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The purpose of this study is to improve the computational efficiency and accuracy of fatigue reliability analysis.

By absorbing the advantages of Markov chain and active Kriging model into the hierarchical collaborative strategy, an enhanced active Kriging-based hierarchical collaborative model (DCEAK) is proposed.

The analysis results show that the proposed DCEAK method holds high accuracy and efficiency in dealing with fatigue reliability analysis with high nonlinearity and small failure probability.

The effectiveness of the presented method in more complex reliability analysis problems (i.e. noisy problems, high-dimensional issues etc.) should be further validated.

The current efforts can provide a feasible way to analyze the reliability performance and identify the sensitive variables in aeroengine mechanisms.

To improve the computational efficiency and accuracy of fatigue reliability analysis, an enhanced active DCEAK is proposed and the corresponding fatigue reliability framework is established for the first time.

To provide valuable information for scholars to grasp the current situations, hotspots and future development trends of reliability analysis area.

In this paper, recent researches on efficient reliability analysis and applications in complex engineering structures like aeroengine rotor systems are reviewd.

The recent reliability analysis advances of engineering application in aeroengine rotor system are highlighted, it is worth pointing out that the surrogate model methods hold great efficiency and accuracy advantages in the complex reliability analysis of aeroengine rotor system, since its strong computing power can effectively reduce the analysis time consumption and accelerate the development procedures of aeroengine. Moreover, considering the multi-objective, multi-disciplinary, high-dimensionality and time-varying problems are the common problems in various complex engineering fields, the surrogate model methods and its developed methods also have broad application prospects in the future.

For the strong demand for efficient reliability design technique, this review paper may help to highlights the benefits of reliability analysis methods not only in academia but also in practical engineering application like aeroengine rotor system.