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• Local and global reliability sensitivity analyses are conducted for robotic manipulators. • A novel analytical framework is proposed for computing Local and global reliability sensitivity. • Uncertainty propagation formula on motion groups is introduced to determine distribution parameters of the pose error. • Chi-square approximation and expectation propagation technique are explored to compute system kinematic reliabilities. • The proposed framework is highly efficient and accurate. This paper develops a novel analytical framework for system kinematic reliability sensitivity analysis of robotic manipulators, which can provide the analytical results of local and global reliability sensitivity defined on the pose and position errors. First, uncertainty analysis of the pose error of the end-effector is accomplished by virtue of the second-order closed-form error propagation formula on motion groups. Then, the system kinematic reliability, namely the probability of the system kinematic error located within the prescribed safe boundary, is analytically calculated. Specifically, the non-central chi-square approximation and expectation propagation technique are employed to compute the system kinematic reliability defined on the position and pose errors, respectively. On this basis, the local and global system kinematic reliability sensitivity of robotic manipulators are analytically obtained. Finally, the effectiveness of the proposed method is validated by comparison with the Monte Carlo simulation and Kriging modeling method. The results indicate the proposed method has good efficacy and efficiency in system kinematic reliability sensitivity analysis for robotic manipulators. [ABSTRACT FROM AUTHOR]