Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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A Study on the Construction and Analysis of Fractional Designs by Using Arrays for Factorial Experiments

배열을 이용한 효과적인 일부실시법의 설계 및 분석방법에 관한 연구

  • 김상익 (건국대학교 상경대학 응용통계학과)
  • Received : 2011.12.02
  • Accepted : 2012.01.09
  • Published : 2012.03.31
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Abstract

For the construction of fractional factorial designs, the various arrays can be widely used. In this paper we review the statistical properties of fractional designs constructed by two arrays such as orthogonal array and partially balanced array, and develop a quick and easy method for analyzing unreplicated saturated designs. The proposed method can be characterized that we control the error rate by experiment-wise way and exploit the multivariate Student $t$-distribution. Especially the proposed method can be used efficiently together with some exploratory analysis methods, such as half normal probability plot method.

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References

  1. 김상익(1995), "균형배열을 이용한 Resolution V $2^t$ 포화부분설계법의 정보행렬에 관한 연구", 한국통계학회 논문집, 2권, 2호, pp.404-413.
  2. 김상익(2006), "2-수준 요인실험에서 주효과 및 교호작용에 대한 효율적인 분석방법 연구", 품질경영학회지, 34권, 1호, pp. 27-33.
  3. Box, G.E.P. and Hunter, J.S.(1961), "The $2^{k-p}$ Fractional Factorial Design I", Technometrics, Vol. 3, pp. 311-351.
  4. Box, G.E.P. and Meyer, R.D.(1986), "An Analysis for Unreplicated Fractional Factorials", Technometrics, Vol. 28, pp. 11-18. https://doi.org/10.1080/00401706.1986.10488093
  5. Chakravartie, I.M.(1956), "Fractional Replications in Asymmetrical Factorial Designs and Partially Balanced Arrays, Sankhya, Vol. 17, pp. 143-164.
  6. Daniel, C.(1959), "Use of Half-Normal Plots in Interpreting Factorial 2-Level Experiments , Technometrics, Vol. 1, pp. 311-342. https://doi.org/10.1080/00401706.1959.10489866
  7. Hahn, G.J. and Hendrickson R.W.(1971), "A Table of Percentage Points of the Distribution of the Largest Absolute Value of q Student t Variates and Its Applications," Biometrika, Vol. 58, pp. 323-332 https://doi.org/10.1093/biomet/58.2.323
  8. Lenth, R. V.(1989), "Quick and Easy Analysis of Unreplicated Factorials," Technometrics, Vol. 31, pp. 469-473. https://doi.org/10.1080/00401706.1989.10488595
  9. Milliken, G. A. and Johnson, D.E.(1989), Analysis of Messy Data, Vol.II, Van Nostrand Reinhold Company, New York.
  10. Montgomery, D.C.(2009), Design and Analysis of Experiments, 7th edition, Wiley, New York.
  11. Neter, J., Wasserman, W. and Kutner, M.H.(1985), Applied Liner Statistical Method, 2nd edition, Richard D. Irwin, Homewood, Illnois.
  12. Raghavarao, D.(1971), Constructions and Combinatorial Problems in Design of Experiments, John Wiely & Sons, Inc., New York.
  13. Raktoe, B.L., Hedagat, A. and Federer, W.T.(1981), Factorial Designs, Wiley, New York.
  14. Srivastava, J.N.(1965), "Optimal Balanced $2^m$ Fractional Factorial Designs", S.N. Roy Memorial Volume, Univ. of North Carolina and Indian Statistical Institute.
  15. Taguchi, G.(1986), Introduction to Quality Engineering, Asian Productivity Organization, Tokyo, Japan.
  16. Taguchi, G.(1987), Systems of Experimental Design, Vol. Two, American Supplier Institute, Dearborn, Michigan.