The performance of a product that is being designed is affected by variations in material, manufacturing process, use, and environmental variables. As a consequence of uncertainties in these factors, some items may fail. Failure is taken very generally, but we assume that it is a random event that occurs at most once in the lifetime of an item. The designer wants the probability of failure to be less than a given threshold. In this paper, we consider three approaches for modeling the uncertainty in whether or not the failure probability meets this threshold: a classical approach, a precise Bayesian approach, and a robust Bayesian (or imprecise probability) approach. In some scenarios, the designer may have some initial beliefs about the failure probability. The designer also has the opportunity to obtain more information about product performance (e.g. from either experiments with actual items or runs of a simulation program that provides an acceptable surrogate for actual performance). The different approaches for forming and updating the designer’s beliefs about the failure probability are illustrated and compared under different assumptions of available information. The goal is to gain insight into the relative strengths and weaknesses of the approaches. Examples are presented for illustrating the conclusions.

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