# An Improved FFIP Method Based on Mathematical Logic and SysML
## 1 Introduction  
With the development of new technology, the demands for system safety, especially in complex industrial systems, are constantly increasing. Currently, there are several safety analysis methods that have been proposed, such as Fault Tree Analysis, Feilure Mode Effect Analysis, Hazard and Operational Analysis, etc. [1]. However, the above methods rely too much on the analyzers' experience and subjective judgment. With increasing complexity of industrial systems, it is difficult to use these traditional safety analysis methods to achieve accurate and complete analysis results. In the past few years, some new safety analysis methods have emerged, for example, the Functional Resonance Analysis Method (FRAM) and the Systems-Theoretic Process Analysis (STPA) method. FRAM [2] is a systematic analysis method, which can be used to model complex social-technology system. Although it is powerful for visualizing and understanding the functions of system, it does not do well in quantization. It is also difficult to obtain safety constraints. STPA [3] is based on the system theory and cybernetics, it treats the research object as a hierarchical control structure. STPA carries out safety analysis by determining analysis objectives, constructing hierarchical control structure, identifying unsafe control actions, and identifying loss scenarios. However, all these analyses methods need to rely on the subjective experience of personnel, which leads to the deviation of the results of different personnel analysis. With the advancement of the whole life cycle of the system, relevant safety analysis is constantly updated, and the MBSA was gradually developed [4]. The purpose of MBSA is to study the modeling of complex industrial systems, implement automated or semi-automated safety analysis and perform verification based on system models [5]. MBSA is executed as follows:1. Establish a general and unified model according to the purpose of system design and analysis. 2. Use formal tools to describe the model. 3. Use simulation or model checking to evaluate the safety of the system based on the model. 4. Generate the analysis results, such as the FTA minimum cut set, FMEA form (Failure Mode Effect Analysis), etc. At present, some typical MBSA methods include Failure Propagation and Transformation Notation (FPTN), Hierarchical Performed Hazard Origin and Propagation Studies (HIP-HOPS), Failure Propagation and Transformation Calculus (FPTC), AltaRica 3.0, etc. FPTN [6; 7] is aimed at software safety analysis. FPTN limits artificial logic reasoning to the module level, reduces the capability requirements for analyzer and increases the accuracy of reasoning. However, this method is not supported by other tools and its scope of application is limited. FPTC [8] is a further development based on FPTN, in which system model is linked with failure model and requires a repeated analysis after injection failure. HIP-HOPS [9; 10] is a hierarchical and modular analysis method, it can be used for system reliability modeling and analysis. In this method, the input failure and output failure are linked, and the SAM tool is used to generate the fault tree and calculate the minimum cut to find all propagation paths that cause the output faults. AltaRica [11; 12] has been one of the most popular modeling languages in the MBSA field, it is advanced description language based on pattern automata. The modeling languages of MBSA also include Systems Modeling Language (SysML), Architecture Analysis & Design Language (AADL), east-adl2, Security Assertion Markup Language (SAML), etc. [13]. When it comes to model checking, MBSA also has a lot of tools. The most representative of them are Symbolic Model Verifier (SMV) and Simple Promela Interpreter (SPIN) [14; 15; 16]. In this paper, we study the Functional Failure Identification and Propagation (FFIP), a graphical evaluation method, which is composed of structural models, functional models, behavior rules, functional failure logic (FFL) analysis and failure simulation.