Safety Analysis Method of Mixed Failure Model using Temporal Bayesian Network

Abstract

Dynamic Fault Tree (DFT) is used widely in the community of reliability and safety analysis of a complex system. DFT is a high-level modeling language lacking formal semantics, so we need to convert it to a mathematical model to analyze. The conventional analysis method can only solve the DFT with discrete or exponential distribution, but not the DFT with mixed distributions. To this end, we first propose a TBN framework to represent the DFT with mixed failure distribution by extending the BN and introduce Dirac delta functions and unit-step functions into the framework to represent the logical relationship and temporal relationship between the nodes, respectively. To run the standard BN inference algorithm over TBN, we fit the failure distribution of the nodes by using k-piece and n-degree polynomials. We then propose a transformation method from DFT to TBN and prove the equivalence of the transformation. Finally, the analysis of the DFT model of the X2000 avionics system shows that our approach can effectively analyze the reliability of mixed distribution failure models. Moreover, the accuracy and efficiency of the analysis are significantly better than current mainstream methods.