Power-hierarchy of dependability-model types

This paper formally establishes a hierarchy, among the most commonly used types of dependability models, according to their modeling power. Among the combinatorial (non-state-space) model types, we show that fault trees with repeated events are the most powerful in terms of kinds of dependencies among various system components that can be modeled. Reliability graphs are less powerful than fault trees with repeated events but more powerful than reliability block diagrams and fault trees without repeated events. By virtue of the constructive nature of our proofs, we provide algorithms for converting from one model type to another. Among the Markov (state-space) model types, we consider continuous-time Markov chains, generalized stochastic Petri nets, Markov reward models, and stochastic reward nets. These are more powerful than combinatorial-model types in that they can capture dependencies such as a shared repair facility between system components. However, they are analytically tractable only under certain distributional assumptions such as exponential failure- and repair-time distributions. They are also subject to an exponentially large state space. The equivalence among various Markov-model types is briefly discussed.>