BDD based analysis of parametric fault trees

Several extensions of the Fault Tree (FT) [1] formalism have been proposed in the literature. One of them is called Parametric Fault Tree (PFT) [2] and is oriented to the modeling of redundant systems, and provides a compact form to model the redundant parts of the system. Using PFTs instead of FTs to model systems with replicated parts, the model design is simplified since the analyst can fold subtrees with the same structure in a single parametric subtree, reducing the number of elements in the model. The method based on Binary Decision Diagrams (BDD) [3, 4, 5] for the quantitative analysis of FTs, is adapted in this paper to cope with the parametric form of PFTs: an extension of BDDs called Parametric BDD (pBDD) is used to analyze PFTs. The solution process is simplified by using pBDDs: comparing the pBDD obtained from a PFT, with the ordinary BDD obtained from the unfolded FT, we can observe a reduction of the number of nodes inside the pBDD. Such reduction is proportional to the level of redundancy inside the PFT and leads to a consequent reduction of the number of steps necessary to perform the analysis. Concerning the qualitative analysis, we can observe that several Minimal Cut Sets (MCS) obtained from the FT model of a redundant system, involve basic events relative to similar components. A Parametric MCS (pMCS) allows to group such MCSs in an equivalence class, and consequently, to evidence only the failure pattern, regardless the identity of replicated components. A method to derive pMCSs from a PFT is provided in the paper.