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This paper presents a mathematical framework for modeling the dynamic effects of three fault categories and six fault variants in the ink channels of high-end industrial printers. It also introduces a hybrid approach that combines model-based and data-based methods to detect and isolate these faults effectively. A key challenge in these systems is that the same piezo device is used for actuation (generating ink droplets) and for sensing and, as a consequence, sensing is only available when there is no actuation. The proposed Fault Detection (FD) filter, based on the healthy model, uses the piezo self-sensing signal to generate a residual, while taking the above challenge into account. The system is flagged as faulty if the residual energy exceeds a threshold. Fault Isolation (FI) is achieved through linear regression or a k-nearest neighbors approach to identify the most likely fault category and variant. The resulting hybrid Fault Detection and Isolation (FDI) method overcomes traditional limitations of model-based methods by isolating different types of faults affecting the same entries (i.e., equations) in the ink channel dynamics. Moreover, it is shown to outperform purely data-driven methods in fault isolation, especially when data is scarce. Experimental validation demonstrates superior FDI performance compared to state-of-the-art methods.