Abstract: Based on the concept of system response, this paper analyzes the open-chain industrial robot with N degrees of freedom which is divided into several systems in series or parallel connections. By analysies, the error transmission relation of these systems is found out and the conicept of system response of error is presented. In the paper, a probability approach is adopted to set up a mathematical model for analysis and optimal distributions of accuracy of the industrial robot. Meanwhile, the distributions of hand error and all kind of initial random errors resulting in hand error are preliminarily analyzed. Finally, as an example, an assembling robot with five degrees of freedom is designed by the probability approach.