Template:Lognormal distribution mean: Difference between revisions
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===The Mean or MTTF=== | ===The Mean or MTTF=== | ||
The mean of the lognormal distribution, <math>\mu </math> , is given by [18]: | The mean of the lognormal distribution, <math>\mu </math> , is given by [[Appendix: Weibull References|[18]]]: | ||
::<math>\mu ={{e}^{{\mu }'+\tfrac{1}{2}\sigma | ::<math>\mu ={{e}^{{\mu }'+\tfrac{1}{2}\sigma'^{2}}}</math> | ||
The mean of the natural logarithms of the times-to-failure, <math>\mu'</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma | The mean of the natural logarithms of the times-to-failure, <math>\mu'</math> , in terms of <math>\bar{T}</math> and <math>{{\sigma }}</math> is givgen by: | ||
::<math>{\mu }'=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma | ::<math>{\mu }'=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right)</math> | ||
Revision as of 16:41, 13 February 2012
The Mean or MTTF
The mean of the lognormal distribution, [math]\displaystyle{ \mu }[/math] , is given by [18]:
- [math]\displaystyle{ \mu ={{e}^{{\mu }'+\tfrac{1}{2}\sigma'^{2}}} }[/math]
The mean of the natural logarithms of the times-to-failure, [math]\displaystyle{ \mu' }[/math] , in terms of [math]\displaystyle{ \bar{T} }[/math] and [math]\displaystyle{ {{\sigma }} }[/math] is givgen by:
- [math]\displaystyle{ {\mu }'=\ln \left( {\bar{T}} \right)-\frac{1}{2}\ln \left( \frac{\sigma^{2}}{{{{\bar{T}}}^{2}}}+1 \right) }[/math]