The validity of Weibull estimators

Abstract

The parameters of the two-parametric Weibull distribution, the Weibull modulus and the scale parameter, were estimated by using not only analytical means but also Monte-Carlo simulations. The precision of the measurement of both parameters, i.e. their variation coefficient, has been calculated. It is shown that the variation coefficient of the scale parameter is dependent on the number of experiments, M, which were performed, and on the Weibull modulus itself, whereas the variation coefficient of the Weibull modulus is only dependent on M. Furthermore, the correctly interpreted results show that each single measurement gives the statistically correct Weibull parameters and the biasing arises only from the method of adding single measurements to obtain a mean value. Thus, in practice, when only one set of experiments for further evaluation is available, there is no need for adjustment factors.