Many industrial plants encounter infrequent faults and failures (anomalies) during operation which generate significant increases in costs. Modelling and detection of these anomalies is challenging due to unbalanced (few anomalous observations) and unlabeled (no class information) historical data. Previous works require large, labeled, and balanced training datasets which are typically not available in industry. This work relies solely on data taken from normal plant operation to construct anomaly detection models.Single-class neural network autoencoders and principal component analysis are developed as quality monitoring and anomaly detection solutions for resistive seam welding. Monitoring models of the welding process, which facilitate anomaly detection through interpretable metrics, are constructed from easily obtained normal welding process data. No examples of poor-quality welds, nor designed experiments, are required. The methods are applied to industrial data from a steel galvanizing line which encounters infrequent yet costly weld failures. It is shown that these two monitoring approaches are capable of robustly detecting infrequent weld-breaks, without requiring examples of weld failures or poor-quality welds, using only online industrial production data from normal welding operation. Additionally, the monitoring metrics, visualizations, and root-cause analysis functionality also provided by these models are demonstrated.