This paper studies the failure diagnosis of discrete-time stochastic systems with linear-time temporal logic (LTL) as correctness requirement—A fault is a violation of the LTL specification. The detection problem is first reduced to stochastic reachability estimation problem for an input-output stochastic hybrid automaton (I/O-SHA) introduced in this paper, based on which the likelihood of no-fault is recursively computed for issuing a detection decision. The performance of the detection scheme is measured in terms of false alarm (FA) and missed detection (MD) rates, and the condition for the existence of a detector to achieve any desired rates of FA and MD is captured in form of Stochastic-Diagnosability. The proposed method of fault detection is illustrated by a practical example.
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