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Weibull Fit to Computer Generated Fracture Data

In this Demonstration, a sample size of fracture values can be generated from a two-parameter (2P) Weibull distribution function with parameters and . Subsequently, another 2P Weibull distribution with parameters and can be used to fit the generated fracture data. The Kolmogorov–Smirnov and Anderson–Darling goodness of fit test results are shown above the graph comparing the fracture data to the fitted distribution; a higher -value gives a better fit. The Anderson–Darling test gives more weight to the tails than the Kolmogorov–Smirnov test. The method of moments estimators and are calculated from the generated fracture data and can be used as inputs for Weibull distribution fit parameters. Blue points represent the fracture data, the green curve represents the cumulative distribution function (CDF) and the red curve represents the probability density function (PDF) of the fitted Weibull distribution function with parameters and .
Standards such as BS EN 843-1 require at least 30 specimens for the experimental determination of Weibull statistics in order to decrease the scatter in the fitted parameters [1]. However, the fitted distribution depends not only on the fitting technique but also on the number of specimens (the sample size, ). Additionally, different goodness of fit tests can result in favor of different fitting parameters. As a result, reliability calculations for specific applications can be misleading.

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Reference
[1] BS EN 843-1, Advanced Technical Ceramics, Monolithic Ceramics, Mechanical Tests at Room Temperature. Part I: Determination of Flexural Strength, 1995.
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