THE VALIDITY OF WEIBULL ESTIMATORS - EXPERIMENTAL-VERIFICATION

A sufficiently large number of bending tests of a recrystallized silic on carbide ceramic was performed, which gave a fundamental set of stre ngth values. From this fundamental set, arbitrary subsets of size M we re chosen by a Monte-Carlo procedure and the parameters of the two-par ametric Weibull distribution were calculated by the maximum likelihood method. The dependence of the statistical distribution of the two par ameters, obtained by this procedure, on the size of the subset M was i nvestigated. It was found that the variation coefficient of the scale parameter could be well described by the equations given in the litera ture, whereas the variation coefficient of the Weibull modulus was muc h higher. It has been shown that the reason for this behaviour is that the distribution of flaws and therefore the strength of the material does not perfectly obey the Weibull statistics, for which the theoreti cal equations were derived. Thus, in real ceramics the numerical value for the Weibull modulus obtained from a certain number of experiments is even more indeterminate than described by the theoretical solution .