Safe diagnosis of pattern faults of stochastic discrete-event systems and verification algorithm

In many real-world applications, faults often result from specific events occurring in succession (i.e., pattern faults) rather than from a single failure event. This paper investigates the safe diagnosis of pattern faults in stochastic discrete-event systems (SDESs). First, the notions of S$$ S $$-type and T$$ T $$-type pattern safe diagnosability for SDESs are formalized. Roughly speaking, a stochastic automaton is called S$$ S $$-type (or T$$ T $$-type) pattern safe diagnosable if the detection of S$$ S $$-type (or T$$ T $$-type) pattern faults is achieved with high probability (i.e., the probability of not detecting pattern faults is sufficiently low) before the system performs risky actions. The necessary and sufficient conditions for the pattern safe diagnosability of SDESs are then presented after constructing a pattern safe diagnoser and recognizer of a forbidden language from a given stochastic system. Consequently, an algorithm for verifying the pattern safe diagnosability of SDESs is proposed, demonstrating how the pattern-safe diagnoser can be used for the safe diagnosis of pattern faults.