Online prognosis of stochastic discrete event systems with guaranteed performance bound

In this paper, we consider the online prognosis of stochastic discrete event systems. Even though it is easy to predict the occurrence of faults in advance accurately for a prognosable discrete event system, it is much more difficult to do so for systems that are not prognosable. In this paper, we solve the online prognosis problem in a stochastic discrete event system framework. Our idea is to calculate the probability of the occurrence of faults in the future when a no-fault observable string is observed. We say an observable string is no-fault if no faults have occurred when it is observed. We then compare the probability with a pre-set threshold to decide whether to issue an alert or not. We develop a method to calculate the lower bound for possible thresholds, which has the fewest false alerts and no missed alerts of faults. For a given threshold, we use the rate of missed fault alerts and the rate of false fault alerts to evaluate the performance of fault prognosis. We formally define these two rates and develop algorithms to calculate them. These results can guide us in choosing a proper threshold to achieve the best trade-off between false fault alerts and missed alerts of faults.