Template:Alta eyring-weibull

Eyring-Weibull
The $$pdf$$  for 2-parameter Weibull distribution is given by:


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

The scale parameter (or characteristic life) of the Weibull distribution is $$\eta $$. The Eyring-Weibull model $$pdf$$  can then be obtained by setting  $$\eta =L(V)$$:


 * $$\eta =L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}$$


 * or:


 * $$\frac{1}{\eta }=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}$$

Substituting for $$\eta $$  into the Weibull $$pdf$$ yields:


 * $$f(t,V)=\beta \cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}{{\left( t\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta -1}}{{e}^{-{{\left( t\cdot V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} \right)}^{\beta }}}}$$