
    • 2
  • Yoshifumi Hyodo
    • 2
  • Masahide Kuwada
    • 1
  1. 1.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Graduate School of InformaticsOkayama University of ScienceOkayamaJapan

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