Top-down versus bottom-up processing of influence diagrams in probabilistic analysis

Recent work by Phillips et al and Selby et al has shown that influence diagram methodology can be a useful analytical tool in reactor safety studies. In some instances, an influence diagram can be used as a graphical representation of probabilistic dependence within a system or event sequence. Under these circumstances, Bayesian statistics is employed to transform the relationships depicted in the influence diagram into the correct expression for a desired marginal probability (e.g., the top node). In the references cited above, the authors demonstrated the usefulness of influence diagrams for assessing the reliability of operator performance during pressurized thermal shock transients. In addition, the use of influence diagrams identified the critical variables that had the greatest impact on operator reliability for a particular scenario (e.g., control room design, procedures, etc.). Top-down and bottom-up algorithms have emerged as the dominant methods for quantifying influence diagrams. The purpose of this paper is to demonstrate a potential error in employing the bottom-up algorithm when dealing with interdependencies.