The rotary vector (RV) reducer is one of the widely used mechanical components in industrial systems, specifically in robots. The stability of the transmission performance of the RV reducer is crucial for the efficient operation of industrial equipment. The manufacturing and assembly errors of various components of the RV reducer during the production process are important factors that affect the transmission performance. However, in previous research work, the coupling effect of multiple errors on the transmission accuracy of RV reducer has not been fully considered. Furthermore, a vague relationship between system transmission errors and various errors also has not been thoroughly discussed, which presents a challenge to analyze and optimize the errors of components using the simulation technology of virtual prototype. Therefore, we propose a novel approach to use the response surface method (RSM) to investigate the transmission accuracy of RV reducer. Firstly, based on the constructed virtual prototype of RV reducer, the individual effects of different original errors on the overall transmission error are analyzed. Secondly, a response surface approximation model using RSM is constructed to analyze the effect of multiple error interactions on the transmission accuracy of the RV reducer, and the potential functional relationship between multiple error factors and the overall transmission error is also explored. Finally, the authenticity of the proposed approach is verified by setting up some comparative experiments. This study provides a reference for the efficient analysis and optimization of the transmission accuracy of RV reducers.