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Formal Dynamic Fault Trees Analysis using an Integration of Theorem Proving and Model Checking
Technical Report
Abstract
Dynamic fault trees (DFTs) have emerged as an important tool for capturing the dynamic behavior of system failure. These DFTs are then analyzed qualitatively and quantitatively using stochastic or algebraic methods to judge the failure characteristics of the given system in terms of the failures of its sub-components. Model checking has been recently proposed to conduct the failure analysis of systems using DFTs with the motivation to provide a rigorous failure analysis of safety-critical systems. However, model checking has not been used for the DFT qualitative analysis and the reduction algorithms used in model checking are usually not formally verified. Moreover, the analysis time grows exponentially with the increase of the number of states. These issues limit the usefulness of model checking for analyzing complex systems used in safety-critical domains, where the accuracy and completeness of analysis matters the most. To overcome these limitations, we propose a comprehensive methodology to perform the qualitative and quantitative analysis of DFTs using an integration of theorem proving and model checking based approaches. For this purpose, we formalized all the basic dynamic fault tree gates using higher-order logic based on the algebraic approach and formally verified some of the simplification properties. This formalization allows us to formally verify the equivalence between the original and reduced DFTs using a theorem prover, and conduct the qualitative analysis. We then use model checking to perform the quantitative analysis of the formally verified reduced DFT. We applied our methodology to five benchmarks and the results show that the formally verified reduced DFT was analyzed using model checking with up to six times less states and up to 133000 times faster.
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