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Manufacturing tolerances as well as measuring errors have a great influence on products designed by optimization technique, etc., to improve their characteristics and reduce the production cost. Therefore, tolerance analysis technique is required to find the tolerance band of design variables for minimizing the effect and estimating the characteristic distribution of the products. This paper represents the torque characteristics considering the manufacturing tolerance of an electric machine. In order to analyze the tolerance of the brushless DC (BLDC) motor, stochastic response surface methodology (SRSM), which treats input data as stochastic variables, is introduced. It can analyze the tolerances from the electrical point of view and find a robust optimal solution that has insensitive performance on its change of the design variables by applying the optimization technique. A surface permanent-magnet BLDC motor is used to confirm the validity of this method. It must be noted that the statistical torque characteristics analyzed by SRSM has a great advantage in the design and manufacture stage over conventional method.