Parametric Fault Tree for the Dependability Analysis of Redundant Systems and Its High-Level Petri Net Semantics

In order to cope efficiently with the dependability analysis of redundant systems with replicated units, a new, more compact fault-tree formalism, called Parametric Fault Tree (PFT), is defined. In a PFT formalism, replicated units are folded and indexed so that only one representative of the similar replicas is included in the model. From the PFT, a list of parametric cut sets can be derived, where only the relevant patterns leading to the system failure are evidenced regardless of the actual identity of the component in the cut set. The paper provides an algorithm to convert a PFT into a class of High-Level Petri Nets, called SWN. The purpose of this conversion is twofold: to exploit the modeling power and flexibility of the SWN formalism, allowing the analyst to include statistical dependencies that could not have been accommodated into the corresponding PFT; to exploit the capability of the SWN formalism to generate a lumped Markov chain, thus alleviating the state explosion problem. The search for the minimal cut sets (qualitative analysis) can be often performed by a structural T-invariant analysis on the generated SWN. The advantages that can be obtained from the translation of a PFT into a SWN are investigated considering a fault-tolerant multiprocessor system example.