Industrial batch processes employ similar or identical equipment to manufacture various specification products, hence multi-batch data exhibit common characteristics. Additionally, complex characteristics exist within each batch. In this paper, a multi-level monitoring method based on slow independent component analysis-tensor decomposition (SICA-TD) is proposed considering the characteristics of industrial batch processes. In the first-level monitoring model, SICA is used to identify whether the current batch is faulty. An integrated control limit is constructed to enhance robustness. When a fault is detected, fault and normal data features are combined into a tensor. Subsequently, the second-level monitoring model extracts common features through TD. The disparity in common feature distribution between normal and fault conditions is measured via Bhattacharyya distance (BD) statistics to ascertain whether the fault affects all batches. The method is validated through an actual hot strip mill process (HSMP) and implemented in a process monitoring platform for a steel manufacturing company.