Methods for estimating Weibull parameters for brittle materials

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 ofWi=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.