# Hardware Reliability Analysis of a Coal Mine Gas Monitoring System Based on Fuzzy-FTA
## 2 The Principle of the Fuzzy-FTA Analysis  
### Fault Tree Analysis Method Process  
The fault tree analysis is a graphical analysis method of causality and logical relationship that finds the various factors related to the disaster accident from the result to the cause. This method is used to analysis what may happen in the system. Therefore, it is placed at the top of the graph and is called the top event. According to the relationship between the elements of the system, the causes related to disasters and accidents are analyzed. These reasons may be the result of other reasons, called the intermediate cause event (or intermediate event), and should continue to be analyzed until the reasons cannot be analyzed further. These reasons are called the basic cause event (or basic event). The causal relationships in the figure are connected by different logic gates to get an image of an upside-down tree. The basic procedure of the FTA method is shown in Figure 1. The first step is to get familiar with the system that needs to be analyzed, by understanding the system status and various parameters, and drawing the process flow chart or floor plan. Second, the information on the accident cases (which occurred in the same industry and on similar devices at home and abroad) is collected, and the accidents that have serious consequences and can easily occur as top events are identified. Based on the experiences, lessons, and accident cases, after the statistical analysis, the probability (frequency) of the accident is calculated, and the target value of the accident to be controlled is determined. Then, the fault tree is constructed from the top event according to the logical relationships among the events. If the constructed fault tree does not conform to the on-site conditions, it is also necessary to collect the missing information, re-analyze system failures and abnormalities, until the established fault tree is in line with the actual on-site conditions. Finally, a qualitative analysis is performed to determine the structural importance of each basic event, the probability is calculated, and a quantitative analysis is performed. 1. Construction of the fault tree  
The construction of the fault tree starts from the top event. The direct, indirect, necessary, and sufficient causes of the top event are determined by deduction and reasoning. Usually, these reasons are not basic events but intermediate events that need further development. 2. Qualitative analysis of the fault tree  
The qualitative analysis is based only on the structure of the fault tree and the causal relationships of the events leading to the accident. The analysis includes finding the minimum cut set, the minimum path set, and the structural importance of basic events. 3. Quantitative analysis of the fault tree  
The purpose of this analysis is to calculate the occurrence probability of the top event and evaluate the safety and reliability of the system. Specifically, the method consists of comparing the calculated probability of the top event with the predetermined target value. If the latter is exceeded, the necessary system improvement measures should be taken to reduce it below the target value. Figure 1: Workflow of the FTA method. (4) Preparation of documentation on the results  
The final step is to compile the result file. The analyst should provide the description of the analysis system, a discussion of the problems, the fault tree model itself, the minimum cut set, the minimum path set, and the structural importance analysis. Moreover, the analyst should give relevant conclusions for the fault tree analysis of coal mine gas monitoring system. The main principles of the Fuzzy-FTA method are as follows. Although the data recorded on site are insufficient, managers and experts with rich experience in the front line have a relatively accurate perceptual grasp of the failure probability. Therefore, confidence intervals for the occurrence of basic events can be estimated by analyzing the responses to the questionnaires administered to them.