Aggregation error in Bayesian analysis of reliability systems

Perfect aggregation in Bayesian system reliability analysis has been shown to be extremely unlikely. In other words, aggregation error is almost inevitable. Consequently, analysts have to deal with the following dielmma: on one hand, an aggregate analysis (i.e., an analysis at the system level), while relatively inexpensive, may be misleading. On the other hand, a disaggregate analysis (i.e., at the component level) provides more accurate results, but may be costly and impractical. Therefore, simple techniques to estimate the size of aggregation error are necessary to help analysts choose the most appropriate level of detail for an analysis. In this paper, reasonable bounds on the aggregation error are derived for a variety of reliability models. In particular, these bounds will never be more than twice the actual error. Tools to compute these bounds (and in some cases the actual error) are also provided.