Abstract: To evaluate the effect of failure mode correlations on the mechanical system reliability， a system reliability analysis method and its implementation procedures were proposed based on FORM approximation. FORM was used to calculate the reliabilities and sensitivities of all the failure modes in the system， and then the failure mode correlation coefficient matrix for determining how they are correlated was obtained. The solving of the system reliability model was converted to the integration of multivariate normal distributions， and the efficient approximation algorithm was used to get reliability degree. The definition of failure mode sensitivity and the corresponding calculation method were proposed based on the numerical difference， as well as the definition of random parameter sensitivity and its calculation method through the composite derivative theorem. The results demonstrated the efficiency of the proposed method for quantifying the mechanical system reliability with failure mode correlations， and also the feasibility for identifying the key failure modes and random parameters.

Key words: failure mode correlations, system reliability, reliability analysis, sensitivity analysis, correlation coefficient matrix, multi-normal integration