Template:Weibull-bayesian distribution

The Weibull-Bayesian Distribution

Another approach is the Weibull-Bayesian model which assumes that the analyst has some prior knowledge about the distribution of the shape parameter ( [math]\displaystyle{ \beta ) }[/math] of the Weibull distribution. There are many practical applications for this model, particularly when dealing with small sample sizes and/or some prior knowledge for the shape parameter is available. For example, when a test is performed, there is often a good understanding about the behavior of the failure mode under investigation, primarily through historical data or physics-of-failure.
Note that this is not the same as the so called WeiBayes model. The so called WeiBayes model is really a one-parameter Weibull distribution. It assumes a fixed value (constant) for the shape parameter and solves for the scale parameter. The Weibull-Bayesian model in Weibull++ 7 is actually a true WeiBayes model and offers an alternative to the one-parameter Weibull by including the variation and uncertainty that is present in the prior estimation of the shape parameter.
The Weibull-Bayesian distribution and its characteristics are presented in more detail in the Weibull-Bayesian Analysis section in Chapter 8.