Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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weibull_uncertain


Aleatory uncertain variable - Weibull

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): INTEGER

Default: no weibull uncertain variables

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required alphas First parameter of the Weibull distribution
Required betas Second parameter of the Weibull distribution
Optional initial_point

Initial values

Optional descriptors

Labels for the variables

Description

The Weibull distribution is also referred to as the Type III Smallest Extreme Value distribution. The Weibull distribution is commonly used in reliability studies to predict the lifetime of a device. It is also used to model capacity variables such as material strength.

The density function for the Weibull distribution is given by:

\[f(x) = \frac{\alpha}{\beta} \left(\frac{x}{\beta}\right)^{\alpha-1} e^{-\left(\frac{x}{\beta}\right)^{\alpha}}\]

where $\mu_W = \beta \Gamma(1+\frac{1}{\alpha})$ and $\sigma_W = \sqrt{\frac{\Gamma(1+\frac{2}{\alpha})}{\Gamma^2(1+\frac{1}{\alpha})} - 1} \mu_W$