Definition 
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 
σ^{2} = η^{2}[Γ(1+2/β)  Γ^{2}(1+1/β)] 