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 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.