A kinematic model considering joint clearance is developed for the variable stator vane (VSV) adjustment mechanism of an aero-engine. A reliability model of the mechanism’s kinematic accuracy is constructed considering the failure correlation among stator vanes, as well as the stochastic nature of driving errors, dimensional tolerances, and assembly clearances. Based on the BP neural network (BPNN) surrogate model, the mechanism’s reliability is evaluated through Monte Carlo simulation. The effects of the number of stator vanes and the failure threshold on the system’s reliability are investigated. Compared with the system model of the unit failure independent assumption and the complete correlation, the mechanism system kinematic accuracy reliability model considering failure correlation is more reasonable. Lastly, a method for estimating the complex system’s reliability error caused by surrogate model approximation is proposed, and the accuracy and credibility of the VSV adjustment mechanism’s reliability assessment are confirmed.