This paper assesses the fault-detection capabilities of modern deep-learning models. It highlights that a naive deep-learning approach optimized for accuracy is unsuitable for learning fault-detection models from time-series data. Consequently, out-of-the-box deep-learning strategies may yield impressive accuracy results but are ill-equipped for real-world applications. The paper introduces a methodology for estimating fault-detection delays when no oracle information on fault occurrence time is available. Moreover, the paper presents a straightforward approach to implicitly achieve the objective of minimizing fault-detection delays. This approach involves using pseudo-multi-objective deep optimization with data windowing, which enables the utilization of standard deep-learning methods for fault detection and expanding their applicability. However, it does introduce an additional hyperparameter that needs careful tuning. The paper employs the Tennessee Eastman Process dataset as a case study to demonstrate its findings. The results effectively highlight the limitations of standard loss functions and emphasize the importance of incorporating fault-detection delays in evaluating and reporting performance. In our study, the pseudo-multi-objective optimization could reach a fault-detection accuracy of 95% in just a fifth of the time it takes the best naive approach to do so.