Influence of measurement uncertainties on the determination of the Weibull distribution

The influence of measurement uncertainties (MU) on the determination of the parameters of a distribution function has been analyzed using a Monte Carlo simulation technique on the example of the Weibull distribution, which describes the strength of brittle materials. It is shown that in the parameter range which is relevant for strength testing of brittle materials (e.g. ceramics) very high precision measurements are necessary if the Weibull modulus of the parent distribution is m ≥ 20. In that case the MU should be lower than ±2% of the measured value to obtain the same confidence level compared to the ideal case (MU = 0). Otherwise a significant underestimation of m becomes very probable. However, if m ≤ 10, even relatively large MU (up to ±10%) are tolerable. In summary, the precision of the measurements is acceptable as long as the width of the error distribution be much smaller than the width of the parent distribution.