Template:Lognormal distribution conditional reliability: Difference between revisions
Jump to navigation
Jump to search
| Line 2: | Line 2: | ||
The lognormal conditional reliability function is given by: | The lognormal conditional reliability function is given by: | ||
::<math>R(t|T)=\frac{R(T+t)}{R(T)}=\frac{\int_{\text{ln}(T+t)}^{\infty }\tfrac{1}{{{\sigma | ::<math>R(t|T)=\frac{R(T+t)}{R(T)}=\frac{\int_{\text{ln}(T+t)}^{\infty }\tfrac{1}{{{\sigma' }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{x-{\mu }'}{{{\sigma' }}} \right)}^{2}}}}ds}{\int_{\text{ln}(T)}^{\infty }\tfrac{1}{{{\sigma' }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{x-{\mu }'}{{{\sigma' }}} \right)}^{2}}}}dx}</math> | ||
Once again, the use of standard normal tables is necessary to solve this equation, as no closed-form solution exists. | Once again, the use of standard normal tables is necessary to solve this equation, as no closed-form solution exists. | ||
Revision as of 16:58, 13 February 2012
The Lognormal Conditional Reliability
The lognormal conditional reliability function is given by:
- [math]\displaystyle{ R(t|T)=\frac{R(T+t)}{R(T)}=\frac{\int_{\text{ln}(T+t)}^{\infty }\tfrac{1}{{{\sigma' }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{x-{\mu }'}{{{\sigma' }}} \right)}^{2}}}}ds}{\int_{\text{ln}(T)}^{\infty }\tfrac{1}{{{\sigma' }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{x-{\mu }'}{{{\sigma' }}} \right)}^{2}}}}dx} }[/math]
Once again, the use of standard normal tables is necessary to solve this equation, as no closed-form solution exists.