Abstract The connectivity of a network is an important indicator for assessing its reliability and fault tolerability. However, currently various kinds of connectivity do not well reflect the network’s fault tolerance when facing certain attacks such as Botnet attacks, DDoS attacks, and Local Area Network Denial attacks. Therefore, Lin et al. (A novel measurement for network reliability. IEEE Trans Comput 2021; 70: 17191731.) proposed a new measurement for network reliability. This measurement method can resist the block attack by taking into account of the dispersity of the remaining nodes. Let $G$ be a network, $C \subset V(G)$, and $G[C]$ be a connected subgraph. Then $C$ is called an $h$-faulty-block of $G$ if $G-C$ is disconnected, and every component of $G-C$ has at least $h+1$ nodes. The minimum cardinality over all $h$-faulty-block of $G$ is called $h$-faulty-block connectivity, denoted by $FB_{k_{h}}(G)$. In this paper, we determine $FB_{k_{h}}(Q_{n}^{k})$ for $k$-ary $n$-cube $Q_{n}^{k}$ ($k\geq 3$), a classic interconnection network. We prove that $FB_{k_{0}}(Q_{n}^{3})=3n-1$, $FB_{k_{1}}(Q_{n}^{3})=5n-4$, and $FB_{k_{2}}(Q_{n}^{3})=7n-9$ for $n\geq 3$. Also, we show that $FB_{k_{0}}(Q_{n}^{k})=4n-1$ for $k\geq 4$ and $n\geq 2$, $FB_{k_{1}}(Q_{n}^{4})=6n-4$ for $n\geq 3$, $FB_{k_{1}}(Q_{n}^{k})=6n-3$ for $k\geq 5$ and $n\geq 3$, $FB_{k_{2}}(Q_{n}^{4})=8n-7$ for $n\geq 4$, $FB_{k_{2}}(Q_{n}^{5})=8n-6$ for $n\geq 4$, and $FB_{k_{2}}(Q_{n}^{k})=8n-5$ for $k\geq 6$ and $n\geq 5$.

Under the rapidly changing environment, forecasting the order exactly is the key of improving the flexibility and competition for enterprises. This paper utilized the recognition and regression forecasting function of the support vector machine to put forward the order forecasting model, and proves its validity through handling practical case. Finally, this paper compares the result of this model with the BP neural network, in the condition of the same samples.