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With the fast evolvement of embedded deep-learning computing systems, applications powered by deep learning are moving from the cloud to the edge. When deploying neural networks (NNs) onto the devices under complex environments, there are various types of possible faults: soft errors caused by cosmic radiation and radioactive impurities, voltage instability, aging, temperature variations, and malicious attackers. Thus the safety risk of deploying NNs is now drawing much attention. In this paper, after the analysis of the possible faults in various types of NN accelerators, we formalize and implement various fault models from the algorithmic perspective. We propose Fault-Tolerant Neural Architecture Search (FT-NAS) to automatically discover convolutional neural network (CNN) architectures that are reliable to various faults in nowadays devices. Then we incorporate fault-tolerant training (FTT) in the search process to achieve better results, which is referred to as FTT-NAS. Experiments on CIFAR-10 show that the discovered architectures outperform other manually designed baseline architectures significantly, with comparable or fewer floating-point operations (FLOPs) and parameters. Specifically, with the same fault settings, F-FTT-Net discovered under the feature fault model achieves an accuracy of 86.2% (VS. 68.1% achieved by MobileNet-V2), and W-FTT-Net discovered under the weight fault model achieves an accuracy of 69.6% (VS. 60.8% achieved by ResNet-20). By inspecting the discovered architectures, we find that the operation primitives, the weight quantization range, the capacity of the model, and the connection pattern have influences on the fault resilience capability of NN models.