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The [math]\displaystyle{ pdf }[/math] of the 1-parameter exponential distribution is given by:
- [math]\displaystyle{ f(t)=\lambda \cdot {{e}^{-\lambda \cdot t}} }[/math]
It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by:
- [math]\displaystyle{ \lambda =\frac{1}{m} }[/math]
- thus:
- [math]\displaystyle{ f(t)=\frac{1}{m}\cdot {{e}^{-\tfrac{t}{m}}} }[/math]
The Eyring-exponential model [math]\displaystyle{ pdf }[/math] can then be obtained by setting [math]\displaystyle{ m=L(V) }[/math] in Eqn. (eyring):
- [math]\displaystyle{ m=L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]
and substituting for [math]\displaystyle{ m }[/math] in Eqn. (pdfexpm2):
- [math]\displaystyle{ f(t,V)=V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}{{e}^{-V\cdot {{e}^{\left( A-\tfrac{B}{V} \right)}}\cdot t}} }[/math]
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