Reliability analysis of multi-trigger binary systems subject to competing failures

This paper suggests two combinatorial algorithms for the reliability analysis of multi-trigger binary systems subject to competing failure propagation and failure isolation effects. Propagated failure with global effect (PFGE) is referred to as a failure that not only causes outage to the component from which the failure originates, but also propagates through all other system components causing the entire system failure. However, the propagation effect from the PFGE can be isolated in systems with functional dependence (FDEP) behavior. This paper studies two distinct consequences of PFGE resulting from a competition in the time domain between the failure isolation and failure propagation effects. As compared to existing works on competing failures that are limited to systems with a single FDEP group, this paper considers more complicated cases where the systems have multiple dependent FDEP groups. Analysis of such systems is more challenging because both the occurrence order between the trigger failure event and PFGE from the dependent components and the occurrence order among the multiple trigger failure events have to be considered. Two combinatorial and analytical algorithms are proposed. Both of them have no limitation on the type of time-to-failure distributions for the system components. Their correctness is verified using a Markov-based method. An example of memory systems is analyzed to demonstrate and compare the applications and advantages of the two proposed algorithms.