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====Reliability Function==== | ====Reliability Function==== | ||
For the lognormal distribution, the reliability for a mission of time <math>T</math> , starting at age 0, is given by: | For the lognormal distribution, the reliability for a mission of time <math>T</math>, starting at age 0, is given by: | ||
<br> | <br> | ||
::<math>R(T)=\int_{T}^{\infty }f(t)dt</math> | ::<math>R(T)=\int_{T}^{\infty }f(t)dt</math> | ||
or: | or: | ||
::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt</math> | ::<math>R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\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. | There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables. | ||
<br> | <br> | ||
Revision as of 16:55, 7 March 2012
Reliability Function
For the lognormal distribution, the reliability for a mission of time [math]\displaystyle{ T }[/math], starting at age 0, is given by:
- [math]\displaystyle{ R(T)=\int_{T}^{\infty }f(t)dt }[/math]
or:
- [math]\displaystyle{ R(T)=\int_{{{T}^{^{\prime }}}}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\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.