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).
The figure at the right shows the Weibull distribution for various β value, holding η constant at η=200.
||The Weibull distribution occurs mainly when investigating the mean time to failure of materials.
||μ = ηΓ(1+1/β)|
||σ2 = η2[Γ(1+2/β) - Γ2(1+1/β)]|