Weibull parameter estimation and goodness-of-fit for glass strength data. (July 2018)

• Record Type: Journal Article
• Authors: Datsiou, Kyriaki Corinna; Overend, Mauro
• Is Part Of: Structural safety. Volume 73(2018)
• Page Start: 29
• Page End: 41
• Publication Date: 2018-07
• Subjects: Glass strength -- Statistical analysis -- 2-Parameter Weibull distribution -- Goodness of fit -- Small samples; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2018.02.002
• Languages: English
• ISSNs: 0167-4730

Abstract

Highlights: A 2-parameter Weibull distribution can successfully describe glass strength data. Manual and computational methods were tested for estimating the Weibull parameters. The Anderson Darling goodness-of-fit was used for evaluating the estimation methods. The weighted least squares regression is identified as the most effective method. Goodness-of-fit increase up to 80% is noted compared to existing recommendations. Abstract: 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.