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

Revision as of 18:16, 16 January 2012

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.
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-::<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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-::<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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 •	 <math>\overline{{{T}'}}=</math> mean 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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