Recently, the study of fault diagnosis and prognosis of discrete-event systems (DESs) has received considerable attention. This article aims to investigate the decentralized fault prognosis of stochastic DESs (SDESs). The notion of $m$ -step stochastic-coprognosability, called $S_{m} $ -coprognosability, is formalized to capture the capability of stochastic systems to predict a fault at least $m$ steps in advance under the decentralized framework. The verifier is constructed from the stochastic decentralized system, in which $n$ local prognosers are deployed to send the local prognostic decisions to a coordinator for calculating the final prognostic decision. In particular, a necessary and sufficient condition of $S_{m}$ -coprognosability of stochastic systems is derived, and an algorithm for testing $S_{m} $ -coprognosability is given, which is polynomial to the number of states and events but exponential to the number of local sites. Furthermore, the maximum number of $m$ for making the given SDES to be $S_{m} $ -coprognosable is discussed. Note to Practitioners—This article extends the fault prognosis methods of SDESs from centralized framework to decentralized framework, such that for many technologically complex systems whose information collection is scattered in physically separated different sites, every local site makes decision based on information collected by own sensors, without communicating with other local sites, which is more appropriate than the centralized method.
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