# A Comprehensive Failure Risk Assessment Method of
## 2 Comprehensive Risk Assessment of the Machining Center Component Based on Topological Analysis
### Calculation of Independent Failure Risk of Machining Center Component Based on ANP
#### 2.1.2 ANP-Based Calculation of Influence Degree of Failure Mode of Machining Center Component  
Different failure modes cause different levels of failure damage to components, and the same failure mode has different effects on different components, and there is a certain correlation between the failure modes. That is, the occurrence of one failure is likely to cause the occurrence of another failure, for example, the loosening of the locking component will cause the component to fall off. Therefore, based on the analysis of the failure mode of the machining center, considering the correlation of the failure mode, a correlation analysis method ANP is introduced to calculate the failure mode influence degree of the component.  
ANP was proposed by Professor [PERSON] of the University of Pittsburgh in 1996 and is widely used in many fields such as politics, economy, society, and management. The advantage of ANP is that it abandons the assumption of independence between each element and considers the mutual influence between the elements within the hierarchy, using the form of proportional scale to quantify the correlation between elements by a specific value. Therefore, the use of ANP can combine qualitative and quantitative methods,which can meet the needs of correlation analysis between failure modes of machining centers. A typical ANP model is shown in Figure 3.  
The basic steps of the ANP method are as follows:  
(1) Correlation analysis of elements  
Figure 3: Typical ANP model.  
Figure 2: Block diagram of the calculation of the failure mode frequency ratio of the machining center.  
The objective problem is analyzed and then considers whether there is an interdependent relationship between the elements.  
(2) Construction of network hierarchical model  
Generally, the elements are divided into two layers. The first one is the control layer or the target layer, which refers to the decision-making criterion. At least one criterion should exist. The second is the network layer, which contains all elements and is governed by the control layer. The elements have an interdependent relationship.  
(3) Construction of judgment matrix  
The elements are compared in pairs to construct the judgment matrix. The judgment matrix is usually quantified on a scale of 1-9, as shown in Table 1. Experts compare elements in different situations based on experience and give different quantitative levels.  
(4) Construction of unweighted matrix and weighted matrix  
The unweighted matrix \(\mathbf{w}\) is derived by comparing the elements in pairs. Each column in the matrix, a sorting weight is based on a certain element. For the convenience of calculation, each column of the unweighted matrix needs to be normalized to obtain the weighted matrix \(\mathbf{W}_{ij}\left(\mathbf{W}_{ij}=a_{ij}w_{ij}\right)\).  
(5) Establishment of a super-limit matrix  
The size of the weighted matrix element \(\mathbf{W}_{ij}\) reflects the one-step dominance of element \(i\) to element \(j\). Similarly, through the multi-step self-multiplication of the matrix, a super limit matrix that tends to be stable is obtained. There is only one value corresponding to each element in the matrix, that is, the final influence degree of the element, which is the failure mode influence degree \(\beta_{ij}\) sought in this paper.  
Since the ANP model is a network model, the final super matrix calculation is complicated; thus, the ANP analysis method generally chooses to use the matching Super Decisions software or calculation program to assist in the calculation.