Template:WeibullDistribution: Difference between revisions

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-===The Weibull Distribution===
+#REDIRECT [[The Weibull Distribution]]
-The Weibull distribution is a general purpose reliability distribution used to model material strength, times-to-failure of electronic and mechanical components, equipment or systems. In its most general case, the three-parameter Weibull <math>pdf</math> is defined by:
-<br>
-::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>
-<br>
-with three parameters  <math>\beta </math> ,  <math>\eta </math>  and  <math>\gamma ,</math>  where  <math>\beta =</math>  shape parameter,  <math>\eta =</math>  scale parameter and location parameter.
-<br>
-If the location parameter,  <math>\gamma </math> , is assumed to be zero, the distribution then becomes the two-parameter Weibull or:
-::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}</math>
-One additional form is the one-parameter Weibull distribution, which assumes that the location parameter, <math>\gamma ,</math> is zero, and the shape parameter is a known constant, or <math>\beta =</math> constant <math>=C</math>, so:
-::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}
-</math>
-Chapter 6 of this reference fully details the Weibull distribution and presents many examples of its use in Weibull++.
-<br>
-{{weibull-bayesian distribution}}