The key is the left tail of the distribution of P 1 ( σ σ k ) . It was not successfully identified until Weibull in 1939 recognized that the tail is a power law. Denoting the tail exponent as m , one can then show that, if the structure is sufficiently larger than one RVE (i.e., if N/l 0 → ∞), the failure probability of a structure as a function of σ σ N is