Statistical properties of Weibull estimators

Abstract

The Weibull parameters were estimated for data produced by Monte Carlo simulations using three different approaches: linear regression, moments method, and maximum likelihood method. The last of these was shown to be the most appropriate approach for the whole range of sample sizes of 4 to 100 for estimating the Weibull parameters of a brittle material. In each simulation 10000 estimators were produced. Using these values histograms of the estimators were created, which showed the asymmetry of the Weibull modulus distribution. The integrals of these density functions were directly used to determine confidence intervals for the estimated Weibull moduli. Furthermore it was reaffirmed that a minimum of 30 samples are required for a good characterization of the strength of a brittle material.