## 1 Introduction  
In recent years, due to the complex correlation of components in complex systems, local faults may have a great effect on the overall system by fault propagation [1; 2; 3]. Therefore, the safety and risk analysis of such complex systems has attracted more and more attention. Safety analysis and risk assessment aims to eliminate and control various hazards through the design system and take preventive measures to prevent accidents that will cause personal injury, equipment damage, and task failure during system operation. With the development of science and technology, a series of analysis methods for evaluating system failures and risk events have been developed, especially in high-risk fields such as aerospace, chemical, nuclear, and other industrial fields [4; 5]. However, there are still a number of safety problems in these methods caused by the coupling and correlation characteristics in complex systems. Traditional safety modeling and analysis methods are mainly based on the logical process of induction and deduction to carry out system safety analysis. From the local characteristics of the system or the direct relationship between internal components, these methods are used to find the root cause of safety problems and carry out safety work such as analysis, verification, assurance, etc. Typical analysis methods are Fault Tree Analysis (FTA) [6], Event Tree Analysis (ETA) [7; 8], Failure Modeand Effects Analysis (FMEA) [9; 10; 11], Hazard and Operability Analysis (HAZOP), Probability Risk Assessment (PRA) [12; 13], etc. These methods have applications in nuclear power, chemical, and even aerospace. [PERSON] [14] proposed a modified FMEA based on Dempster-Shafer evidence theory to analyze safety of aircraft turbine rotor blades. [PERSON], [PERSON]. [15] used a Monte Carlo simulation and cost-based FMEA to account for the uncertainties in: detection time, fixing time, occurrence, delay time, down time, and model complex scenarios. [PERSON] [16] proposed a time-dependent probabilistic approach of FMEA to evaluate safety of automotive-manufacturing. [PERSON] [17] proposed an FTA-based method for risk decision-making in emergency response and applied it in H1N1 infectious diseases. [PERSON] [18] proposed a fuzzy multi-attribute HAZOP technique and Analytic Hierarchy Process (AHP) to determine the weight of risk factors and to prioritize the hazards. Moreover, with the development of the accident theory, a large number of modern methods for safety analysis, such as Markov process, Analysis and Design Language (AADL), Petri nets, Bayesian networks, etc., have also been invented. [PERSON] [19] proposed the staged Bayesian failure model for girth welds of a pipeline, using the tree-type accident theory and Bayesian survival analysis method. [PERSON] [20] applied the continuous-time Markov chains to analyze reliability of the reconfigurable integrated modular avionics. [PERSON] [21] applied Petri nets to estimate performability to ensure system dependability requirements and did the performance analysis of safety critical and control systems that helps to estimate the risk. [PERSON] [22] presented AADL based on model-driven specification and probabilistic model checking to automatically analyze safety-based availability before synthesizing the embedded software product. [PERSON]'s team at the University of York in the United Kingdom proposed the theory and analysis techniques of safety case [23; 24; 25; 26] to confirm that the system reaches an acceptable level of safety by establishing a correlation between safety requirements and safety evidence. The Functional Resonance Accident Model (FRAM) [27; 28] was proposed by [PERSON], based on the principle of stochastic resonance in the system. However, the above safety analysis methods mainly focused on a qualitative description and the study of coupling mechanisms, and lack the quantitative analysis and evaluations of coupling and correlation relationships between components in the system.