# Hardware Reliability Analysis of a Coal Mine Gas Monitoring System Based on Fuzzy-FTA
###### Abstract  
The hardware reliability of a gas monitoring system was investigated using the fuzzy fault tree analysis method. A fault tree was developed considering the hardware failure of the gas monitoring system as a top event. Two minimum path sets were achieved through qualitative analysis using the ascending method. The concept of fuzzy number of the fuzzy set theory was applied to describe the probability of basic event occurrence in the fault tree, and the fuzzy failure probabilities of the middle and top events were calculated using fuzzy AND and OR operators. The results show that the proposed fuzzy fault tree is an effective method of reliability analysis for gas monitoring systems. Results of calculations using this method are more reasonable than those obtained with the conventional fault tree method. fuzzy; FTA; gas; reliability; monitoring system +
Footnote †: journal: Applied Sciences  
11 October 2021  
11 November 2021  
this paper uses the fuzzy fault tree analysis method that combines fuzzy mathematics and fault tree analysis to analyze the hardware reliability of the gas monitoring system. The research of the fuzzy fault tree analysis began with scholars such as [PERSON] et al. [4]. They realized that the probability of the bottom event and top event in a fault tree is often not a fixed value, and it has a certain degree of ambiguity. In this case, they first proposed the replacement of the fixed probability of events in the fault tree with the fuzzy probability. In addition, they described the fuzzy probability of each bottom event in the system with a fuzzy number according to the fuzzy algorithm, in which the fuzzy number replaces the traditional accurate value and approximate value. [PERSON] et al. proposed a fuzzy analysis method of the fault tree in the machining system, and actually constructed a fault tree in the machining system [5]. [PERSON] et al. introduced the generalized maximum and minimum method in the fuzzy fault tree analysis [6], which defined the fuzzy number as a triangular distribution to calculate the probability distribution of the occurrence of the bottom event. [PERSON] et al. further used the triangular fuzzy numbers to stipulate fuzzy numbers for the analysis and research [7], and proposed a new analysis method for the importance of bottom events. [PERSON] et al. constructed a complete fault tree of the hydraulic system of the water jet propulsion using the fuzzy fault tree analysis method [8], and finally obtained the probability interval of the occurrence of the top event. [PERSON] et al. used fuzzy numbers rather than an accurate probability to deal with uncertain problems [9], which reduced the difficulty of obtaining the accurate value of event probability. [PERSON] et al. used the L-R fuzzy number to define the probability of the bottom event for the first time [10], and provided the probability calculation method under the L-R fuzzy number. [PERSON] et al. constructed a fault tree for a simple system [11], combined with a fuzzy algorithm to take the probability of the bottom event as a fuzzy number, and then took the \(\lambda\) cut set to obtain the probability of the top event. [PERSON] and [PERSON] used a discrete method to discretize the membership function of the bottom event [12], then used the fuzzy expansion principle and fuzzy operator to calculate the interval, and finally obtained the probability of the top event. [PERSON] et al. used the fuzzy probability to analyze the event tree [13]. The event tree is a dual form of the fault tree. Moreover, their conclusions bring certain significance to the study of the fault tree. [PERSON] et al. extended the concept of traditional importance and used the fuzzy integral to provide a new fuzzy importance, then applied it to the actual reliability engineering [14].