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| ==Eyring-Exponential==
| | #REDIRECT [[Eyring_Relationship#Eyring-Exponential]] |
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| <br>
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| The <math>pdf</math> of the 1-parameter exponential distribution is given by:
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| <br>
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| ::<math>f(t)=\lambda \cdot {{e}^{-\lambda \cdot t}}</math>
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| <br>
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| It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail [[Distributions used in Accelerated Testing#The Exponential Distribution|here]]) is given by:
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| <br>
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| ::<math>\lambda =\frac{1}{m}</math>
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| <br>
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| thus:
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| <br>
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| ::<math>f(t)=\frac{1}{m}\cdot {{e}^{-\tfrac{t}{m}}}</math>
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| <br>
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| The Eyring-exponential model <math>pdf</math> can then be obtained by setting <math>m=L(V)</math>:
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| ::<math>m=L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}</math>
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| <br>
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| and substituting for <math>m</math> in the exponential <math>pdf</math> equation:
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| <br>
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| ::<math>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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| <br>
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| {{eyring-ex stat prop sum}}
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| ===Parameter Estimation===
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| <br>
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| {{eyring-ex mle}}
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