# Reliability Prediction and FMEA of Loading and Unloading Truss Robot for CNC Punch
## 3 Results
### Reliability Prediction
#### 3.2.2 Reliability Prediction of Mechanical System and Pneumatic System
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**System** & **Cut Set** & **Complexity** & **Technical Level** & **Working Hours** & **Environmental Conditions** \\ \hline \multirow{8}{*}{M} & 0 & (7.50, 9.50) & (1.13, 2.49) & (6.27, 8.27) & (3.99, 5.99) \\  & 0.2 & (7.70, 9.30) & (1.20, 2.29) & (6.47, 8.07) & (4.19, 5.79) \\  & 0.4 & (7.90, 9.10) & (1.27, 2.09) & (6.67, 7.87) & (4.39, 5.59) \\  & 0.6 & (8.10, 8.90) & (1.35, 1.89) & (6.87, 7.67) & (4.59, 5.39) \\  & 0.8 & (8.30, 8.70) & (1.42, 1.69) & (7.07, 7.47) & (4.79, 5.19) \\  & 1 & (8.50, 8.50) & (1.49, 1.49) & (7.27, 7.27) & (4.99, 4.99) \\ \hline \multirow{8}{*}{P} & 0 & (1.76, 3.76) & (2.81, 4.81) & (8.05, 9.86) & (6.08, 8.08) \\  & 0.2 & (19.36, 3.56) & (3.01, 4.61) & (8.25, 9.70) & (6.28, 7.88) \\  & 0.4 & (21.6, 3.36) & (3.21, 4.41) & (8.45, 9.54) & (6.48, 7.68) \\  & 0.6 & (2.36, 3.16) & (3.41, 4.21) & (8.65, 9.37) & (6.68, 7.48) \\  & 0.8 & (2.56, 2.96) & (3.61, 4.01) & (8.89, 9.21) & (6.88, 7.28) \\  & 1 & (2.76, 2.76) & (3.81, 3.81) & (9.05, 9.05) & (7.08, 7.08) \\ \hline \multirow{8}{*}{E} & 0 & (6.45, 8.45) & (5.57, 7.57) & (8.33, 10.00) & (1.00, 2.27) \\  & 0.2 & (6.65, 8.25) & (5.77, 7.37) & (8.53, 9.87) & (1.05, 2.07) \\  & 0.4 & (6.88, 8.05) & (5.97, 7.17) & (8.73, 9.73) & (1.11, 1.87) \\  & 0.6 & (7.05, 7.85) & (6.17, 6.97) & (8.93, 9.60) & (1.16, 1.67) \\  & 0.8 & (7.25, 7.68) & (6.37, 6.77) & (9.13, 9.46) & (1.22, 1.47) \\  & 1 & (7.45, 7.45) & (6.57, 6.57) & (9.33, 9.33) & (1.27, 1.27) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(\lambda\) cut set of each system evaluation factor. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cut Set** & \(\frac{\vec{\omega}^{1}}{\omega^{2}+\omega^{2}+\omega^{3}+\omega^{2}}\) & \(\frac{\vec{\omega}^{2}}{\omega^{2}+\omega^{2}+\omega^{3}+\omega^{2}}\) & \(\frac{\vec{\omega}^{3}}{\omega^{4}+\omega^{2}+\omega^{3}+\omega^{2}}\) & \(\frac{\vec{\omega}^{4}}{\omega^{2}+\omega^{2}+\omega^{3}+\omega^{2}}\) \\ \hline
0 & (0.189, 0.624) & (0.164, 0.576) & (0.088, 0.400) & (0.076, 0.336) \\
0.2 & (0.228, 0.569) & (0.194, 0.524) & (0.109, 0.358) & (0.090, 0.297) \\
0.4 & (0.267, 0.514) & (0.224, 0.472) & (0.129, 0.317) & (0.103, 0.259) \\
0.6 & (0.306, 0.459) & (0.255, 0.420) & (0.150, 0.275) & (0.117, 0.221) \\
0.8 & (0.346, 0.404) & (0.285, 0.367) & (0.170, 0.233) & (0.131, 0.183) \\
1 & (0.349, 0.349) & (0.315, 0.315) & (0.191, 0.191) & (0.145, 0.145) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Fuzzy weight \(\lambda\) cut set of evaluation factors for loading and unloading truss robot for CNC punch. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**System** & **Score Centroid Value** & **Scoring Factor** & **MTBF Value (h)** & **Failure Rate (1/h)** \\ \hline Mechanical system & 1.840 & 0.867 & 2756.319 & \(3.628\times 10^{-4}\) \\ Pneumatic system & 1.797 & 0.847 & 2691.464 & \(3.715\times 10^{-4}\) \\ Electrical control system & 2.122 & 1.000 & 3179.145 & \(3.146\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The expected MTBF of each system of the loading and unloading truss robot for CNC punch. According to Table 8, the total failure rate of the loading and unloading truss robot of the CNC punch press is 1.049 \(\times\) 10\({}^{-3}\) (1/h), that is, the total MTBF value is 953.289 h.