Reliability modeling of multi-state systems under probabilistic failure competition with random propagation time

Multi-State Systems (MSSs) play a critical role on the Internet of Things (IoT)-enabled infrastructures, where components undergo gradual degradation and operate across multiple performance states. A key challenge in MSS reliability modeling involves capturing the dynamic competition between failure isolation and failure propagation, particularly in systems exhibiting probabilistic functional dependence, such as relay-assisted Wireless Sensor Networks (WSNs) used in IoT applications. In these relay-assisted systems, Local Failures (LFs) and Propagated Failures with Global Effects (PFGEs) compete temporally. Specifically, if an LF occurs in a relay node prior to the occurrence of a PFGE originating from a dependent component, the PFGE may be successfully isolated by the failed relay. Conversely, if the PFGE precedes the LF, it may propagate throughout the system, resulting in extensive disruption. Existing reliability models typically assume instantaneous failure propagation, thereby disregarding the random Propagation Times (PTs) observed in real-world scenarios, such as those caused by jamming attacks or environmental interferences. To overcome this limitation, a combinatorial analytical framework is introduced that incorporates stochastic PTs, enabling more accurate reliability evaluation of MSSs under probabilistic failure competition. An illustrative case study involving WSNs in intelligent high-speed railway systems is used to demonstrate the significant impact of random PTs on overall system performance.