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Fault Tree (FT) is a standard failure modeling technique that has been extensively used to predict reliability, availability and safety of many complex engineering systems. In order to facilitate the formal analysis of FT based analyses, a higher-order-logic formalization of FTs has been recently proposed. However, this formalization is quite limited in terms of handling large systems and transformation of FT models into their corresponding Reliability Block Diagram (RBD) structures, i.e., a frequently used transformation in reliability and availability analyses. In order to overcome these limitations, we present a deep embedding based formalization of FTs. In particular, the paper presents a formalization of AND, OR and NOT FT gates, which are in turn used to formalize other commonly used FT gates, i.e., NAND, NOR, XOR, Inhibit, Comparator and majority Voting, and the formal verification of their failure probability expressions. For illustration purposes, we present a formal failure analysis of a communication gateway software for the next generation air traffic management system.

Formalization of Fault Trees in Higher-Order Logic: A Deep Embedding Approach