## 5 Robust Failure Mode Definition and Formulation of Multiple Resource Replacement Strategies  
### Definition of Failure Modes for Robustness Analysis  
The definition of failure modes is the key to robustness analysis. Based on a combination of the cloud manufacturing characteristics and the spatial topology structure of the CMN, this paper proposes two types of failure modes: cloud resource failure based on the initial topology, and cloud resource failure based on the recomputed topology.  
The initial topology refers to the initial structural characteristics of the CMN, which is a static network. The recalculated topology refers to the structural characteristics of the CMN that are obtained through recalculation after the initial network is attacked, which is a dynamic network that changes step by step with the attack steps.  
Both failure modes are subdivided into degree-based and betweenness-based resource failures. The degree is widely used to measure the importance of the nodes: it represents how closely a resource node is connected to other resource nodes in the CMN. The betweenness reflects the structural importance of the nodes in the network [46; 47]: a node with high betweenness has greater control over the logistics and information flow in the network. The specific failure mode definitions are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Failure Mode** & **Failure Mode Calculation Process** \\ \hline \multirow{6}{*}{Resource failure based on initial topology} & Initial node degree & Sort the resource nodes in the initial network (Network-0) by degree, from largest to smallest. Remove one node at a time, and repeat a times until all nodes in the network are removed. \\  & loss (ID) & Sort the resource nodes in the initial network (Network-0) by betweenness, from largest to smallest. Remove one node at a time, and repeat a times until all nodes in the network are removed. \\  & & Sort the resource nodes in the initial network (Network-0) by degree, from largest to smallest. Remove the first node and generate a new network (Network-1). Recalculate and sort the resource nodes in the new network (Network-2) by degree, from largest to smallest. Remove the first node and generate a new network (Network-2)... and so on, until all nodes in the network are removed. \\  & & Sort the resource nodes in the initial network (Network-0) by betweenness, from largest to smallest. Remove the first node and generate a new network (Network-1). Recalculate and sort the resource nodes in the new network (Network-1) by betweenness, from largest to smallest. Remove the first node and generate a new network (Network-2)... and so on, until all nodes in the network are removed. \\ \hline \hline \end{tabular} Note: The removal of nodes is handled differently in the complex network model and the multi-agent model: (1) In the complex network model, the corresponding resource nodes and all connected edges on the nodes are deleted. (2) In the multi-agent model, the corresponding resource agent is changed to a “fault” state, which means the resource is unable to provide services.  
\end{table}
Table 1: Resource failure based on initial topology and recomputed topology.