Limitations of the Weibull distribution related to predicting the probability of failure initiated by flaws

In equation (3) σ is the loading stress, V is the stressed volume, σ0 and m are constants.

The theoretical justification of the Weibull distribution is the extreme value theory. According to the extreme value theory (Gumbel, 1958), provided that a specific condition related to the lower tail is fulfilled, the Weibull model is the asymptotic distribution for the minimum of a large number of bounded on the left, identically distributed random variables.