# An Improved FFIP Method Based on Mathematical Logic and SysML
## 2 Functional Failure Logic and Propagation Model  
### Functional Architecture of the System  
The MBSA emphasizes the model as the basis and core of safety analysis [31]. Building the unified model is one of the major differences between MBSA and traditional safety analysis. Based on the model, it carries out more efficient safety analysis than the traditional methods. Generally, designers tend to start with the functional requirements of the system and build the model from top to bottom. On the other hand, analysts prefer from bottom to top based on the functional state of the system. However, in order to build a unique system model, we need to unify the modeling process and standards [32, 33]. Therefore, a modeling framework based on function, behavior and structure is formed, as shown in Figure 1.  
In the function-behavior-structure modeling framework, defining the overall function is the beginning of system design. The overall function describes the tasks that the system needs to complete. Based on the understanding of the overall function, the framework breaks it down to different levels of functions, builds the relationship between the functions, and constitutes the functional model. As the realization of function depends on the implementation of behavior, we need to extend the function model to behavior and the behavior relationship, and then constitute the behavior model. Behavior needs specific structure to perform, so we need to obtain structure and structural relationship in the components of the system, using them to constitute the structural model. In a system design, function is the king, while behavior is the foundation of function realization. Structure is the basis of building the whole system. It is the foundation of the existence of the system.  
FFIP is a modeling method based on the mapping of function, behavior and structure [17]. FFIP is composed of three parts. The first part is the structure and function modeling: to draw the structure flow chart and function model diagram according to the system schematic diagram. The second part is behavior modeling, including setting behavior rules and analyzing the FFL. The third part is functional failure propagation simulation, to analyze the path of functional failure propagation. The FFIP is based on the function-behavior-structure relationship mapping, which realizes the systematic safety analysis of failure simulation and qualitative reasoning. In specific failure scenarios, FFIP can simulate the potential function failure mode and determine the fault propagation paths using a qualitative method, to evaluate the impact of the functional failure.  
The purpose of FFIP is to find the path of failure propagation. Therefore, FFL is the core of FFIP. This paper focuses on the component failures, which is manifested by the deviation of the key process variables. These variables include flow, pressure, signal, amplitude, etc. In the process of system operation, human factors and external events could also cause system fault, these are all valuable things we need to spend some time on. The common result of these unexpected events is the changes of the key process variables of the components. However, the changes of these variables do not always cause system failure. In other words, component failures do not necessarily cause system fault. Therefore, it is meaningful to analyze the component failures and carry out failure simulation.