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(Created page with '====Arrhenius-Lognormal Reliability Function==== <br> The reliability for a mission of time <math>T</math> , starting at age 0, for the Arrhenius-lognormal model is determined b…') |
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The reliability for a mission of time <math>T</math> , starting at age 0, for the Arrhenius-lognormal model is determined by: | The reliability for a mission of time <math>T</math> , starting at age 0, for the Arrhenius-lognormal model is determined by: | ||
<br> | <br> | ||
::<math>R(T,V)=\ | ::<math>R(T,V)=\int_{T}^{\infty }f(t,V)dt</math> | ||
vor: | vor: | ||
<br> | <br> | ||
::<math>R(T,V)=\ | ::<math>R(T,V)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\ln (C)-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math> | ||
<br> | <br> | ||
There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables. Since the application automatically solves for the reliability, we will not discuss manual solution methods. | There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables. Since the application automatically solves for the reliability, we will not discuss manual solution methods. | ||
<br> | <br> | ||
Revision as of 00:15, 14 February 2012
Arrhenius-Lognormal Reliability Function
The reliability for a mission of time [math]\displaystyle{ T }[/math] , starting at age 0, for the Arrhenius-lognormal model is determined by:
- [math]\displaystyle{ R(T,V)=\int_{T}^{\infty }f(t,V)dt }[/math]
vor:
- [math]\displaystyle{ R(T,V)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\ln (C)-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt }[/math]
There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables. Since the application automatically solves for the reliability, we will not discuss manual solution methods.