A comparison of statistical approaches for assessing reliability

Reliability estimates are useful for making design decisions. We consider the case where a designer must choose between an existing component whose reliability is well-established and a new component that has an unknown reliability. This paper compares the statistical approaches for updating reliability assessments based on additional simulation or experimental data. We consider four statistical approaches for modelling the uncertainty about a new component's failure probability: a classical approach, a precise Bayesian approach, a robust Bayesian approach and an imprecise probability approach. We show that an imprecise beta model is compatible with both the robust Bayesian approach and the imprecise probability approach. The different approaches for forming and updating the designer's beliefs about the product reliability are illustrated and compared under different scenarios 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.