## 3 Reliability Sensitivity Analysis of Emergence Extension
### Reliability Analysis
#### 3.1.2 Reliability Analysisof Emergency Extension Based on Fault Tree  
With regard to the reliability model, the failure probability \(\mathrm{P}_{Xi}\) of \(i\)th bottom event \(\mathrm{X}_{i}\) can be calculated quantitatively when the NLG emergency extension cannot be lowered at different flight speeds. According to engineering experiments, we find that the maximum failure of bottom event \(\mathrm{X}_{1}\) occurs at [\(0^{\circ}\), \(2.66^{\circ}\)]. Therefore, we only consider the starting failure probability of the emergence extension mechanism as the failure probability of bottom event \(\mathrm{X}_{1}\) in this paper. The results on the failure probability \(\mathrm{P}_{Xi}\) under different flight speeds (\(270\) Kts, \(250\) Kts, \(220\) Kts and \(180\) Kts) are shown in Table 4.  
As shown in Table 4, the failure probability of the top event (emergence extension) increases with the decreasing flight speed. When the flight speed is at \(180\) Kts, the failure probability increases to the maximum \(6.6256\times 10^{-5}\). The main reason is that the strut aerodynamic torque of landing gear and the aerodynamic torques of forward and after doorsreduce with the decline of the flight speed. In this condition, the total torque of NLG and the angular acceleration of the rotating axis drop. Therefore, when the emergency extension of NLG is put down, a large angular velocity is obtained for the rotating axis due to large flight speeds, besides smaller failure probability for emergency extension. In other words, low flight speed and angular velocity obtained against the rotating shaft will lead to larger failure probability of emergency extension.  
From the above analysis, it is seen that the starting reliability is the main factor influencing the failure probability of emergency extension. Therefore, the sensitivities of the nine torques on starting reliability were discussed to determine the specific influence of torques on the start reliability of emergence extension system.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Failure Probability**} & \multicolumn{6}{c}{**Flight Speed**} \\ \cline{2-7}  & **270 Kts** & **250 Kts** & **220 Kts** & **180 Kts** \\ \hline \(\mathrm{P}_{\mathrm{X1}}\) & \(1.2728\times 10^{-5}\) & \(2.2401\times 10^{-5}\) & \(4.0683\times 10^{-5}\) & \(6.1819\times 10^{-5}\) \\ \(\mathrm{P}_{\mathrm{X2}}\) & & & \(5.7905\times 10^{-8}\) & & \\ \(\mathrm{P}_{\mathrm{X3}}\) & & & \(5.7026\times 10^{-8}\) & & \\ \(\mathrm{P}_{\mathrm{X4}}\) & & & \(5.7026\times 10^{-8}\) & & \\ \(\mathrm{P}_{\mathrm{X5}}\) & & & & \(4.2655\times 10^{-6}\) & & \\ \(\mathrm{P}_{\mathrm{T1}}\) & \(1.7165\times 10^{-5}\) & \(2.6838\times 10^{-5}\) & \(4.5120\times 10^{-5}\) & \(6.6256\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Failure probability of bottom events in fault tree.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Torques** & \(\mathbf{M_{1}}\) & \(\mathbf{M_{2}}\) & \(\mathbf{M_{3}}\) & \(\mathbf{M_{4}}\) & \(\mathbf{M_{5}}\) & \(\mathbf{M_{6}}\) & \(\mathbf{M_{7}}\) & \(\mathbf{M_{8}}\) & \(\mathbf{M_{9}}\) \\ \hline Variable coefficient \(C_{i}\) & 0.03 & 0.03 & 0.08 & 0.03 & 0.03 & 0.03 & 0.08 & 0.08 & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Variable coefficients of nine torque.