The failure of Bayes system reliability inference based on data with multi-level applicability

When test or operation-experience data are used that apply at once to two or more system-levels, Bayes reliability inferences at different levels generally give inconsistent results. This inconsistency, quite counter-intuitive when it is first recognized, is particularly important in major analyses of occurrence rates of failures and consequent hazards in space and missile launches. It arises as the lack of perfect aggregation in other applications, as well. Others might consider this inconsistency merely a modeling error, and then attempt, with negligible success, to find means for ameliorating it. The author believes it represents a fundamental breakdown in the usual Bayes methodology in the circumstances noted. A basic restructuring of the Bayes procedure is required (e.g. by exchanging the roles of engineering and experience data). The author gives an illustrative example