Weibull parameter estimation and goodness-of-fit for glass strength data

Strength data from macroscopically identical glass specimens is commonly described by a two-parameter Weibull distribution, but there is lack of research on the methods used for fitting strength data to the Weibull distribution. This study investigates 4 different methods for fitting data and estimating the parameters of the Weibull distribution namely, good linear unbiased estimators, least squares regression, weighted least squares regression and maximum likelihood estimation. These methods are implemented on fracture surface strength data from 418 annealed soda-lime-silica glass specimens, grouped in 30 nominally identical series, including as-received, naturally aged and artificially aged specimens. The strength data are evaluated based on their goodness of fit. Comparison of conservativeness of strength estimates is also provided. It is found that a weighted least squares regression is the most effective fitting method for the analysis of small samples of glass strength data.