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Arrhenius-Exponential
The $$pdf$$  of the 1-parameter exponential distribution is given by:


 * $$f(t)=\lambda {{e}^{-\lambda t}}$$

It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by:


 * $$\lambda =\frac{1}{m}$$

thus:


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

The Arrhenius-exponential model $$pdf$$  can then be obtained by setting  $$m=L(V)$$  in Eqn. (arrhenius). Therefore:


 * $$m=L(V)=C{{e}^{\tfrac{B}{V}}}$$

Substituting for $$m$$  in Eqn. (pdfexpm) yields a $$pdf$$  that is both a function of time and stress or:


 * $$f(t,V)=\frac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot {{e}^{-\tfrac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot t}}$$