Online failure diagnosis of stochastic discrete event systems

This paper deals with the detection of (permanent) fault in the setting of 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), and we establish that S-Diagnosability is a necessary and sufficient condition for achieving any desired levels of MD and FA rates. Next we 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 only any FA rate can be met, and there exists a minimum MD rate that increases as FA rate is decreased.