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Reliability of a Weibull analysis using the maximum-likelihood method

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Abstract

We have performed extensive Monte-Carlo computer simulations of the 2-parameter Weibull statistical distribution using data groups with sizes from 5 up to 100 samples. The maximum-likelihood method was used to evaluate the resulting Weibull modulus and the scale parameter, which may be different to the input values. We confirmed some trends in the evaluation of the statistical parameters for small data groups, such as a significant biasing of the Weibull modulus. We revealed the log-normal statistical distribution of the Weibull parameters obtained from repeated Monte-Carlo simulations for several groups. We also considered the influence of the measurement uncertainty on the determination of the statistical parameters. For the experimental evidence we used bend-strength data for alumina test samples from serial production in this year. The experimental data were randomly divided into several subgroups to compare the corresponding biasing of the Weibull modulus with the Monte-Carlo results.

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Acknowledgements

This research was supported by the Ministry of Education and Sport of Republic of Slovenia and the European Social Fund. We thank the company Hidria AET for providing the experimental data.

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Authors and Affiliations

  1. Jožef Stefan International Postgraduate School, Jamova 39, 1000, Ljubljana, Slovenia

    Milan Ambrožič

  2. Physics Department, Faculty for Natural Sciences and Mathematics, University of Maribor, 2000, Maribor, Slovenia

    Milan Ambrožič

  3. Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia

    Lovro Gorjan

  4. Hidria AET, Tolmin, Slovenia

    Lovro Gorjan

Authors
  1. Milan Ambrožič
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  2. Lovro Gorjan
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Correspondence to Lovro Gorjan.

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Ambrožič, M., Gorjan, L. Reliability of a Weibull analysis using the maximum-likelihood method. J Mater Sci 46, 1862–1869 (2011). https://doi.org/10.1007/s10853-010-5014-2

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  • DOI: https://doi.org/10.1007/s10853-010-5014-2

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