Methods for estimating Weibull parameters for brittle materials
- 337 Downloads
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.
KeywordsWeight 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.
- 1.ASTM standard C1239-00, “Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics”, ASTM InternationalGoogle Scholar
- 6.Weibull W (1951) J Appl Mech 18:293Google Scholar
- 9.Sullivan JD, Lauzon PH (1986) ibid 5:1245Google Scholar
- 12.Faucher B, Tyson WR (1988) ibid 7:1199Google Scholar
- 13.Langlois R (1991) ibid 10:1049Google Scholar
- 14.Wu DF, Jiang H (2003) ibid 22:1745Google Scholar
- 20.Kapur KC, Lamberson LR (1977) Reliability in engineering design. Wiley, New YorkGoogle Scholar
- 22.Fernandez-Saez J, Chao J, Duran J, Amo JM (1993) J Mater Sci Lett 12:1493Google Scholar
- 23.Barbero E, Fernandez -Saez J, Navarro C (1999) ibid 18:1441Google Scholar
- 24.Cox DR (1987) Applied statistics, principles and examples. Chapman Hall, LondonGoogle Scholar
- 27.Peterlik H (1995) ibid 30:1972Google Scholar