Discrete Event Dyn Syst (2009) 19:167–187 DOI 10.1007/s10626-008-0056-1 Event Counting of Partially-Observed Discrete-Event Systems with Uniformly and Nonuniformly Bounded Diagnosis Delays Tae-Sic Yoo · Humberto E. Garcia Received: 29 March 2007 / Accepted: 20 October 2008 / Published online: 14 November 2008 © Springer Science + Business Media, LLC 2008 Abstract We present an approach dealing with repeated fault events in the frame- work of model-based monitoring of discrete-event systems (DES). Various notions of diagnosability reported in the literature deal with uniformly bounded finite detection of counting delays over all faulty behaviors (uniform delays for brevity). The situation where the diagnosability notion of interest fails to hold under a given observation configuration leads typically to the deployment of more observa- tional devices (e.g., sensors), which may be costly or infeasible. As an alternative to the additional deployment of observational devices, one might want to relax the uniformity of delays, while delays remain finite. To this end, we introduce a notion of diagnosability characterized with nonuniformly bounded finite counting delays (nonuniform counting delays for brevity), where finite delay bounds can vary on faulty behaviors. To evaluate the introduced notion of diagnosability with nonuniform counting delays, a polynomial-time verification algorithm is developed. Notably, the developed verification technique can readily be modified to construct a computationally superior verification algorithm for diagnosability under uniformly bounded finite counting delays (uniform counting delays for brevity) as compared to an algorithm previously reported in the literature. We also develop a novel on- line event counting algorithm that improves the time and space complexities of the currently available algorithms for the counting of special events. Keywords Discrete-event systems · Fault diagnosis · Repeated/intermittent faults · Computational complexity T.-S. Yoo Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-6180, USA e-mail: Tae-Sic.Yoo@inl.gov H. E. Garcia (B ) Sensor and Decision Systems Group, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-3605, USA e-mail: Humberto.Garcia@inl.gov