We study the problem of decentralized fault prognosis of partially-observed discrete event systems. In order to capture the prognostic performance issue in the prognosis problem, we propose two new criteria: (1) all faults can be predicted K steps ahead; and (2) a fault will occur for sure within M steps once a fault alarm is issued; and we refer to (M, K) as the performance bound of the prognostic system. A necessary and sufficient condition for the existence of a decentralized supervisor satisfying these two criteria is provided, which is termed as (M, K)-coprognosability. A polynomial-time algorithm for the verification of (M, K)-coprognosability is also proposed. Finally, we show that the proposed approach is applicable to both disjunctive and conjunctive architectures. Our results generalize previous work on decentralized fault prognosis. (C) 2016 Elsevier Ltd. All rights reserved.