Dependability Analysis of Hierarchical Systems with Modular Imperfect Coverage

We consider the dependability analysis of hierarchical fault tolerant computer based systems in this paper. The hierarchical nature of the system aids in fault coverage: if an undetected error escapes from one level of the system, it may be covered or tolerated at a higher level. A fault that remains uncovered through all levels of the hierarchy, and thus appears at the output, causes immediate system failure despite the remaining redundancy in the system. The difficulty in dependability analysis arises because the dependencies among components and/or modules across the different levels in the hierarchy introduced by such modular imperfect coverage have not been addressed in the solution. We offer a means by which to resolve this difficulty. Our analysis approach uses a generalized coverage model for each component. This coverage model defines the conditional coverage probabilities associated with each level in the hierarchy. The resulting approach is applicable to Markov analyses and combinatorial methods such as FT, RBD, or MBDD for the analysis of both reliability and availability. We present the general approach in terms of a dynamic fault tree, and provide an analysis of a sample hierarchical system.