Failure Boundary Detection: Admissibility Limits in Engineering System Stability

Engineering systems operate within defined limits determined by structural capacity, material behaviour, and operational constraints. Detecting when systems approach these limits is critical for maintaining safety and preventing catastrophic failure. This paper interprets failure boundary detection within the Paton System framework as the identification of admissibility thresholds governing the persistence of engineered systems. Systems remain stable while operational behaviour remains compatible with structural and functional constraints. When system behaviour approaches admissibility boundaries, instability risk increases. Detecting these boundaries allows engineers to intervene before structural or operational collapse occurs. Understanding failure boundary detection through admissibility provides a structural interpretation of engineering safety and reliability.