## 6 Conclusions  
In this paper, the reliability of redundant systems of offshore wind turbines considering component swapping is assessed. Survival signature-based component swapping is introduced to express the new structure-function of redundant systems after swapping. FT based reliability model considering component swapping is proposed to obtain the realistic reliability assessment of redundant systems. Moreover, both marginal reliability importance index and joint reliability importance index of critical components with and without swapping are calculated to explore the influences of component swapping on component reliability importance and rank the importance of individual components. The effects of the imprecision of failure rates on component reliability importance are also studied. Considering component swapping can significantly improve system reliability, which is shown in Figure 10. Furthermore, as shown in Figure 11, the improvement (\(\Delta R_{sys}(t)\)) of system reliability is increasing first and then decreasing with the increase of time \(t\). The \(\Delta R_{sys}(t)\) obtains the maximum value (0.0551) at time \(t=8800\) h. The influences of different swapping components on system reliability are explored, and the findings show that swapping components of Type 1 (the temperature sensor) is the \"best\" option of swapping strategies, which means that the location of components of Type 1 is more important than that of other types (the cooling fan and the cooling pump). Therefore, components of Type 1 should be allocated more resources for repair, maintenance and inspection than other components. To quantify the importance degree of critical components, the marginal reliability importance measure and joint reliability importance measure without and with swapping are performed. The findings show that considering component swapping decreases component reliability importance (MRI and JRI). The importance degrees of individual and a couple of components are ranked to help conduct an optimal allocation of resources for operation and maintenance. The ranks of the MRIs of individual components without swapping are MRI(28;\(t\)) \(>\) MRI(5;\(t\)) \(>\) MRI(30;\(t\)) \(>\) MRI(29;\(t\)) \(>\) MRI(45;\(t\)) \(>\) MRI(47;\(t\)). The ranks of the JRIs of components without and with swapping are the same JRI\({}^{(w)}(5,28;t)>\) JRI\({}^{(w)}(29,45;t)>\) JRI\({}^{(w)}(30,47;t)\). The lower and upper bounds of MRI and JRI of components at a given time \(t\) are obtained. The results indicate that the proposed method is a practical and efficient method to perform reliability analysis of redundant systems considering component swapping and examine component reliability importance. In future work, we intend to establish a reliability optimization model considering constraints of the number, cost, weight, and volume of redundant components and explore the optimal swapping strategy for the improvement of system reliability of offshore wind turbines. Conceptualization, Y.L. ; methodology, Y.L. and C.Z. ; software, C.Z. ; validation, Z.W. and Y.L. ; formal analysis, C.Z. ; investigation, Y.L. ; resources, C.Z. ; data curation, Z.W. ; writing--original draft preparation, Y.L. ; writing--review and editing, C.Z. ; visualization, Z.W. ; supervision, C.Z. ; project administration, C.Z. ; funding acquisition, C.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key R&D Program of China (Grant No. 2018 YFB1501300), Chongqing Innovation and Application Program (Grant No. cstc2019 jscx-mbdx30003), and Central University Basic Scientific Research Project of Chongqing University (Grant No. 2019 CDCGJX0017). The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} \(SWO\) & switch does not fail open \\ \(SWQ\) & switch does not fail in the quiescent mode \\ \(SE\) & sensing subsystem \\ \(1E\) & component 1 in the energized mode \\ \(SWC\) & switch does not fail closed \\ \end{tabular}