Dakota Reference Manual: weibull_uncertain

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weibull_uncertain

Aleatory uncertain variable - Weibull

## Topics

This keyword is related to the topics:

- continuous_variables
- aleatory_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: no weibull uncertain variables

Child Keywords:

| 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 for variables
| 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:

and