Deriving Universal Mathematical Expressions for Identifying Minimal Cut Sets in Complex Series-Parallel Networks

This study examines the role of minimum cut sets (MCSs) as a fundamental tool for reliability modeling and performance evaluation in complex series- parallel (CSP) systems. Our aim was to systematically extract MCS across both system and subsystem levels, reducing complexity while preserving accuracy. We developed advanced mathematical models and an efficient algorithm, supported by equations derived with precision. Our findings offer new insights into MCS dynamics within intricate configurations, validated through comparisons with existing studies. These findings enhance theoretical frameworks in network reliability and improve practical efficiency in fields like communications and logistics. The work highlights key implications for system design and calls for further refinement of MCS extraction techniques, advancing network analysis and performance.