Inference for Multicomponent Systems with Dependent Failures

Multicomponent systems may experience failures with correlations amongst failure times of groups of components, and some subsets of components may experience common cause, simultaneous failures. We present a novel, general approach to model construction and inference in multicomponent systems incorporating these correlations in an approach that is tractable even in very large systems. In our formulation, the system is viewed as being made up of independent overlapping subsystems (IOS). In these systems, components are grouped together into overlapping subsystems, and further into nonoverlapping subunits. Each subsystem has an independent failure process, and each component's failure time is the time of the earliest failure in all of the subunits of which it is a part. We apply this method to observations of an IOS model based on a multicomponent system accumulating damage due to a series of shocks, and with no repair/rectification actions. The model associates individual shock processes with each subsystem, and includes the Marshall-Olkin multivariate exponential model as a special case. We present approaches to simulation and to the estimation of the parameters of the model, given component failure data for various system configurations (series, parallel, and other arrangements).