Development of Maximum-Vulnerability Diagrams for Barrier-Based Safety Systems: Quantifying and Visualizing Operational Risk Exposure

Barrier-based safety systems are fundamental to preventing accidents in high-hazard industrial operations. However, traditional Hazard Identification (HAZID) and risk screening frameworks aggregate safety safeguards at a macro-hazard level, creating a systemic blind spot that masks threat-specific vulnerabilities and single points of failure. To address this gap, this study develops ‘Maximum-Vulnerability Diagrams’ (MVD), a network-based modeling approach that maps and quantifies threat–barrier pathways using matrix algebra and conditional probability. Validated across empirical cases of working-at-height (H-06.01) and heavy rotary equipment (H-08.01) operations in the oil extraction industry, the MVD successfully isolates high-criticality, zero-redundancy pathways. We mathematically establish that multiplexed defenses require a target individual efficiency of η ≥ 95% to reliably suppress system failure probability below a strict 5% operational threshold. The findings demonstrate that aggregate safeguard volume is a deceptive safety metric, and that systemic resilience depends entirely on network architecture. This framework transitions risk governance from passive compliance checking to predictive, threat-driven barrier management, offering an actionable methodology to optimize safety resources before accidents occur.