The usage of deep neural networks in safety-critical systems is limited by our ability to guarantee their correct behavior. Runtime monitors are components aiming to identify unsafe predictions and discard them before they can lead to catastrophic consequences. Several recent works on runtime monitoring have focused on out-of-distribution (OOD) detection, i.e., identifying inputs that are different from the training data. In this work, we argue that OOD detection is not a well-suited framework to design efficient runtime monitors and that it is more relevant to evaluate monitors based on their ability to discard incorrect predictions. We call this setting out-ofmodel-scope detection and discuss the conceptual differences with OOD. We also conduct extensive experiments on popular datasets from the literature to show that studying monitors in the OOD setting can be misleading: 1. very good OOD results can give a false impression of safety, 2. comparison under the OOD setting does not allow identifying the best monitor to detect errors. Finally, we also show that removing erroneous training data samples helps to train better monitors.

Machine Learning (ML) models, such as deep neural networks, are widely applied in autonomous systems to perform complex perception tasks. New dependability challenges arise when ML predictions are used in safety-critical applications, like autonomous cars and surgical robots. Thus, the use of fault tolerance mechanisms, such as safety monitors, is essential to ensure the safe behavior of the system despite the occurrence of faults. This paper presents an extensive literature review on safety monitoring of perception functions using ML in a safety-critical context. In this review, we structure the existing literature to highlight key factors to consider when designing such monitors: threat identification, requirements elicitation, detection of failure, reaction, and evaluation. We also highlight the ongoing challenges associated with safety monitoring and suggest directions for future research.