Template:Lognormal distribution reliable life: Difference between revisions

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::<math>{{R}_{T}}=\int_{\text{ln}(T)}^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{s-{\mu }'}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}ds</math>
::<math>{{R}_{t}}=\int_{\text{ln}(t)}^{\infty }\frac{1}{{{\sigma' }}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{s-{\mu }'}{{{\sigma' }}} \right)}^{2}}}}ds</math>


for <math>T</math> .
for <math>t</math> .

Revision as of 17:03, 13 February 2012

The Lognormal Reliable Life

As there is no closed-form solution for the lognormal reliability equation, no closed-form solution exists for the lognormal reliable life either. In order to determine this value, one must solve the equation:


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

for [math]\displaystyle{ t }[/math] .

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