## 5 Conclusions  
Aiming at the problems that the failure of engineering system is difficult to predict and the accurate statistics are lack, this paper presented the fuzzy Markov method integrating the fault tree analysis, fuzzy comprehensive evaluation and the Markov model. The method, comprehensively taking the normal operation, faults, maintenance, maintenance tests and periodic tests of the system into consideration, evaluate the availability, reliability index and the impact of uncertainty on system reliability. The proposed method was validated by the subsea wellhead connector. The results of the study of the subsea wellhead connector proved the benefits of the proposed methodology in general. Compared with other traditional methods, the fuzzy Markov can not only analyze risks, reliability, availability and maintainability, but also obtain unknown failure data. Moreover, the analysis of uncertainties was improved significantly. As shown in the discussion and results, the availability and reliability curves of the wellhead connector, the impacts of different components on system availability and the mean time to failure are obtained. According to the impact analysis, relevant recommendations for reliability design and relatively effective methods to improve system availability can be obtained. Most importantly, the model can update the system reliability according to the type of accident when the uncertainty occurs, which cannot be achieved by traditional methods. The analysis results obtained from this study can be provided as the reference for risk decision-making in the wellhead connector operations. The method in this paper can be used to obtain the corresponding conclusions of other complex engineering system. The fuzzy Markov proposed in this paper takes full advantage of the fault tree, fuzzy comprehensive evaluation and Markov method to make the analysis of risk, reliability, availability and uncertainty all in one, which a single traditional method cannot do. Compared with the previous fuzzy Markov method, the method adds dynamic iteration when failure of engineering systems occurs. It can follow the system state in real time, not limited to a fixed fuzzy range and any sets of cases, and can classify the uncertainties of different failure modes in different states of the system. According to the occurrence and severity of the uncertain problems, it can iterate the \"Failure Cause Probability\" of the corresponding failure mode, and update the real-time risk and reliability prediction model, which is more convenient and accurate for solving the uncertain problems of the engineering systems. This paper assumes that the maintenance rate is constant. A future scope of the work can be directed toward the evaluation of the maintenance rate of engineering system, and more specific results can be obtained by referring to the method in this paper with specific maintenance rates. Conceptualization, N.P. and P.L. ; Data curation, P.L. ; Formal analysis, F.Y. ([PERSON]) and X.W. ; Funding acquisition, P.J. and L.W. ; Investigation, N.P. and F.Y. ([PERSON]); Methodology, N.P. and P.J. ; Resources, P.J. ; Validation, F.Y. ([PERSON]), L.Z. and L.W. ; Writing--original draft, N.P. ; Writing--review and editing. P.J. and F.Y. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This work was supported by the National Key Research and Development Program of China (grant number 2018 YFC0310500); the High-Tech Ship Research Projects Sponsored by the Ministry of Industry and Information Technology (grant number 2018 GXB01); Fundamental Research Funds for the Central Universities (grant number 3072019 CF0705); the School Land Integration Development Project of Yantai (grant number 2019 XDRIXMPT29); National Natural Science Foundation of China (grant number 51779064); the Science and Technology Projects Sponsored by the West Coast of Qingdao New District (grant number 2019-157-2018-1-1); Fundamental Research Funds for the Central Universities, grant number 3072020 CFT0702.