Template:WeibullDistribution

The Weibull Distribution
The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the three-parameter Weibull p'd'f is defined by:


 * $$f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}$$

with three parameters β, η and γ, where β = shape parameter, η = scale parameter and γ = location parameter. If the location parameter, γ, is assumed to be zero, then the distribution becomes the two-parameter Weibull or:


 * $$f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}$$

One additional form is the one-parameter Weibull distribution, which assumes that the location parameter, γ, is zero, and the shape parameter is a known constant, or β = constant = C, so:


 * $$f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}

$$

The chapter The Weibull Distribution of this reference fully details the Weibull distribution and presents many examples of its use in Weibull++.