Abstract
Functional dependence (FDEP) exists in many real-world systems, where the failure of one component (trigger) causes other components (dependent components) within the same system to become isolated (inaccessible or unusable). The FDEP behavior complicates the system reliability analysis because it can cause competing failure effects in the time domain. Existing works have assumed noncascading FDEP, where each system component can be a trigger or a dependent component, but not both. However, in practical systems with hierarchical configurations, cascading FDEP takes place where a system component can play a dual role as both a trigger and a dependent component simultaneously. Such a component causes correlations among different FDEP groups, further complicating the system reliability analysis. Moreover, the existing works mostly assume that any failure propagation originating from a system component instantaneously takes effect, which is often not true in practical scenarios. In this work, we propose a new combinatorial method for the reliability analysis of competing systems subject to cascading FDEP and random failure propagation time. The method is hierarchical and flexible without limitations on the type of time-to-failure distributions for system components. A detailed case study is performed on a sensor system used in smart home applications to illustrate the proposed methodology.