ALTA ALTA Standard Folio Data Arrhenius-Exponential: Difference between revisions
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The <math>pdf</math> of the 1-parameter exponential distribution is given by: | The <math>pdf</math> of the 1-parameter exponential distribution is given by: | ||
<br> | <br> | ||
<math>f(t)=\lambda {{e}^{-\lambda t}}</math> | <math>f(t)=\lambda {{e}^{-\lambda t}}</math> | ||
<br> | <br> | ||
It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by: | It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail in Chapter 5) is given by: | ||
<br> | <br> | ||
<math>\lambda =\frac{1}{m}</math> | <math>\lambda =\frac{1}{m}</math> | ||
<br> | <br> | ||
thus: | thus: | ||
<br> | <br> | ||
<math>f(t)=\frac{1}{m}{{e}^{-\tfrac{t}{m}}}</math> | <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). | 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: | Therefore: | ||
<br> | <br> | ||
<math>m=L(V)=C{{e}^{\tfrac{B}{V}}}</math> | <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: | Substituting for <math>m</math> in Eqn. (pdfexpm) yields a <math>pdf</math> that is both a function of time and stress or: | ||
<br> | <br> | ||
<math>f(t,V)=\frac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot {{e}^{-\tfrac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot t}}</math> | <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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Revision as of 21:46, 10 February 2012
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Reliability Web Notes |
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| Standard Folio Data Arrhenius-Exponential |
| ALTA |
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The [math]\displaystyle{ pdf }[/math] of the 1-parameter exponential distribution is given by:
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