Event Tree Reliability Analysis of Safety-Critical Systems Using Theorem Proving

Abstract

Event tree (ET) analysis is widely used as a forward deductive safety analysis technique for decision-making at the design stage of safety-critical systems, such as smart power grids. An ET is a schematic diagram representing all possible complete/partial reliability and failure consequence events in a system so that one of these events can occur. In this article, we propose to use formal techniques based on theorem proving for the formal modeling and step-analysis of ET diagrams. To this end, we develop a formalization in higher order logic enabling the mathematical modeling of the graphical diagrams of ETs and the formal analysis of system-level failure/reliability. We propose new mathematical ET probabilistic formulations, based on a generic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">list</i> -datatype, which are capable of analyzing large scale ETs that consist of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {N}$</tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multistate</i> system components and enable the formal ET probabilistic analysis for any given probabilistic distribution. We demonstrate the practical effectiveness of the proposed ET formalization by performing the formal reliability analysis of a standard IEEE 118-bus electrical power grid system and also formally determine its reliability indices, such as system/customer average interruption frequency and duration (SAIFI, SAIDI, and CAIDI). To assess the accuracy of our proposed approach, we compare our formal ET analysis results for the grid with those obtained by MATLAB Monte Carlo simulation, the commercial Isograph software as well as manual paper-and-pencil analysis.