Failure Detection Framework for Stochastic Discrete Event Systems With Guaranteed Error Bounds

This paper studies the online fault detection for stochastic discrete-event systems (DESs) under partial observability of events. Prior works have only studied the verification of the stochastic diagnosability (S-Diagnosability) property. To the best of our knowledge, this is a first paper that investigates the online detection schemes and also introduces the notions of their missed detections (MDs) and false alarms (FAs). Due to the probabilistic nature of the problem, MDs and FAs are possible even for S-Diagnosable systems, and we establish that S-Diagnosability is a necessary and sufficient condition for achieving any desired levels of MD and FA rates. We also provide a detection scheme, that can achieve the specified MD and FA rates, based on comparing a suitable detection statistic, that we define, with a suitable detection threshold, that we algorithmically compute. We also algorithmically compute the corresponding detection delay bound. The detection scheme also works for non-S-Diagnosable systems, with the difference that in this case there exists a lower bound for achievable MD rate, that increases as the FA rate requirement is made more stringent by decreasing it.