Aiming at the problem that the traditional statistical analysis of machining error based on single variable can not solve the influence of multiple associated variables on machining error, a machining error analysis system based on multi-dimensional random variables is proposed. The probability of effective machining error is analyzed by analyzing the correlation dimension of machining parts and establishing the distribution law of machining error with Matlab. The statistical product and service solution (SPSS) is used to carry out Q-type clustering analysis on the measured correlation dimension groups to analyze the sections where processing errors are prone to occur, and the three-dimensional point diagram method is used to analyze the systematic errors and random errors caused by the correlation dimensions; A systematic analysis model of the machining error of ring shaft parts is established. The results show that the analysis system can improve the accuracy of machining error analysis.