Geometric parameter calibration is an effective method to improve the end-effector positioning accuracy of industrial robots, which directly affects operational precision, product quality, and production safety. It is significant to analysis and study on the positioning accuracy reliability of calibrated robots. Firstly, an MDH model is established and the axis measurement method is developed to calibrate the robot geometric parameters in this paper. Secondly, the positioning accuracy reliability is analyzed and formulated, and robot positioning accuracy reliability analysis method based on AMCS is proposed. Finally, calibration experiments are conducted on Staubli TX60 robot using Leica AT960 laser tracker under uncertain factors affected by measurement repeatability, joint motion ranges, joint motion step sizes, joint motion velocities, etc. Experimental results demonstrate that the proposed AMM improves the robot′s positioning accuracy by approximately 22.9%, verifying its effectiveness for geometric parameter calibration. In the meantime, AMCS and MCS are used to calculate the positioning accuracy reliability of calibrated robot under the influence of different measurement factors. The results show that joint motion range, joint motion speed, and measurement repeatability significantly impact the reliability of robot positioning accuracy. When the numerical tolerance values are set to 0.01 and 0.02, he probability distribution function (PDF) characteristics of positioning accuracy reliability obtained by AMCS exhibit maximum relative errors of only 1.1% and 1.9%, respectively, compared with MCS, while computation times are reduced to about 1/4 and 1/9 of MCS. It has been confirmed that the proposed AMCS can control the convergence speed and accuracy of the algorithm by setting different numerical tolerances, providing an efficient and reliable tool for analyzing the positioning accuracy reliability of calibrated robots. It is suitable for practical engineering applications in robot calibration and reliability evaluation.