Template:Lognormal distribution conditional reliability

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 }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{s-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}ds}{\int_{\text{ln}(T)}^{\infty }\tfrac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{s-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}ds} }[/math]

Once again, the use of standard normal tables is necessary to solve this equation, as no closed-form solution exists.