In order to improve the efficiency of online diagnose of faults in discrete event system, from the viewpoint of the observable events judging occurrence of faults, this paper proposed a method called minimal observation sequences of faults. The finite state automaton was selected to model the discrete event system. First, a fault model of system was established in the offline, which was used to exclude the path independent of the system failure. Then, a minimal observation sequence model of faults was established according to the fault model. When the discrete event system is diagnosed online, it is necessary to compare the observations received by sensors with the model of minimal observation sequences. If any path in the model is found to satisfy the online observations, the fault in the termination state of the path will be described. Otherwise, no fault occurs. By comparing with the experiment results, the model of minimal observation sequences of faults can be used to determine the occurrence of faults as soon as possible. That is to say, the model for the system can find the faults timely and save the cost of online diagnosis.