Probabilistic Reliability Analysis of Complex Engineering Systems under Uncertainty using Bayesian Networks

The reliability assessment of complex engineering systems is increasingly challenged by the intricate interdependencies between components and the pervasive presence of uncertainty. Traditional probabilistic risk assessment methods, such as Fault Tree Analysis and Event Tree Analysis, often struggle to accommodate multi-state variables, common cause failures, and the dynamic updating of probabilities based on new evidence. This paper presents a comprehensive framework for utilizing Bayesian Networks (BNs) to model and analyze the reliability of complex systems under significant uncertainty. We explore the theoretical underpinnings of BNs as adirected acyclic graph formalism that encodes probabilistic dependencies among system variables. Furthermore, the study details the methodology for constructing network structures from physical system topologies and quantifying conditional probability tables using a hybrid of historical failure data and expert elicitation. Through a detailed analysis of a hypothetical complex mechanical assembly, we demonstrate the superiority of the Bayesian approach in handling both aleatory and epistemic uncertainties. The results indicate that Bayesian Networks provide a robust platform for diagnostic reasoning, predictive analysis, and decision-making in maintenance planning, offering a dynamic alternative to static reliability models.