Fault Detection and Classification (FDC) are essential for semiconductor process equipment/facility monitoring, providing in-time warning message with corresponding potential root causes to save time and financial cost in wafer fabrication. Often, FDC algorithms are constructed by sensor data from the different equipment and components. Traditionally, threshold-based methods employ fixed tolerances but struggle with bias, often using conservative limits to avoid oversight. Pure data-driven machine learning based like multilayer perceptron (MLP) have become popular for accurate FDC predictions. However, MLP-based approaches face two main issues: the neural networks building blocks often lack direct links to physical equipment parameters, that hinders engineers from identifying the root causes of failures, such as equipment aging or process delays. Another issue of MLP is its adaptivity to data points that is extrapolated from the training set. To address these issues, we propose a modularized NN for FDC in mass flow controller (MFCs) in etching process. The proposed framework integrates two functional modules: (1) an effective model representer net by Stage-based equipment parameter (K) Generator (SKG) and a Constitutive Artificial Neural Network (CANN), and (2) a fault classification algorithm based on ARCANA approach. The SKG construct the equipment parameter network blocks by using recipe-stages while CANN predicts the MFCs model by assembly potential physical equations of gas flow rules. It is benchmarked in our testing that SKG-CANN outperforms MLPs in terms of accuracy, stability, and efficiency. ARCANA frames anomaly explanation as an optimization problem to reconstruct the data while removing the anomalous properties. The idea is to find a similar version of the input with only a few explanatory anomalous features left. By combining SKG-CANN with ARCANA, we obtained a human-interpretable explanation of which features are likely the root cause of the anomaly, establishing a robust foundation for next-generation FDC systems.