Weibull Fit to Computer Generated Fracture Data

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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
.
Contributed by: Ozgur Keles (November 2012)
Open content licensed under CC BY-NC-SA
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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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