Template:Lognormal distribution reliability function

The Lognormal Reliability Function

The reliability for a mission of time [math]\displaystyle{ t }[/math] , starting at age 0, for the lognormal distribution is determined by:

[math]\displaystyle{ R(t)=\int_{t}^{\infty }f(x)dx }[/math]

or:

[math]\displaystyle{ {{R}({t})}=\int_{\text{ln}(t)}^{\infty }\frac{1}{{{\sigma' }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{x-{\mu }'}{{{\sigma' }}} \right)}^{2}}}}dx }[/math]

As with the normal distribution, there is no closed-form solution for the lognormal 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.