The operation error of a robot that occurs inevitably due to the manufacturing tolerance needs to be controlled within a certain range to achieve proper performance of the robot system. The reduction of manufacturing tolerance, however, increases the manufacturing cost in return. Therefore, design engineers try to solve the problem of maximizing the tolerance to reduce the manufacturing cost while minimizing the operation error to satisfy the performance requirement. In the present study, a revolute joint model considering uncertainties due to joint clearance is employed to perform a reliability analysis of the robot manipulator operation. The reliability analysis procedure employs single Monte-Carlo simulation and a statistical relation between the tolerance and the operation error. Significant reduction of computing time can be achieved with the proposed method. The present method is especially effective if sensitivity information is hard to be obtained for the analysis.