Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Weibull Distribution

With β=1 the Weibull distribution becomes the exponential distribution (which means that the exponential distribution can be applied to problems having a constant failure rate, while the Weibull distribution can handle situations with increasing or falling failure rates, as well).
Graphic Representation The figure at the right shows the Weibull distribution for various β value, holding η constant at η=200.
Applications The Weibull distribution occurs mainly when investigating the mean time to failure of materials.
Mean μ = ηΓ(1+1/β)
Variance σ2 = η2[Γ(1+2/β) - Γ2(1+1/β)]