In this paper we extend a previously developed coding-based methodology for monitoring faults in discrete event systems that are described by Petri nets. We present a systematic design that enables us to non-concurrently detect and identify a maximum of 2k-1 transition faults and a maximum of k place faults that may occur at various instants during the operation of the system. Using an encoded Petri net model with 2k redundant places (and the connections and tokens associated with them) the worst-case complexity of the detection and identification procedure is O(k/sup 2/(m+n)), where n and m are respectively the number of places and transitions in the given Petri net model. The proposed fault detection and identification approach does not need to explicitly track or reconstruct the system state evolution and is well-suited for non-concurrent diagnosis.