A method to evaluate the position performance for a stochastically defined planar robot manipulator is presented. Performance is defined as the operational reliability based upon the positional errors of the manipulator tip. An analytical method is developed and applied to a two-link robot manipulator through forward kinematics. This study includes uncertainties in the link length, pin center location and radial clearance. By virtue of the effective link length model, only the nominal manipulator model and statistical information on the uncertainties are required. The results from the analytical method is compared to those from the Monte Carlo simulation.