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Note that this is not the same as the so called WeiBayes model. The 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 Bayesian-Weibull feature in Weibull++ is actually a true Bayesian 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.

This analysis method and its characteristics are presented in detail in Weibull-Bayesian Analysis.