On Qualitative Analysis of Fault Trees Using Structurally Persistent Nets

A fault tree (FT) defines an undesired top event, characterizing it using logic combinations of lower-level undesired events. In this paper, we focus on coherent FTs, i.e., the logic is restricted to AND/OR formulas. FT analysis is used to identify and assess the minimal cut sets (MCSs) of an FT, which define the minimal set of events leading to the undesired state. The dual of MCS is minimal path set (MPS). MCS and MPS are commonly used for qualitative evaluation of FTs in safety and reliability engineering. This paper explores computation of the MCS/MPS of an FT by means of structural analysis (namely, computation of minimal p-semiflows) of a Petri net (PN) that represents the FT. To this end, we propose a formal definition of a coherent FT and a transformation from this model to a PN subclass (namely, structurally persistent nets). We also prove the relationship between minimal p-semiflows and MCS/MPS in an FT. In addition, we propose an algorithm that uses linear programming techniques to compute the MCS/MPS in an FT. Finally, we put our findings into practice by qualitatively evaluating the FT of a pressure tank system.