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The [math]\displaystyle{ pdf }[/math] for 2-parameter Weibull distribution is given by:
- [math]\displaystyle{ f(t)=\frac{\beta }{\eta }{{\left( \frac{t}{\eta } \right)}^{\beta -1}}{{e}^{-{{\left( \tfrac{t}{\eta } \right)}^{\beta }}}} }[/math]
The scale parameter (or characteristic life) of the Weibull distribution is [math]\displaystyle{ \eta }[/math] . The Eyring-Weibull model [math]\displaystyle{ pdf }[/math] can then be obtained by setting [math]\displaystyle{ \eta =L(V) }[/math] in Eqn. (eyring):
- [math]\displaystyle{ \eta =L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]
- or:
- [math]\displaystyle{ \frac{1}{\eta }=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}} }[/math]
Substituting for [math]\displaystyle{ \eta }[/math] into Eqn. (Eyrpdf):
- [math]\displaystyle{ 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 }}}} }[/math]
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