Formal FT-based Cause-Consequence Reliability Analysis using Theorem Proving

TL;DR

This paper introduces a formal, theorem-proving-based approach using HOL4 for cause-consequence reliability analysis, providing rigorous verification of system dependability properties beyond traditional simulation methods.

Contribution

It formalizes Cause-Consequence Diagrams in Higher-Order Logic with HOL4, enabling precise reliability analysis and verification for critical systems.

Findings

Successfully modeled CCDs in HOL4 for the IEEE 39-bus power network

Accurately determined system reliability metrics like FOR and SAIDI

Validated results against Monte Carlo simulations and existing methods

Abstract

Cause-consequence Diagram (CCD) is widely used as a deductive safety analysis technique for decision-making at the critical-system design stage. This approach models the causes of subsystem failures in a highly-critical system and their potential consequences using Fault Tree (FT) and Event Tree (ET) methods, which are well-known dependability modeling techniques. Paper-and-pencil-based approaches and simulation tools, such as the Monte-Carlo approach, are commonly used to carry out CCD analysis, but lack the ability to rigorously verify essential system reliability properties. In this work, we propose to use formal techniques based on theorem proving for the formal modeling and step-analysis of CCDs to overcome the inaccuracies of the simulation-based analysis and the error-proneness of informal reasoning by mathematical proofs. In particular, we use the HOL4 theorem prover, which is a computer-based mathematical reasoning tool. To this end, we developed a formalization of CCDs in Higher-Order Logic (HOL), based on the algebraic approach, using HOL4. We demonstrate the practical effectiveness of the proposed CCD formalization by performing the formal reliability analysis of the IEEE 39-bus electrical power network. Also, we formally determine the Forced Outage Rate (FOR) of the power generation units and the network reliability index, i.e., System Average Interruption Duration Index (SAIDI). To assess the accuracy of our proposed approach, we compare our results with those obtained with MATLAB Monte-Carlo Simulation (MCS) as well as other state-of-the-art approaches for subsystem-level reliability analysis.