Failure diagnosis in real time stochastic discrete event systems

Discrete Event System (DES) has been used for Failure Detection and Diagnosis (FDD) of a wide range of systems. For real time systems, timed DES based frameworks diagnose failures leading to violation of delays or deadlines. These schemes declare a failure to be diagnosable if it always i.e., in all timed-traces, results in timing violations within finite time of its occurrence. The basic assumption is, probability of any trace can be 1 or 0. So, even if there is a trace where failure is manifested, still its probability can be 0, leading to non-diagnosability. However in many systems this basic assumption may not hold. To address this issue, Thorsley et al. have augmented probability values to transitions and termed the framework as stochastic DES. Here, failure is diagnosable if there are traces where failure effect is manifested and probability of occurrence of those traces increase with time and cross a threshold. However, the scheme was for un-timed systems. In the present paper we propose a DES based FDD framework for stochastic timed systems. The scheme is illustrated with an example of a hydraulic punching machine.