ALTA ALTA Standard Folio Data TNT-Lognormal: Difference between revisions

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The T-NT lognormal model <math>pdf</math> can be obtained first by setting <math>\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{T}=L(V)</math>  
The T-NT lognormal model <math>pdf</math> can be obtained first by setting <math>\overline{T}=L(V)</math>  
in Eqn. (Temp-Volt).  
in Eqn. (Temp-Volt).  
<br>
<br>

Revision as of 18:34, 16 January 2012

Reliability Web Notes

Standard Folio Data TNT-Lognormal
ALTA

The T-NT lognormal model [math]\displaystyle{ pdf }[/math] can be obtained first by setting [math]\displaystyle{ \overline{T}=L(V) }[/math] in Eqn. (Temp-Volt).
Therefore:


[math]\displaystyle{ \breve{T}=L(V)=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}} }[/math]


or:


[math]\displaystyle{ {{e}^{{{\overline{T}}^{\prime }}}}=\frac{C}{{{U}^{n}}}{{e}^{\tfrac{B}{V}}} }[/math]


Thus:


[math]\displaystyle{ {{\overline{T}}^{\prime }}=\ln (C)-n\ln (U)+\frac{B}{V} }[/math]


Substituting Eqn.(TV-logn-mean)into Eqn. (TV-logn-pdf) yields the T-NT lognormal model [math]\displaystyle{ pdf }[/math] or:


[math]\displaystyle{ f(T,U,V)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\ln (C)+n\ln (U)-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}} }[/math]

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