Diagnosing nozzle faults in high-end industrial printers, such as the ones developed by Canon Production Printing (CPP), remains challenging due to the interplay of fluid dynamics and mechanical actuation. These systems rely on self-sensing signals that are often subtle and nonlinear, complicating both detection and interpretation. However, accurate and timely diagnosis is essential to maintain print quality, minimize waste, and reduce maintenance effort. This thesis investigates hybrid fault diagnosis methods that integrate model-based and data-driven techniques to improve detection reliability and generalization, particularly for piezoelectric inkjet systems. Traditional fault detection approaches in this context often rely on rule-based thresholds applied to features extracted from self-sensing signals. Although these methods can be effective, they are typically sensitive to variations in operating conditions. In contrast, model-based techniques use simplified system dynamics to generate residual signals that reflect deviations from expected behavior. In this thesis, we propose a hybrid framework that addresses the Fault Detection and Isolation (FDI) problem from a frequency domain perspective. By learning from signal characteristics, the method avoids the need for manually defined thresholds and predefined reference signatures. Instead, it uses classifiers trained to distinguish between different fault types and improve the adaptability to unseen cases. Building on this framework, the second part of the thesis addresses Fault Estimation (FE), aiming to reconstruct how faults evolve over time. A linear model-based estimation scheme is developed in both discrete-time and continuous-time forms. Even though this approach simplifies certain nonlinear dynamics, it provides useful fault tracking results, particularly for moderate fault levels. The evaluation on synthetic datasets shows that the proposed FDI and FE methods offer interpretable and reasonably accurate results. However, challenges remain when applied to physics-based data, particularly due to nonlinear effects, variable initial conditions, and numerical sensitivity.