Modern manufacturing systems collect a huge amount of data which gives an opportunity to apply various Machine Learning (ML) techniques. The focus of this paper is on the detection of anomalous behavior in industrial manufacturing systems by considering the temporal nature of the manufacturing process. Long Short-Term Memory (LSTM) networks are applied on a publicly available dataset called Modular Ice-cream factory Dataset on Anomalies in Sensors (MIDAS), which is created using a simulation of a modular manufacturing system for ice cream production. Two different problems are addressed: anomaly detection and anomaly classification. LSTM performance is analysed in terms of accuracy, execution time, and memory consumption and compared with non-time-series ML algorithms including Logistic Regression, Decision Tree, Random Forest, and Multi-Layer Perceptron. The experiments demonstrate the importance of considering the temporal nature of the manufacturing process in detecting anomalous behavior and the superiority in accuracy of LSTM over non-time-series ML algorithms. Additionally, runtime adaptation of the predictions produced by LSTM is proposed to enhance its applicability in a real system.