Compositional Temporal Fault Tree Analysis

HiP-HOPS (Hierarchically-Performed Hazard Origin and Propagation Studies) is a recent technique that partly automates Fault Tree Analysis (FTA) by constructing fault trees from system topologies annotated with component-level failure specifications. HiP-HOPS has hitherto created only classical combinatorial fault trees that fail to capture the often significant temporal ordering of failure events. In this paper, we propose temporal extensions to the fault tree notation that can elevate HiP-HOPS, and potentially other FTA techniques, above the classical combinatorial model of FTA. We develop the formal foundations of a new logic to represent event sequences in fault trees using Priority-AND, Simultaneous-AND, and Priority-OR gates, and present a set of temporal laws to identify logical contradictions and remove redundancies in temporal fault trees. By qualitatively analysing these temporal trees to obtain ordered minimal cut-sets, we show how these extensions to FTA can enhance the safety of dynamic systems.