# Risk Factor Analysis of Elevator Brake Failure Based on DEMATEL-ISM
## 4 Analysis of Risk Factors for Elevator Brake Failure  
### Grey DEMATEL-ISM Computational Analysis  
In order to analyze the relevance and importance of the risk factors of elevator brake failure, the grey DEMATEL method was applied. The five experts selected cover five key aspects of elevator research, manufacturing, inspection, supervision and installation. They are all personnel who have been working in the elevator industry for many years and have participated in the development of China's national standards for elevators, making them representative. They have rich knowledge of the elevator drum brake studied, and are able to evaluate the influencing factors of the elevator drum brake and make reasonable ratings among them. In addition, five experts have been requested to avoid subjective judgments as much as possible during the scoring process, ensuring the rationality of the results. This assessment yielded a comprehensive influence matrix, as shown in Figure 2 (Figure 2 was created using Microsoft Office LTSC Standard 2021 software). Based on the comprehensive influence matrix, Influence Degree, Influenced Degree, Centre Degree and Cause Degree of each influencing factor were calculated, as shown in Table 5. Based on the data in Table 5, a Centre Degree-Cause Degree diagram was created, as shown in Figure 3.  
Figure 2: Comprehensive influence matrix.  
Based on the grey DEMATEL method, the ISM method is employed to construct a multi-level progressive structure model to analyze the influence relationship among the risk factors of elevator brake failure. Based on the comprehensive influence matrix calculation of the grey DEMATEL method, the mean \(a\) and standard deviation \(b\) of all factors in the comprehensive influence matrix are calculated, and \(a\) = 0.0979, \(b\) = 0.0677, with a threshold \(\lambda\) = 0.1656 is obtained, and the reachable matrix is obtained. Furthermore, the reachable set, the set of antecedents, and the intersection of the reachable set and the set of antecedents are obtained. The failure risk factors are divided into hierarchical levels, and the hierarchical diagram of elevator brake failure risk factors is obtained by combining Centre Degree and Cause Degree, as shown in Figure 4. The processes in this section were calculated by Python software (version 3.11).  
Figure 3: Centre Degree–Cause Degree diagram.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Influence Degree** & **Influenced Degree** & **Centre Degree** & **Cause Degree** \\ \hline S1 & 1.6616 & 2.0082 & 3.6697 & \(-\)0.3466 \\ S2 & 1.8239 & 2.0012 & 3.8252 & \(-\)0.1773 \\ S3 & 0.2010 & 2.1550 & 2.3560 & \(-\)1.9540 \\ S4 & 0.4510 & 1.8158 & 2.2669 & \(-\)1.3648 \\ S5 & 0.2699 & 2.0886 & 2.3585 & \(-\)1.8187 \\ S6 & 0.4178 & 1.9282 & 2.3460 & \(-\)1.5103 \\ S7 & 0.3043 & 1.9625 & 2.2668 & \(-\)1.6582 \\ S8 & 2.2648 & 0.6861 & 2.9510 & 1.5787 \\ S9 & 2.3034 & 1.4071 & 3.7105 & 0.8963 \\ S10 & 2.2342 & 1.2882 & 3.5224 & 0.9461 \\ S11 & 2.2606 & 1.3206 & 3.5812 & 0.9400 \\ S12 & 2.2932 & 1.4918 & 3.7850 & 0.8014 \\ S13 & 2.5663 & 1.4158 & 3.9821 & 1.1505 \\ S14 & 2.3651 & 1.7197 & 4.0848 & 0.6454 \\ S15 & 1.6247 & 1.5324 & 3.1571 & 0.0923 \\ S16 & 2.0205 & 0.2411 & 2.2616 & 1.7794 \\ \hline \end{tabular}
\end{table}
Table 5: The results of the calculation of Influence Degree, Influenced Degree, Centre Degree and Cause Degree.