Dynamic risk-informed verification prioritization for Complex Product Systems: A tri-metric approach using a Multi-State Hierarchical Bayesian Network

Complex Product Systems (CoPS) present unique challenges for Design Verification and Validation (V&V) due to tightly coupled, multi-disciplinary parameters and dynamic failure propagation. To address these challenges, this paper proposes a Multi-State Hierarchical Bayesian Network (MHBN) framework, coupled with a tri-metric approach — integrating the Degree of System Risk Reduction, Degree of System Performance Enhancement, and an Attribution Entropy measure. By reframing conventional failure mode analysis into hierarchical decomposition, fuzzy-driven probability modeling, and the formulation of a novel verification priority criterion, the method holistically captures interdependencies and uncertainties often overlooked by static approaches. In a case study on an automatic chemiluminescence immunoassay analyzer, empirical results and expert feedback revealed three key outcomes. First, the MHBN-based method distinguished mid-level components with clearer causal relationships as more cost-effective verification targets compared to top-level subsystems. Second, implementing the tri-metric guidance reduced total test hours by approximately 27% through strategic resource reallocation from high-entropy nodes to pivotal ones. Third, improved differentiation of critical priorities enabled early detection of design flaws — especially in the Pipette Mechanism — thus avoiding expensive rework. Overall, these findings underscore the value of integrating Bayesian inference with entropy concepts to support informed V&V decision-making in CoPS, offering a robust and adaptive alternative to conventional failure mode analysis.