Template:Weibull Distribution Definition

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 3-parameter Weibull $$pdf$$ is defined by:


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

where $$\beta \,\!$$ = shape parameter, $$\eta \,\!$$ = scale parameter and $$\gamma\,\!$$ = location parameter.

If the location parameter, $$\gamma\,\!$$, is assumed to be zero, then the distribution becomes the 2-parameter Weibull or:


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

One additional form is the 1-parameter Weibull distribution, which assumes that the location parameter, $$\gamma\,\!$$ is zero, and the shape parameter is a known constant, or $$\beta \,\!$$ = constant = $$C\,\!$$, so:


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

$$

For a detailed discussion of this distribution, see The Weibull Distribution.