Machine fault diagnosis is important in modern industries, such as smart manufacturing, because machine failure can increase maintenance costs and safety risks. Although deep learning-based fault diagnosis approaches have succeeded remarkably in recent years, they often encounter challenges in accurately diagnosing machine faults in noisy environments using resource-constrained edge devices in real time. We propose full-receptive-field convolution (FRFconv)-TDSNet, a lightweight, noise-robust convolutional neural network (CNN) that prioritizes global feature extraction and integration between deep learning and vibration statistics. The key components of FRFconv-TDSNet are a full-receptive-field (FRF) CNN and a time-domain statistics (TDS) extractor. A fundamental element of the FRF CNN is the FRF convolution block, which has a kernel size that is the same as the length of the input data; therefore, the FRF CNN can extract high-level features throughout the input data range. We ensure that the model is highly robust to noise while suppressing the increase in the computational costs of FRF convolution using small-channel depthwise separable convolutions and a downsampling block. The TDS values capture the necessary characteristics indicating machine conditions, such as the signal magnitude. We further improve the model's noise robustness by concatenating the four TDS values calculated from raw vibration signals with the FRF CNN output. The evaluation results demonstrate the superiority of our model over ten comparison models in terms of accuracy for heavily noisy data and inference time on an edge device. Furthermore, visual interpretation of the model shows how FRF convolution and TDS integration contribute to the robustness of our model to data noise.