Kinematic reliability of robotic manipulators is the linchpin for restraining the positional errors within acceptable limits. This work develops an efficient reliability analysis method to account for random dimensions and joint angles of robotic mechanisms. It aims to proficiently predict the kinematic reliability of robotic manipulators. The kinematic reliability is defined by the probability that the actual position of an end-effector falls into a specified tolerance sphere, which is centered at the target position. The motion error is indicated by a compound function of independent standard normal variables constructed by three co-dependent coordinates of the end-effector. The saddle point approximation is then applied to compute the kinematic reliability. Exemplification demonstrates satisfactory accuracy and efficiency of the proposed method due to the construction and the saddle point since random simulation is spared.