Reliability-Based Decision Making: A Comparison of Statistical Approaches

This paper considers the problem of choosing between an existing component whose reliability is well established and a new component that has an unknown reliability. In some scenarios, the designer may have some initial beliefs about the new component’s reliability. The designer may also have the opportunity to obtain more information and to update these beliefs. Then, based on these updated beliefs, the designer must make a decision between the two components. This paper examines the statistical approaches for updating reliability assessments and the decision policy that the designer uses. We consider four statistical approaches for modeling the uncertainty about the new component and updating assessments of its reliability: a classical approach, a precise Bayesian approach, a robust Bayesian approach, and an imprecise probability approach. The paper investigates the impact of different approaches on the decision between the components and compares them. In particular, given that the test results are random, the paper considers the likelihood of making a correct decision with each statistical approach under different scenarios of available information and true reliability. In this way, the emphasis is on practical comparisons of the policies rather than on philosophical arguments. AMS Subject Classification: 62F10, 62F15, and 62F35