The fault transitivity of machining center components causes their fault propagation indexes to demonstrate dynamic time variability, which affects their importance. The method proposed in this study overcomes the biases of existing methods of evaluating the importance of system components, as they are mostly based on single indexes; the fault propagation probability and fault propagation risk are selected to perform a comprehensive evaluation. This study first establishes a network hierarchical structure model for machining center components, and the degree of influence of fault propagation among the components is calculated. On this basis, the improved adjacent spreading paths (ASP) algorithm is used to calculate the fault propagation index of each component; from the two perspectives of fault propagation probability and fault propagation risk, an evaluation mechanism involving the combined variable weight is used to comprehensively evaluate components’ importance. Taking a certain type of machining center as an example, through a comparison with ranking results from other node importance methods, it is verified that the proposed method can more effectively distinguish the differences in the importance of each component, thus illustrating the effectiveness and practical value of this method.