A minimization algorithm for automata generated fault trees with priority gates

Fault tree analysis is still widely practiced in high-hazard industries. We propose in this article an algorithm for the reduction of fault tree expressions that are generated from automata representations of failure behaviors. Automata formalisms are increasingly being used to describe systems exhibiting sequence-dependent failures—i.e., the overall outcome like a total failure of the system can depend on the order in which events occur. A set of paths leading to a safety-relevant state is encoded as a standard sum of product canonical form, and without any loss of the significance of the sequencing of events. That is, the corresponding fault tree expression is basically a Boolean formula which is extended with the necessary temporal features (event occurrence priority). Such expressions can then be reduced into minimal canonical forms by using the Boolean methods together with the required temporal logic calculus. Since minimal failure sequences can be determined from the obtained reduced models, the proposed approach can improve the analysis of the dynamic effects of the sequencing of faults and propagated errors in such models. As a consequence, it can have a positive impact on the design of failure prevention measures. A fault tolerant example system exhibiting dynamic behavior is used to highlight the benefits of the approach.