Sensor attacks compromise the reliability of cyber-physical systems (CPSs) by altering sensor outputs with the objective of leading the system to unsafe system states. This paper studies a probabilistic intrusion detection framework based on \(\lambda \) -sensor-attack detectability ( \(\lambda \) -sa), a formal measure that evaluates the likelihood of a system being under attack based on observed behaviors. Our framework enhances detection capabilities by using probabilistic information to detect attacks across the class of all complete, consistent, and successful sensor attack strategies, which enables the detection of sensor attacks that remain undetectable to current detection methodologies. We develop a polynomial-time algorithm that verifies \(\lambda \) -sa detectability by constructing a weighted verifier automaton and solving the shortest path problem. Additionally, we propose a method to determine the maximum detection confidence level ( \(\lambda \) *) achievable by the system, ensuring the highest probability of identifying attack-induced behaviors.
