With the development of network science, the static network has been unable to clearly characterize the dynamic process of the network. In real networks, the interaction between individuals evolves rapidly over time. This network model closely links time to interaction process. Compared with static networks, dynamic networks can clearly describe the interaction time of nodes, which has more practical significance. Therefore, how to better describe the behavior changes of networks after being attacked based on time series is an important problem in the existing cascade failure research. In order to better answer this question, a failure model based on time series is proposed in this paper. The model is constructed according to time, activation ratio, number of edges and connection probability. By randomly attacking nodes at a certain time, the effects of four parameters on sequential networks are analyzed. In order to validate the validity and scientificity of this failure model, we use small social networks in the United States. The experimental results show that the model is feasible. The model takes into account the time as well as the spreading dynamics and provides a reference for explaining the dynamic networks in reality.