|
|
| (2 intermediate revisions by one other user not shown) |
| Line 1: |
Line 1: |
| ==Normal Statistical Properties==
| | #REDIRECT [[The_Normal_Distribution]] |
| | |
| {{normal mean median and mode}}
| |
| | |
| {{normal standard deviation}}
| |
| | |
| {{normal reliability function}}
| |
| | |
| {{normal conditional reliability function}}
| |
| | |
| ===The Normal Reliable Life===
| |
| | |
| Since there is no closed-form solution for the normal reliability function, there will also be no closed-form solution for the normal reliable life. To determine the normal reliable life, one must solve:
| |
| | |
| ::<math>R(T)=\int_{T}^{\infty }\frac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\mu }{{{\sigma }_{T}}} \right)}^{2}}}}dt</math>
| |
| ::for <math>T</math> .
| |
| | |
| ===The Normal Failure Rate Function===
| |
| | |
| The instantaneous normal failure rate is given by:
| |
| | |
| ::<math>\lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{T-\mu }{{{\sigma }_{T}}} \right)}^{2}}}}}{\int_{T}^{\infty }\tfrac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\mu }{{{\sigma }_{T}}} \right)}^{2}}}}dt}</math>
| |