Template:WeibullDistribution: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
(Redirected page to The Weibull Distribution)
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
=== 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 <span class="texhtml">''p''''d''''f''</span> 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 <span class="texhtml">β</span> , <span class="texhtml">η</span> and <span class="texhtml">γ,</span> where <span class="texhtml">β = </span>shape parameter, <span class="texhtml">η = </span>scale parameter and γ =&nbsp;location parameter. <br>If the location parameter, <span class="texhtml">γ</span> , is assumed to be zero, then the&nbsp;distribution&nbsp;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, <span class="texhtml">γ,</span> is zero, and the shape parameter is a known constant, or <span class="texhtml">β = </span>constant <span class="texhtml">= ''C''</span>, so:
 
::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}
</math>
 
The Weibull distribution and its characteristics are presented in detail in [[The Weibull Distribution]].
 
<br>{{weibull-bayesian distribution}}

Latest revision as of 10:12, 9 August 2012

Redirect to:

Retrieved from "https://www.reliawiki.com/index.php?title=Template:WeibullDistribution&oldid=30823"