The WeiBayes distribution is a special case of the Weibull distribution. It requires only one parameter, characteristic life, because the second Weibull parameter, the shape factor (β), is already known from prior knowledge. Related to Bayesian analysis, the WeiBayes distribution is a powerful method that was developed to solve the problems that occur when traditional Weibull analysis has large uncertainties. The WeiBayes distribution is more accurate than two-parameter Weibull distributions when the sample has fewer than 10 failures. Additionally, it is the only distribution that can be used when there are 0 failures.

For example, after a design change corrects an existing failure mode, success data from tests can be used to determine a lower confidence bound for the Weibull line for the new design called a WeiBayes line. When parts exceed their design life, a Weibull analysis with no failures can be constructed to extend their life. Because the WeiBayes distribution can be used without the requirement of testing to failure, it is of extreme importance in situations where failures involve safety or extreme costs.