A Recursive Algorithm for Computing Joint Probabilities in a Bayesian Network, Illustrated by its Application to Safety Analysis of an Industrial Facility

Bayesian networks are direct acyclic graphs used to model and analyze dependencies between random events linked by cause-effect relationships. Among other applications, they provide a suitable tool for both qualitative and quantitative analysis of safety-related scenarios in industrial environments. The qualitative analysis consists in a detailed examination of the network structure. A top-down examination aims to predict potential consequences of hazard-triggering initial events. In turn, a bottom-up one allows for identifying possible root causes (initial events) of hazards, damages, accidents, etc. (secondary events). The purpose of the quantitative approach is to assess the chances of various scenarios. It inherently involves calculating conditional joint probabilities of several secondary events (effects) given the occurrence of particular initial events (causes). Apart from these "forward" probabilities, we may also need to compute the "backward" ones, which are the joint probabilities of possible causes given that particular effects occur. However, the computing time is likely to increase rapidly with the network size and complexity. This paper presents a novel method for computing the above probabilities in a reasonable time for networks of a small to medium width, employing a recursive formula. Here, the network width is defined as the maximum number of nodes in one layer, where the definition of a layer is given further in the paper. The presented method is illustrated with the safety model of a biogas production unit in a biogas plant.

Keywords: Bayes network, cause-effect relation, forward/reverse probability, extended CPT, recursive procedure.