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| ==Arrhenius-Exponential==
| | #REDIRECT [[Arrhenius_Relationship#Arrhenius-Exponential]] |
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| The <math>pdf</math> of the 1-parameter exponential distribution is given by:
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| ::<math>f(t)=\lambda {{e}^{-\lambda t}}</math>
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| It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by:
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| ::<math>\lambda =\frac{1}{m}</math>
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| thus:
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| ::<math>f(t)=\frac{1}{m}{{e}^{-\tfrac{t}{m}}}</math>
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| The Arrhenius-exponential model <math>pdf</math> can then be obtained by setting <math>m=L(V)</math> in Eqn. (arrhenius).
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| Therefore:
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| ::<math>m=L(V)=C{{e}^{\tfrac{B}{V}}}</math>
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| Substituting for <math>m</math> in Eqn. (pdfexpm) yields a <math>pdf</math> that is both a function of time and stress or:
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| ::<math>f(t,V)=\frac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot {{e}^{-\tfrac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot t}}</math>
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| {{aae stat prop sum}}
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| ===Parameter Estimation===
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| {{aae mle}}
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