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Journal of Materials Science

, Volume 43, Issue 6, pp 1914–1919 | Cite as

Unbiased estimates of the Weibull parameters by the linear regression method

  • Murat Tiryakioğlu
  • David Hudak
Article

Abstract

For sample sizes from 5 to 100, the bias of the scale parameter was investigated for probability estimators, P = (i − a)/(n + b), which yield unbiased estimates of the shape parameter. A class of unbiased estimators for both the shape and scale parameters was developed for each sample size. In addition, the percentage points of the distribution of unbiased estimate of the shape parameter were determined for all sample sizes. The distribution of the scale parameter was found to be normal by using the Anderson-Darling goodness-of-fit test. How the results can be used to establish confidence intervals on both the shape and scale parameters are demonstrated in the paper.

Keywords

Monte Carlo Simulation Shape Parameter Scale Parameter Maximum Likelihood Method Unbiased Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Khalili A, Kromp K (1991) J Mater Sci 26:6741CrossRefGoogle Scholar
  2. 2.
    Langlois R (1991) J Mater Sci Lett 10:1049CrossRefGoogle Scholar
  3. 3.
    Bergman B (1984) J Mater Sci Lett 3:689CrossRefGoogle Scholar
  4. 4.
    Trustrum K, de Jayatilaka AS (1979) J Mater Sci 14:1080CrossRefGoogle Scholar
  5. 5.
    Wu D, Zhoua J, Li Y (2006) J Eur Cer Soc 26:1099CrossRefGoogle Scholar
  6. 6.
    Tiryakioğlu M (2006) J Mater Sci 41:5011CrossRefGoogle Scholar
  7. 7.
    Tiryakioğlu M, Hudak D (2007) J Mater Sci 42:10173CrossRefGoogle Scholar
  8. 8.
    Thoman DR, Bain LJ, Antle CE (1969) Technometrics 11:445CrossRefGoogle Scholar
  9. 9.
    Ritter J, Bandyopadhyay N, Jakus K (1981) Amer Cer Soc Bull 60:788Google Scholar
  10. 10.
    Gong J, Wang J (2002) Key Eng Mater 224–226:779CrossRefGoogle Scholar
  11. 11.
    Barbero E, Fernandez-Saez J, Navarro C (2000) Composites: Par2 31:375CrossRefGoogle Scholar
  12. 12.
    Barbero E, Fernandez-Saez J, Navarro C (2001) J Mater Sci Lett 20:847CrossRefGoogle Scholar
  13. 13.
    Anderson TW, Darling DA (1954) J Amer Stat Assoc 49:765CrossRefGoogle Scholar
  14. 14.
    Stephens MA (1974) J Amer Stat Assoc 69:730CrossRefGoogle Scholar
  15. 15.
    Stephens MA (1986) In: D’Agostino RB, Stephens MA (eds) Goodness of fit techniques. Marcel Dekker, p 97Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Engineering, School of Engineering, Mathematics and ScienceRobert Morris UniversityMoon TownshipUSA
  2. 2.Department of Mathematics, School of Engineering, Mathematics and ScienceRobert Morris UniversityMoon TownshipUSA

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