# A Comprehensive Failure Risk Assessment Method of
## 3 Case Application
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Sort** & **Row** & **Col** & **Current Val** & **Beat Val** & **Old Inconsist.** & **New Inconsist.** \\ \hline
1 & W103 & W302 & 6.000 & 11.049 & 0.0246 & 0.008 \\
2 & W103 & W610 & 4.000 & 2.261 & 0.0246 & 0.009 \\
3 & W301 & W302 & 2.000 & 1.320 & 0.0246 & 0.017 \\
4 & W301 & W610 & 2.000 & 1.388 & 0.0246 & 0.018 \\
5 & W302 & W610 & 3.000 & 2.444 & 0.0246 & 0.023 \\
6 & W103 & W301 & 5.000 & 5.015 & 0.0246 & 0.025 \\ \hline \end{tabular}
\end{table} 
Table 6: Inconsistency report of W101. Figure 8: Super limit matrix of failure mode of machining center (W). Figure 9: The failure mode influence degree of the cooling system. Table 7 summarizes the influence degree of the failure mode of each component of the machining center and the frequency ratio of the failure mode of each component. Substituting the calculation results in Table 7 into Equation (1), the independent failure risk value of each component of the machining center at 4000 h can be obtained, as shown in Table 8.  
From Table 8, the ranking results of the independent failure risk values of the failure modes of each component of the machining center at 4000 h is \(M>NC>V>K>W>G>L>J>S\). That is, at this time, the component with the largest independent failure risk value of the failure mode is the tool magazine, and the smallest component is the spindle system. According to the ANP model (Figure 10a) of the machining center, it is abstracted into the topological structure model of the machining center, as shown in Figure 10b. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Code** & **Pattern Code** & \(\alpha_{ij}\) & \(\beta_{ij}\) & **Code** & **Pattern Code** & \(\alpha_{ij}\) & \(\beta_{ij}\) \\ \hline \multirow{8}{*}{\(M\)} & 0101 & 0.3158 & 0.3421 & & 0410 & 0.2308 & 0.2444 \\  & 0503 & 0.1579 & 0.1175 & & 0101 & 0.1538 & 0.0325 \\  & 0202 & 0.1053 & 0.0320 & & 0202 & 0.1538 & 0.0115 \\  & 0605 & 0.1053 & 0.0023 & & 0605 & 0.1538 & 0.0111 \\  & 0201 & 0.0526 & 0.0021 & & 0203 & 0.0769 & 0.0084 \\  & 0205 & 0.0526 & 0.1398 & \multirow{2}{*}{\(S\)} & 0503 & 0.0769 & 0.4367 \\  & 0501 & 0.0526 & 0.1037 & & 0609 & 0.0769 & 0.0678 \\  & 0502 & 0.0526 & 0.1121 & & 0603 & 0.0769 & 0.0092 \\  & 0506 & 0.0526 & 0.0351 & & 0606 & 0.2500 & 0.1785 \\  & 0616 & 0.0526 & 0.1133 & & & & \\ \hline \multirow{8}{*}{\(W\)} & 0101 & 0.2857 & 0.2979 & & 0101 & 0.2857 & 0.3515 \\  & 0302 & 0.2143 & 0.0695 & & 0103 & 0.1429 & 0.3571 \\  & 0301 & 0.1429 & 0.0749 & & 0502 & 0.1429 & 0.0959 \\  & 0805 & 0.1429 & 0.0716 & \multirow{2}{*}{\(J\)} & 0601 & 0.1429 & 0.0420 \\  & 0103 & 0.0714 & 0.2754 & & 0603 & 0.1429 & 0.1377 \\  & 0601 & 0.0714 & 0.0962 & & 0803 & 0.1429 & 0.0157 \\  & 0610 & 0.0714 & 0.1146 & & & & \\ \hline \multirow{2}{*}{\(L\)} & 0103 & 0.5714 & 0.3333 & & 0102 & 0.8750 & 0.2500 \\  & 0301 & 0.2857 & 0.2667 & \multirow{2}{*}{\(V\)} & 0108 & 0.1250 & 0.2500 \\  & 0101 & 0.1429 & 0.4000 & & 0409 & 0.100 & 0.5000 \\ \hline \multirow{2}{*}{\(NC\)} & 0102 & 0.6670 & 0.5000 & & 0403 & 0.4286 & 0.3049 \\  & 0501 & 0.3330 & 0.5000 & & 0301 & 0.2857 & 0.1848 \\ \hline \multirow{2}{*}{\(K\)} & 0101 & 0.5000 & 0.5000 & & 0103 & 0.1429 & 0.2054 \\  & 0501 & 0.5000 & 0.5000 & & 0404 & 0.1429 & 0.3049 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Frequency ratio of failure modes and influence degree of failure modes of each component of machining center. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & \(R_{I_{i}}\) & **Component** & \(R_{I_{i}}\) \\ \hline \(V\) & 0.00003 & G & 0.00001 \\ \(W\) & 0.00003 & J & 0.00011 \\ \(K\) & 0.00008 & S & 0.00002 \\ \(NC\) & 0.00005 & M & 0.00010 \\ \(L\) & 0.00004 & & \\ \hline \hline \end{tabular}
\end{table}