## 5 Component Reliability Importance
### Marginal Reliability Importance  
For the system shown in Figure 9, there are multiple components of the same type in the same location. In this study, components 5 and 28 of Type 1, components 29 and 45 of Type 2, and components 30 and 47 of Type 3 are taken as research objects. The \(\tilde{\Phi}_{1}(l_{1},l_{2},l_{3})\) and \(\tilde{\Phi}_{0}(l_{1},l_{2},l_{3})\) of each component without and with swapping are given in Tables A1-A3 in Appendix A. MRI analysis of components 5, 28, 29, 45, 30, and 47 with and without swapping is performed, the results of which are shown in Figures 13-15. The findings show that MRIs of components 5 and 28 of Type 1 are much larger than that of components 29, 45 of Type 2 and components 30 and 47 of Type 3 by comparisons of three figures. In Figure 13, the MRI of component 5 considering component swapping (MRI\({}^{w}(5;t)\)) is larger than that of component 5 without considering component swapping (MRI\((5;t)\)), which means that considering component swapping can increase the MRI of component 5. The MRI of component 28 considering component swapping (MRI\({}^{w}(28;t)\)) is much less than that of component 28 without considering component swapping (MRI\((28;t)\)), which indicates that component swapping can reduce the MRI of component 28.  
The results of Figure 14 show that the MRI of component 29 without considering component swapping (MRI\((29;t)\)) is much larger than that of the rest cases. In the inner figure of Figure 14, the MRI of component 45 without swapping (MRI\((45;t)\)) is the largest than other cases, and the MRIs of components 45 and 29 with swapping (MRI\({}^{w}(45;t)\) and MRI\({}^{w}(29;t)\)) are second and third. Therefore, considering component swapping can reduce the MRI of components 29 and 45 of Type 2. The same results also occur for components 30 and 47. As shown in Figure 15, the MRI of component 30 without swapping (MRI\((30;t)\)) is the largest than other cases, and the MRI of component 30 with swapping (MRI\({}^{w}(30;t)\)) is larger than that of component 47 without and with swapping (MRI\((47;t)\) and MRI\({}^{w}(47;t)\)). Component swapping can significantly reduce the MRI of components 30 and 47 of Type 3.  
Figure 13: MRI of components (5 and 28) with and without swapping.  
The failure rates of swapping components are uncertain due to different working conditions and random loads. In addition, manufacturers of wind turbines like to apply components from different manufacturers in wind turbines to evaluate their reliability levels and reduce the investment risk. In this paper, the influences of uncertainties of failure rates on the MRI of swapping components are explored. Let the MTBF of Type 1 components be in a interval \([25.696,48.18]\times 10^{4}\) h, MTBF of Type 2 components be in a interval \([86.724,108.405]\times 10^{4}\) h, and MTBF of Type 3 components be in a interval \([61.946,81.472]\times 10^{4}\) h. The lower and upper bounds of components MTBF reflect the best and the worst performance of the components, respectively. Using the proposed method in Section 3.2, lower and upper MRI of each swapping components can be obtained. Figure 16 presents the lower and upper MRI of components 5 and 28 with and without considering component swapping. The imprecision of components' MTBF is translated into the imprecision of MRI of components 5 and 28. The imprecision of components' MTBF greatly affects the MRI of component 28. Lower and upper MRI of components 29 and 45 of Type 2, and components 30 and 47 of Type 3 are given in Figure 17 and Figure 18, respectively. It can be seen from the figures that the uncertainties of components' MRI are increasing with the increase of time \(t\). Moreover, the MRI of components without swapping is still larger than that of components with swapping.  
Figure 14: MRI of components (29 and 45) with and without swapping.  
Figure 15: MRI of components (30 and 47) with and without swapping.