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Reliability of a Weibull analysis using the maximum-likelihood method

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... Full description

Journal Title: Journal of materials science 2010-10-30, Vol.46 (6), p.1862-1869
Main Author: Ambrožič, Milan
Other Authors: Gorjan, Lovro
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Boston: Springer US
ID: ISSN: 0022-2461
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recordid: cdi_proquest_miscellaneous_907932938
title: Reliability of a Weibull analysis using the maximum-likelihood method
format: Article
creator:
  • Ambrožič, Milan
  • Gorjan, Lovro
subjects:
  • Aluminum oxide
  • Analysis
  • Article
  • Bend strength
  • Characterization and Evaluation of Materials
  • Chemistry and Materials Science
  • Classical Mechanics
  • Computer simulation
  • Crystallography and Scattering Methods
  • general
  • Materials Science
  • Methods
  • Monte Carlo method
  • Monte Carlo methods
  • Parameter uncertainty
  • Polymer Sciences
  • Probability distribution
  • Reliability analysis
  • Samples
  • Solid Mechanics
  • Statistical analysis
  • Statistical distributions
  • Statistical methods
  • Subgroups
  • Weibull modulus
ispartof: Journal of materials science, 2010-10-30, Vol.46 (6), p.1862-1869
description: 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.
language: eng
source:
identifier: ISSN: 0022-2461
fulltext: no_fulltext
issn:
  • 0022-2461
  • 1573-4803
url: Link


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descriptionWe 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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subjectAluminum oxide ; Analysis ; Article ; Bend strength ; Characterization and Evaluation of Materials ; Chemistry and Materials Science ; Classical Mechanics ; Computer simulation ; Crystallography and Scattering Methods ; general ; Materials Science ; Methods ; Monte Carlo method ; Monte Carlo methods ; Parameter uncertainty ; Polymer Sciences ; Probability distribution ; Reliability analysis ; Samples ; Solid Mechanics ; Statistical analysis ; Statistical distributions ; Statistical methods ; Subgroups ; Weibull modulus
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abstractWe 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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