Characterizing a confidence space for discrete event timings for fault monitoring using discrete sensing and actuation signals

Many manufacturing systems are controlled using discrete sensors and actuators. The changes in values of the corresponding control I/O signals are events. The timing and sequencing relationships of these events can be used to determine whether a system is operating as expected, or whether a fault may have occurred. We present a method of learning intervened timing relationships using observations from a correctly operating system. The sample statistics of the observation characteristic of correct system operation are used to create a confidence space of possible timing relationships of the underlying system. Any timing relationship used as a specification of correct observation for fault monitoring will result in some level of false alarms and missed detections among all the possible relationships in the confidence space; the timing relationships can be chosen to minimize the worst case total of the false alarm and missed detection costs over the confidence space. Simulations are used to evaluate the performance of the chosen timing relationship over a range of perturbed systems