Performing probabilistic analyses on a complex structure is challenging with a high computational burden, owing to the many components and multiple disciplines involved, with high nonlinearity and many hyperparameters. Despite the advancements in surrogate models, they are still insufficient to accurately model compound functions with many sub-layers and sub-functions. In this paper, we propose the decomposed-coordinated surrogate model method (DCSMM) to improve the modeling accuracy and efficiency of compound functions. This improvement will enable performing expensive probabilistic analyses, which typically involve thousands of Monte Carlo simulation runs, efficiently. This type of analysis would be too computationally expensive to perform when using full-scaled models. The proposed DCSMM uses the decomposition and coordination strategy, and combines it with surrogate modeling methods. In this work, we establish the mathematical model of the DCSMM with quadratic polynomial (QP) and Kriging model, and develop QP-DCSMM (the DCSMM based on QP), K-DCSMM (the DCSMM based on Kriging) and M-DCSMM (the DCSMM based on the mixture of QP and Kriging). The approximation accuracy and simulation performance (including computational precision and efficiency) of the DCSMM are demonstrated with an analytical model and a turbine blisk multi-failure modes of an aeroengine as an engineering case study. The proposed DCSMM is demonstrated to be effective in modeling the high-nonlinearity between output response and input variables, in addition to being robust. These benefits become even more prominent as we increase the number of Monte Carlo simulation runs. Overall, this study shows a high-efficiency and high-precision approximation method for complex compound functions and complex structures. This contribution will further enrich the theory and application of probabilistic statistical analysis as well. This paper also offers useful insights into engineering optimization and reliability design pertaining to multi-model mechanical systems.