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| === The Weibull Distribution ===
| | #REDIRECT [[The Weibull Distribution]] |
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| 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>
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| ::<math>f(t)=\frac{\beta}{\eta } \left( \frac{t-\gamma }{\eta } \right)^{\beta -1}{e}^{-(\tfrac{t-\gamma }{\eta }) ^{\beta}}</math>
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| <br>
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| 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 = location parameter. <br>If the location parameter, <span class="texhtml">γ</span> , is assumed to be zero, then the distribution becomes the two-parameter Weibull or:
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| ::<math>f(t)=\frac{\beta}{\eta }( \frac{t }{\eta } )^{\beta -1}{e}^{-(\tfrac{t }{\eta }) ^{\beta}}</math>
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| 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:
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| ::<math>f(t)=\frac{C}{\eta}(\frac{t}{\eta})^{C-1}e^{-(\frac{t}{\eta})^C}
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| </math>
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| The chapter [[The Weibull Distribution]] of this reference fully details the Weibull distribution and presents many examples of its use in Weibull++.
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| <br>{{weibull-bayesian distribution}}
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