Deep neural networks (DNN) have a high potential for predicting and mitigating equipment failure in large industrial plants. However, plant anomalies are rare events that result in extremely unbalanced datasets, which poses a challenge for traditional DNN classifiers. Weighted loss functions such as focal loss and weighted binary cross-entropy (WBCE) have emerged as a promising approach to deal with class imbalance, where higher weightings are assigned to the anomaly class during training. This study proposes three new weighted loss function variants, i.e. weighted polynomial binary cross entropy (WPBCE) loss, weighted hinge loss and weighted squared hinge loss, and systematically evaluates these across three DNN architectures: long short-term memory (LSTM), temporal convolutional network (TCN), and multi-layer perceptron (MLP). The results show that the weighted loss function variants improve recall and yield more stable configurations across all algorithms, when compared to focal loss and WBCE, for predicting the onset of abnormal operating events in a real-world South African mineral grinding mill. Importantly, this work demonstrates that the weighted squared hinge and WPBCE, when combined with the LSTM model, offer a reliable solution for early and accurate anomaly prediction.