To position and orient the hand of an industrial robot to perform a particular manufacturing process, the joints are commanded to assume certain angles and/or displacements. However, due to position errors at joints, the assumed positions are almost always different from those commanded. These deviations induce a random error to the position and orientation of the hand. The ability of the hand to perform according to the required accuracy depends, among other things, on the extent of joint position errors. The effect of these errors on the accuracy of the operations are studied using a stochastic model. In addition, a procedure is suggested for determining the optimum position error to aim at in a given manufacturing situation. The results are applied to a T3type robot performing an assembly operation.