Journal of Materials Science

, Volume 41, Issue 17, pp 5630–5638 | Cite as

Methods for estimating Weibull parameters for brittle materials

  • Dongfang WuEmail author
  • Jiancheng Zhou
  • Yongdan Li


A Monte Carlo simulation is used to obtain the statistical properties of the Weibull parameters estimated by the linear regression, weighted linear regression, maximum likelihood and moments methods, respectively. Results reveal that the estimated Weibull modulus is always biased, which has a much lower accuracy than the scale parameter. The mean square error is adopted as a criterion for the comparison of the estimation methods. It is shown that both the probability estimators and the weight factors have great effects on the estimation precision of the Weibull modulus. The weighted linear regression with a weight factor of Wi=3.3Pi −27.5[1−(1−Pi)0.025] and a probability estimator of Pi=(i−0.3)/(n+0.4) gives the most accurate estimation for sample sizes of 9–52. The maximum likelihood method recommended for any sample size by previous authors, comes first only for sample sizes larger than or equal to 53; furthermore, it is less conservative than the regression methods, and hence results in a lower safety in reliability predictions.


Weight Factor Fracture Stress Scale Parameter Probability Estimator Moment Method 



The corresponding author gratefully acknowledges financial supports for this work by the Science and Technology Foundation of Southeast University (Grant No. XJ0619243) and the Teaching and Research Program of Southeast University for Excellent Young Teachers.


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.School of Chemistry and Chemical EngineeringSoutheast UniversityNanjingChina
  2. 2.Department of Catalysis Science and Technology, School of Chemical EngineeringTianjin UniversityTianjinChina

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