In order to overcome the locality defects in the reliability analysis of dam structural systems and account for the variation of influencing factors in the entire failure domain, a global correlation coefficient was constructed to replace the approximate linear correlation coefficient based on the global importance assessment of stochastic influencing factors in dam structure reliability. A global measurement method for the correlation between different failure modes was proposed, and the TIS-MCS method was employed to achieve the quantitative analysis of global correlation. Through an engineering case study, the system reliability of a dam structure under multiple failure modes obtained using the global correlation measurement method was compared with results from other methods. The results indicate that the system reliability obtained using the global correlation measurement method is more reasonable, providing a new approach for the reliability analysis of dam structural systems.