Template:Alta al rf: Difference between revisions
Jump to navigation
Jump to search
| Line 2: | Line 2: | ||
<br> | <br> | ||
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)=\int_{T}^{\infty }f(t,V)dt</math> | ::<math>R(T,V)=\int_{T}^{\infty }f(t,V)dt</math> | ||
or: | |||
<br> | <br> | ||
::<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> | ::<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 23:38, 27 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]
or:
- [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.