Analysis Methods for Unreplicated Factorial Experiments

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 71)

Abstract

The analysis of unreplicated designs concentrates much of interest, since these designs enable us to estimate the factorial effects using contrasts, while no degrees of freedom are left to estimate the error variance, so conventional ANOVA techniques cannot be applied to detect the active effects. In this paper we review two effective methods (Angelopoulos and Koukouvinos, J. Appl. Statist 35:277–281, 2008; Angelopoulos et al., Qual. Reliab. Eng. Int 26:223–233, 2010) for the identification of active factors in unreplicated experiments. An illustrative example of the application of the two methods is presented, as also a comparative simulation study, revealing the effectiveness of the two methods.

Keywords

Two-level factorial designs Unreplicated experiments Outliers Projective property Power 

References

  1. 1.
    Aboukalam, M.A.F.: Quick, easy and powerful analysis of unreplicated factorial designs. Commun.Statist.- Theory Meth. 34, 1169–1175 (2005)Google Scholar
  2. 2.
    Angelopoulos, P., Koukouvinos, C.: Detecting active effects in unreplicated designs, J. Appl. Statist. 35, 277–281 (2008)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Angelopoulos, P., Evangelaras, H., Koukouvinos, C.: Analyzing unreplicated 2k factorial designs by examining their projections into k − 1 factors. Qual. Reliab. Eng. Int. 26, 223–233 (2010)CrossRefGoogle Scholar
  4. 4.
    Benski, H.C.: Use of a normality test to identify significant effects in factorial designs. J. Qual. Tech. 21, 174–178 (1989)Google Scholar
  5. 5.
    Box, G.E.P., Meyer, R.D.: An analysis for unreplicated fractional factorials. Technometrics. 28, 11–18 (1986)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Chen, Y., Kunert, J.: A new quantitative method for analysing unreplicated factorial designs. Biometrical J. 46, 125–140 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Daniel, C.: Use of half-normal plots in interpreting factorial two-level experiments. Technometrics. 1, 311–341 (1959)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dong, F.: On the identification of active contrasts in unreplicated fractional factorials. Stat. Sinica. 3, 209–217 (1993)MATHGoogle Scholar
  9. 9.
    Hadi, A.S., Simonoff, J.S.: Procedures for identification of multiple outliers in linear models. J. Am. Stat. Association. 88, 1264–1271 (1993)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hamada, M., Balakrishnan, N.: Analysing unreplicated factorial experiments: A review with some new proposals. Stat. Sinica. 8, 1–41 (1998)MathSciNetMATHGoogle Scholar
  11. 11.
    Lenth, R.V.: Quick and easy analysis of unreplicated factorial. Technometrics. 31, 469–473 (1989)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Miller, A.: The analysis of unreplicated factorial experiments using all possible comparisons. Technometrics. 47, 51–63 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Montgomery, D.C.: Design and analysis of experiments, 6th edn. John Willey and Sons, New York (2009)Google Scholar
  14. 14.
    Voss, D.T., Wang, W.: Analysis of othogonal saturated designs. In: Screening Methods for Experimentation in Industry, Drug Discovery and Genetics, pp. 268–281. Springer, New York (2006)Google Scholar
  15. 15.
    Voss, D.T., Wang, W.: On adaptive testing in orthogonal satutated designs. Stat. Sinica. 16, 227–234 (2006)MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

Personalised recommendations