In order to study the influence of the dimension error of the connecting rod and the angular deviation of the joint on the end-path accuracy of the series robot, the Denavit-Hartenberg(D-H) method is used to establish the reliability model of the end-path accuracy of the robot. Considering that the exact probability distribution of some variables is difficult to obtain and there is cognitive uncertainty, a hybrid non-probability model combining probability-box model and traditional probability model is proposed to analyze the end-path accuracy of series robot. Combined with the quasi-Monte Carlo method and nested interval analysis, the quasi interval Monte Carlo method is proposed to analyze the hybrid reliability model. The case application shows that the proposed method converges faster than the traditional Monte Carlo method, requires less computing resources, and the established model is closer to engineering practice.