The effect of the threshold stress on the determination of the Weibull parameters in probabilistic failure analysis

In the analysis of brittle materials and components the probability of failure is commonly modelled using a two-parameter Weibull distribution. Occasionally, a three-parameter model is used when the material shows significant threshold behaviour. In this paper two methods for determining the three-parameter constants are discussed. Two theoretical two- and three-parameter distributions are then analysed to examine the number of samples needed to determine the parameters accurately. The two-parameter models are the best fits of the three-parameter models and their failure distributions are very similar to the three-parameter distributions. It is concluded that far more specimens need to be tested than is usually the case to be confident that the correct distribution has been found.