ON THE CONCEPT OF PERFECT AGGREGATION IN BAYESIAN-ESTIMATION

Perfect aggregation is here defined as consistency between the results of aggregate (i.e. system-level) and disaggregate (i.e. component-level) reliability analyses of the same system using Bayesian estimation. This paper identifies necessary and sufficient conditions for perfect aggregation in simple two-component systems, and discusses the implications of these results for more complex systems. Unfortunately, we show that even in systems with only two components, perfect aggregation is achieved only in very rare special cases, which will generally not be obtained in practice. Therefore, tools are needed to estimate the magnitude of aggregation error when perfect aggregation is not achieved.