A discretization procedure for rare events in Bayesian networks

• Discretization of basic random variables in a reliability problem for discrete BNs.
• Efficient discretization through optimization based on FORM approximations.
• Development of a heuristic for efficient discretization.
• Application to two verification examples and one from the field of civil aviation.
• Procedure implemented in a Matlab code (available as a supplement to the paper).

Discrete Bayesian networks (BNs) can be effective for risk- and reliability assessments, in which probability estimates of (rare) failure events are frequently updated with new information. To solve such reliability problems accurately in BNs, the discretization of continuous random variables must be performed carefully. To this end, we develop an efficient discretization scheme, which is based on finding an optimal discretization for the linear approximation of the reliability problem obtained from the First-Order Reliability Method (FORM). Because the probability estimate should be accurate under all possible future information scenarios, the discretization scheme is optimized with respected to the expected posterior error. To simplify application of the method, we establish parametric formulations for efficient discretization of random variables in BNs for reliability problems based on numerical investigations. The procedure is implemented into a software prototype. Finally, it is applied to a verification example and an application example, the prediction of runway overrun of a landing aircraft.