## 1 Introduction  
As one of the technical supports for the development of modern intelligent manufacturing, real-time monitoring of the running state of the CNC lathe, rapid identification of key components and tracking the root cause of the fault are effective measures to reduce the probability of fault, improve the reliability level and reduce the maintenance cost [1]. As a complex integrated system, CNC lathe components are associated with each other [2], creating favorable conditions for fault propagation and increasing the difficulties of fault identification and tracking [3]. Therefore, considering the dynamic influence of fault propagation and identifying the key components of the system in real time is of great significance to improve the efficiency of fault diagnosis, control the fault propagation and improve the operation reliability of the lathe. At present, the research methods of key component identification mostly focus on the \"importance measure\" [4], which is manifested as the component importance measure and the node importance measure. The importance measure of components based on system reliability theory mostly uses \"expert knowledge and experience\" to construct a function-oriented system structure model by using fault tree [5], event tree [6] and other methods [7,8]; then, the importance measure is built by combining the reliability index of components to identify key components. Typical methods include Birnbaum importance degree [9], conditional marginal reliability importance (CMRI) [10], integrated importance measure (IIM) [11] and improved-PageRank (IPR) [12; 13]. Although this method is widely used, there are still some defects, such as that the system functional structure modeling cannot fully reflect the system topological structure and the interdependence of system components, which affects the accuracy of identification results. The node importance measure is based on the complex network theory [14], according to the objective law that the essence of any system is the network, the physical structure of the system is abstracted into a topological network model and the key components of the system are evaluated by degrees [15], centrality [16; 17], eigenvectors [18], centrality [19] and degree of cohesion [20]. Although the node importance measure can clearly represent the system structure and its coupling relationship, it only analyzes the topological status of components in the system [21], but does not consider the influence of reliability attributes of components on the system. The component importance measure and the node importance measure are both single measures to identify key components, which may be affected by randomness, uncertainty and different emphasis, resulting in different results in identifying key components with different measures [22], and have disadvantages such as limited application scope and incomplete evaluation results. Therefore, some researchers have proposed to identify key components in the system by integrating multiple importance measures from the perspective of multi-attribute decision making [23]. Commonly used multi-index comprehensive evaluation methods include entropy weight method [24], technique for order preference by similarity to an ideal solution (TOPSIS) [25], grey relation analysis (GRA) [26], etc. Although this method solves the problem of identification deviation of a single measurement, it is mostly a synthesis of the same type of measure, and lacks the recognition from the perspective of the combination of system function and topological structure, and the weight distribution of each index should be considered emphatically.