## 4 Case Studies
### Reliability Uncertainty Analysis on an AEPS
#### 4.2.2 Calculation and Analysis  
Aircraft are routinely inspected systematically every 1000 h, so \(T=1000\) was set here. The results of the importance measure indicators of these eleven components computed \begin{table}
\begin{tabular}{c c c c c} \hline
**Component** & **Function** & **Mode of \(\lambda_{mode}\) (1/H)** & **Low Limit of \(\lambda_{lower}\)** & **Upper Limit of \(\lambda_{upper}\)** \\ \hline TB/GB & \begin{tabular}{c} Current Relay, Contactor \\ and Breaker \\ AC Power Source \\ Direct power distribution \\ to AC loads \\ \end{tabular} & \begin{tabular}{c} 1.33 \(\times\) 10\({}^{-5}\) \\ 5.56 \(\times\) 10\({}^{-5}\) \\ 5.00 \(\times\) 10\({}^{-6}\) \\ 5.00 \(\times\) 10\({}^{-6}\) \\ \end{tabular} & \
\begin{tabular}{c} 1.0 \(\times\) 10\({}^{-5}\) \\ 5.00 \(\times\) 10\({}^{-5}\) \\ 5.00 \(\times\) 10\({}^{-5}\) \\ 5.00 \(\times\) 10\({}^{-6}\) \\ \end{tabular} &
\begin{tabular}{c} 9.9 \(\times\) 10\({}^{-5}\) \\ 5.9 \(\times\) 10\({}^{-5}\) \\ 5.9 \(\times\) 10\({}^{-6}\) \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 3: Failure rate of each component of the AEPS system. through the proposed algorithm are presented in Table 4. From the perspective of the rationality and the engineering application value, the results are discussed. (1) In order to verify the correctness of the proposed method and the significance of the proposed importance measure index to the improvement of system reliability in the design stage, the system was optimized according to the results in Table 4.  
Table 4 shows that components LG BUS and BTB1 contributed most to the uncertainty of power supply reliability of the sink node LG BUS, followed by components LGB and LG. The importance measure indicator values of these four components were 0.3803, 0.3636, 0.1306, and 0.097, respectively, and the total value of the four indicators was 0.97, which means that the contribution of the four components to the power supply reliability uncertainty of the sink node s had the ratio of 0.97. In contrast, the other seven components only contributed 0.023 to the uncertainty of power supply reliability. Therefore, in order to reduce the power supply reliability uncertainty, reducing the failure uncertainty of LG BUS and BTB1 should be the first solution to optimize the system, and if the reliability uncertainty of the optimized system is still high, reducing the failure uncertainty of these four components LG BUS, BTB1, LGB, and LG can also be a good solution. In Table 5, five system reliability improvement/optimization solutions are put forward. As a system reliability optimization measure, reselecting components of less fluctuation in failure rate with flight environment changes means replacing the previous original components with new but the same functional components of more stable performance, which inevitably increases the procurement cost. For the convenience of the analysis, it was assumed that the failure rate of the new, more stable reselected component in each solution did not vary with the flight environment and was a constant value that equaled \(\lambda_{mode}\) in Table 3, while the failure rates of the remaining components still followed the previous triangular distribution. In fact, it is impossible for the component failure rate to remain unchanged with the flight environment, which is an extreme assumption made here to more significantly demonstrate the validity of the proposed method in this paper. The Monte Carlo simulation method was used to compute the power supply reliability of the sink node LG BUS under the five system reliability improvement solutions, and the results are shown in Table 6 and Figure 6. In Table 6, \"Importance degree\" refers to the proposed importance measure index of each component, which quantifies the contribution