Robustness is a vital characteristic of machine learning classifiers that is required to ensure safety and reliability. In the extensively studied domain of adversarial robustness in image classification, it is typically defined as a model’s stability in response to input perturbations within a p-norm distance. However, within the research area focused on robustness against random corruptions, p-norm perturbations are rarely investigated, with an emphasis instead on real-world corruptions. This paper examines the application of random p-norm corruptions to enhance the training and testing datasets of image classifiers. We evaluate model robustness against subtle random p-norm corruptions and propose an associated robustness metric. Through empirical analysis, we investigate whether robustness is transferable across different p-norms and identify which p-norm corruptions are most effective for training and evaluation. Furthermore, we introduce efficient training data augmentation techniques that combine various p-norm corruptions and assess their effectiveness against several state-of-the-art noise injection methods. Our results indicate significant improvements in corruption robustness when utilizing these training approaches, even when combined with other prevalent data augmentation strategies.