An algebra of temporal faults

Faults modelling is essential to anticipate failures in critical systems. Traditionally, Static Fault Trees are employed to this end, but Temporal and Dynamic Fault Trees are gaining evidence due to their enriched power to model and detect intricate propagation of faults that lead to a failure. In previous work, we showed a strategy based on the process algebra CSP and Simulink models to obtain fault traces that lead to a failure. Although that work used Static Fault Trees, it could be used with Temporal or Dynamic Fault Trees. In the present work we define an algebra of temporal faults (with a notion of fault propagation) and prove that it is indeed a Boolean algebra. This allows us to inherit Boolean algebra’s properties, laws and existing reduction techniques, which are very beneficial for faults modelling and analysis. We illustrate our work on a simple but real case study supplied by our industrial partner EMBRAER.