# Fault Analysis of Shearer-Cutting Units Driven by Integrated Importance Measure
## 4 Effectiveness Discussion of IIM Ranking
### Relative Value Distribution Analysis by Radial Bar Charts
So, the relative value of CIM makes it easier to distinguish key fault causes compared to BIM. From Figures 6 and 9, the relative values of IIM and FVIM can clearly distinguish the importance of bottom events. However, C15 (fatigue damage, gearbox dry friction or particle contamination) in FVIM is too large, which makes it difficult to distinguish the importance measure of other bottom events with lower FVIM. Therefore, the relative value distribution of the four importance measure rankings shows that IIM and CIM can clearly distinguish the relative importance of bottom events. * Select \(n\) groups of key elements, assuming that the number of key elements in group \(i\) is \(m_{i}\). * Determine the position \(K_{ij}\) of the key element in a particular ranking, and the key element is the element \(j(j=1,2,\ldots,m_{i})\) in the group \(i(i=1,2,\ldots,n)\). * Calculate the mAP of different rankings under different key element groups, as shown in Equation (5). \[mAP=\frac{1}{n}\sum_{j=1}^{m_{i}}\left(\frac{1}{m_{i}}\left(\sum_{j=1}^{m_{i}} \frac{j}{K_{ij}}\right)\right) \tag{5}\]  
where \(m_{i}\) represents the number of key elements in group \(i\), \(n\) denotes the number of groups of selected key elements, and \(K_{ij}\) represents the position serial number of the key element \(j(j=1,2,\ldots,m_{i})\) in the group \(i(i=1,2,\ldots,n)\) for a specific ranking. In order to compare the average accuracy of rankings for four IMs, select the top \(L\) bottom events with higher IM as a group of key elements. Here, we select three groups of key elements, which means \(n=3\). The key elements in the first group are C10, C12, C17, C18, and C19 when \(L=8\). C10, C17, C18, and C19 are the key elements in the second group when \(L=7\). C17, C18, and C19 are selected as the key elements in the third group when \(L=5\). For these four rankings of IMs, the position information of key elements in each can be recorded as \(K^{\text{IM}}\), \(K^{\text{FVIM}}\), \(K^{\text{BIM}}\), and \(K^{\text{CIM}}\), shown as follows:  
\[K^{\text{IM}}=\left[ \begin{array}{ccc}1&2&3&4&7\\ 1&2&3&4&/\\ 1&2&3&/\end{array} \right],\ K^{\text{FVIM}}=\left[ \begin{array}{ccc}2&3&5&7& 8\\ 2&3&5&7&/\\ 2&3&5&/\end{array} \right],\ K^{\text{BIM}}=K^{\text{CIM}}=\left[ \begin{array}[] {ccc}1&2&4&6&8\\ 1&2&4&6&/\\ 1&2&5&/\end{array} \right].\]  
Therefore, the average accuracy of these four IM rankings can be obtained by substituting \(K^{\text{IM}}\), \(K^{\text{FVIM}}\), \(K^{\text{BIM}}\), and \(K^{\text{CIM}}\) into Equation (5). The mAP values of four IM rankings are shown in Table 7.  
The average accuracy of IM ranking in Table 5 shows that the accuracy of IIM ranking is the highest (94.52%), followed by BIM and CIM ranking accuracy (85.97%), and FVIM accuracy is the lowest (58.87%). Thus, IIM ranking has the best accuracy. The main reason for the low accuracy of the FVIM ranking is that the bottom event C15 is at the top of the FVIM ranking, but it is not at the top in other IM rankings.