In recent years, Deep Learning (DL) technique has been widely used in Internet of Things (IoT) and Industrial Internet of Things (IIoT) for edge computing, and achieved good performances. But more and more studies have shown the vulnerability of neural networks. So, it is important to test the robustness and vulnerability of neural networks. More specifically, inspired by layer-wise relevance propagation and neural network verification, we propose a novel measurement of sensitive neurons and important neurons, and propose a novel neuron coverage criterion for robustness testing. Based on the novel criterion, we design a novel testing sample generation method, named DeepSI, which involves definitions of sensitive neurons and important neurons. Furthermore, we construct sensitive-decision paths of the neural network through selecting sensitive neurons and important neurons. Finally, we verify our idea by setting up several experiments, then results show our proposed method achieves superior performances.