The Weibull distribution is used under these conditions:
This flexible distribution can assume the properties of other distributions. When the shape parameter is equal to 1.0, the Weibull distribution is identical to the exponential distribution. The location parameter lets you set up an exponential distribution to start at a location other than 0.0. When the shape parameter is less than 1.0, the Weibull distribution becomes a steeply declining curve. A manufacturer might find this effect useful in describing part failures during a burn-in period.
When shape parameters equal 1, it is identical to Exponential; when equal to 2, it is identical to Rayleigh.