Template:Normal reliability function: Difference between revisions
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(Created page with '===The Normal Reliability Function=== The reliability for a mission of time <math>T</math> for the normal distribution is determined by: ::<math>R(T)=\int_{T}^{\infty }f(t)dt=…') |
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The reliability for a mission of time <math>T</math> for the normal distribution is determined by: | The reliability for a mission of time <math>T</math> for the normal distribution is determined by: | ||
::<math>R(T)=\int_{T}^{\infty }f(t)dt=\int_{T}^{\infty }\frac{1}{{{\sigma | ::<math>R(T)=\int_{T}^{\infty }f(t)dt=\int_{T}^{\infty }\frac{1}{{{\sigma }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\mu }{{{\sigma }}} \right)}^{2}}}}dt</math> | ||
There is no closed-form solution for the normal 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. For interested readers, full explanations can be found in the references. | There is no closed-form solution for the normal 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. For interested readers, full explanations can be found in the references. | ||
Revision as of 17:59, 10 February 2012
The Normal Reliability Function
The reliability for a mission of time [math]\displaystyle{ T }[/math] for the normal distribution is determined by:
- [math]\displaystyle{ R(T)=\int_{T}^{\infty }f(t)dt=\int_{T}^{\infty }\frac{1}{{{\sigma }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\mu }{{{\sigma }}} \right)}^{2}}}}dt }[/math]
There is no closed-form solution for the normal 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. For interested readers, full explanations can be found in the references.