Template:Eyring-log rf: Difference between revisions
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::<math>R(T,V)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t+\ln (V)+A-\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 (V)+A-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math> | ||
Revision as of 23:53, 27 February 2012
Eyring-Lognormal Reliability Function
The reliability for a mission of time [math]\displaystyle{ T }[/math] , starting at age 0, for the Eyring-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 (V)+A-\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.