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

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The  <math>pdf</math>  of the lognormal distribution is given by:  
The  <math>pdf</math>  of the lognormal distribution is given by:  
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<br>
<math>f(T)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
<math>f(T)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
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where:  
where:  
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<math>{T}'=\ln (T)</math>
<math>{T}'=\ln (T)</math>
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<math>T=\text{times-to-failure}</math>
<math>T=\text{times-to-failure}</math>
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<br>
and:
and:
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• <math>{{\sigma }_{{{T}'}}}=</math> standard deviation of the natural logarithms of the times-to-failure.
• <math>{{\sigma }_{{{T}'}}}=</math> standard deviation of the natural logarithms of the times-to-failure.
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| align="center" valign="middle" | [http://reliawiki.com/index.php/Template:T-h_lognormal T-H Lognormal]
| valign="middle" | [http://reliawiki.com/index.php/Template:T-h_lognormal T-H Lognormal]
 
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Revision as of 22:03, 10 February 2012

Webnotes-alta.png

Reliability Web Notes

Standard Folio Data TH-Lognormal
ALTA

The [math]\displaystyle{ pdf }[/math] of the lognormal distribution is given by:
[math]\displaystyle{ f(T)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}} }[/math]
where:
[math]\displaystyle{ {T}'=\ln (T) }[/math]
[math]\displaystyle{ T=\text{times-to-failure} }[/math]
and:
• [math]\displaystyle{ \overline{{{T}'}}= }[/math] mean of the natural logarithms of the times-to-failure.

• [math]\displaystyle{ {{\sigma }_{{{T}'}}}= }[/math] standard deviation of the natural logarithms of the times-to-failure.

T-H Lognormal


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