The high reliability demand of the machining center emphasizes the accuracy of the fault risk evaluation. In the traditional fault risk evaluation research of the machining center, the influence of fault mode is mostly based on subjective recommendation or does not consider the propagation and diffusion of fault, which makes the risk evaluation results different from the real situation. Therefore, this paper presents a framework to evaluate the fault risk for machining center components. A certain type of machining center is considered as a case study. The fault mode frequency ratio of components is calculated by fault mode analysis. The fault rate calculation is conducted based on the Johnson method. Considering that different fault modes have different influences on fault propagation breadth and depth, the hypergraph theory is used to build a hypernetwork model. The propagation and diffusion influence degree are defined to describe the propagation and diffusion process of faults. Then, the comprehensive influence degree of fault mode is calculated. The risk evaluation is realized by considering the component fault rate, fault mode frequency ratio, and the comprehensive influence degree of fault mode. The method proposed in this paper can provide a reference for the formulation of risk strategies for the machining center.