Stochastic Failure Prognosability of Discrete Event Systems

Abstract

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. Finally, we compare the notion of stochastic prognosability with that of stochastic diagnosability, and show that the former is a stronger notion, as can be expected.