Neural networks have been widely applied for performing tasks in critical domains, such as, for example, the medical domain; their robustness is, therefore, important to be guaranteed. In this paper, we propose a robustness definition for neural networks used for regression, by tackling some of the problems of existing robustness definitions. First of all, by following recent works done for classification problems, we propose to define the robustness of networks used for regression w.r.t. alterations of their input data that can happen in reality. Since different alteration levels are not always equally probable, the robustness definition is parameterized with the probability distribution of the alterations. The error done by this type of networks is quantifiable as the difference between the estimated value and the expected value; since not all the errors are equally critical, the robustness definition is also parameterized with a “tolerance” function that specifies how the error is tolerated. The current work has been motivated by the collaboration with the industrial partner that has implemented a medical sensor employing a Multilayer Perceptron for the estimation of the blood oxygen pressure. After having computed the robustness for the case study, we have successfully applied three techniques to improve the network robustness: data augmentation with recombined data, data augmentation with altered data, and incremental learning. All the techniques have proved to contribute to increasing the robustness, though in different ways.