Failure Prognosability of Stochastic Discrete Event Systems

We study the prognosis of fault, i.e., its prediction prior to its occurrence, in stochastic discrete event systems. We introduce the notion of m-steps Stochastic-Prognosability, called S-m-Prognosability, which allows the prediction of a fault at least m-steps in advance. We formalize the notion of a prognoser and also show that S-m-Prognosability is necessary and sufficient for the existence of a prognoser that can predict a fault at least m steps prior to occurrence, while achieving any arbitrary false alarm and missed detection rates. We also provide a polynomial algorithm for the verification of S-m-Prognosability.