Template:Weibull reliability function: Difference between revisions
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=== The Weibull Reliability Function === | === The Weibull Reliability Function === | ||
The equation for the | The equation for the 3-parameter Weibull cumulative density function, ''cdf'', is given by: | ||
::<math> F(t)=1-e^{-\left( \frac{t-\gamma }{\eta }\right) ^{\beta }} </math>. | ::<math> F(t)=1-e^{-\left( \frac{t-\gamma }{\eta }\right) ^{\beta }} </math>. | ||
This is also referred to as '' | This is also referred to as ''unreliability'' and designated as <math> Q(t) \,\!</math> by some authors. | ||
Recalling that the reliability function of a distribution is simply one minus the cdf, the reliability function for the | Recalling that the reliability function of a distribution is simply one minus the ''cdf'', the reliability function for the 3-parameter Weibull distribution is then given by: | ||
::<math> R(t)=e^{-\left( { \frac{t-\gamma }{\eta }}\right) ^{\beta }} </math> | ::<math> R(t)=e^{-\left( { \frac{t-\gamma }{\eta }}\right) ^{\beta }} </math> | ||
Revision as of 22:51, 24 April 2012
The Weibull Reliability Function
The equation for the 3-parameter Weibull cumulative density function, cdf, is given by:
- [math]\displaystyle{ F(t)=1-e^{-\left( \frac{t-\gamma }{\eta }\right) ^{\beta }} }[/math].
This is also referred to as unreliability and designated as [math]\displaystyle{ Q(t) \,\! }[/math] by some authors.
Recalling that the reliability function of a distribution is simply one minus the cdf, the reliability function for the 3-parameter Weibull distribution is then given by:
- [math]\displaystyle{ R(t)=e^{-\left( { \frac{t-\gamma }{\eta }}\right) ^{\beta }} }[/math]