## 4 Case Studies
### Reliability Uncertainty Analysis on an AEPS
#### 4.2.2 Calculation and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \(\hat{\eta}_{1}^{2}\) & \(\hat{\eta}_{2}^{3}\) & \(\hat{\eta}_{3}^{2}\) & \(\hat{\eta}_{4}^{2}\) & \(\hat{\eta}_{5}^{2}\) & \(\hat{\eta}_{6}^{2}\) & \(\hat{\eta}_{7}^{2}\) & \(\hat{\eta}_{8}^{2}\) & \(\hat{\eta}_{9}^{2}\) & \(\hat{\eta}_{10}^{2}\) & \(\hat{\eta}_{11}^{2}\) \\ \hline Component & LG & LGB & LG BUS & BTB1 & APUG RUS & APUG & BTB2 & RG BUS & RGB & RG \\ Importance & 0.097 & 0.1306 & 0.3803 & 0.3636 & 0.0031 & 0.0061 & 0.0053 & 0.0026 & 0.0006 & 0.0029 & 0.0024 \\ Ranking & 4 & 3 & 1 & 2 & 7 & 5 & 6 & 9 & 11 & 8 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation of the importance of the failure rate of each component of the power supply system (\(T=1000\) h). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Solution** & **Improvement Component** & **Improvement Measures** \\ \hline Solution 1 & LG BUS & Reselect component LG BUS of less fluctuation in failure rate with flight environment changes to replace the original one. \\ \hline Solution 2 & BTB1 & Reselect component BTB1 of less fluctuation in failure rate with flight environment changes to replace the original one. \\ \hline Solution 3 & BTB1, LG BUS & Reselect both components BTB1 and LG BUS of less fluctuation in failure rate with flight environment changes to replace the original ones. \\ \hline Solution 4 & LG, LGB, BTB1, and LG BUS & Reselect components LG, LGB, BTB1 and LG BUS of less fluctuation in failure rate with flight environment changes to replace the original ones. \\ \hline Solution 5 & No. 5 to No. 11 & Reselect components of No. 5 to No. 11 which have less fluctuation in failure rate with flight environment changes to replace the original ones. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Five system reliability improvement/optimization solutions. of the uncertainty of each component's failure rate to the uncertainty of the reliability of the LG BUS power supply, calculated by the method in Section 3.2; \"Mean value\", \"Variance\", and \"Confidence\" in Table 6 represent the mean, variance, and 95% confidence interval of the reliability of the original system and the five optimized systems, respectively; \"Reduction degree\" refers to the degree by which the uncertainty of system reliability is reduced after the system is optimized and because the variance can be used to characterize the degree of the system reliability uncertainty, the reduction degree can be calculated by the formula: reduction degree = 1.0-variance of the optimized system/variance of the original system; \"Improved effect ranking\" represents the improvement effect of the five solutions, which is obtained based on the data of reduction degree; and finally, \"Original\" represents the original system without any optimization measure, so the \"original\" row does not involve the data of \"Importance degree\", \"Reduction degree\", and \"Improved effect ranking\". The improvement results in Table 6 and Figure 6 are discussed from two points. First, in terms of improvement effect, all five solutions could reduce the degree of system reliability uncertainty, and it can be seen that the data in the \"Reduction degree\" column is consistent with the data in the \"Importance degree\" column. That is, the system reliability improvement effect is consistent with the importance measure index of each component, which shows that the proposed importance measure index can indeed reflect the uncertainty contribution of each component's failure rate to the system reliability uncertainty. Second, the results showed that the more components improved did not necessarily lead to a better system reliability improvement effect. This means that if there is no guidance of the importance measure index in system reliability design practice, the designers could have improved many components, but it is still difficult to achieve a good improvement effect, resulting in a longer design cycle.