Modified `practical Bayes-estimators´ [reliability theory]

This paper presents a new formulation of `practical Bayes-estimators´ (PBE) for the 2-parameter Weibull model when both parameters are unknown. Overcoming some limitations of the first formulation gave rise to this work, but the results are beyond this intent. These estimators are a tool to improve technical knowledge by using a few experimental data. In this case, the controversy about whether to use Bayes or classical methods is surmounted since estimators, like maximum likelihood, give estimates that often appear unlikely on the basis of technical knowledge of the engineers. A Monte Carlo study supports the following conclusions: if the shape parameter is greater than one, modified PBE maintain the good properties of practical Bayes estimators; otherwise the modified PBE are much better and do not suffer from the past limitation regarding the formulation of the prior interval on the shape parameter itself; and when there are very few data the modified PBE work as a filter that always improves (on average) the prior information if it is poor, or substantially confirms it if it is good. From this viewpoint, Bayes theorem allows statistics to help engineering and not vice versa