Stochastic production systems (SPS) have demonstrated significant potential in various fields, including fermentation, pharmaceuticals, and composite material production. However, ensuring product quality in such scenarios is a critical challenge due to the stringent quality constraints. SPS is known for its intrinsic stochasticity and measurement uncertainty, making process monitoring essential but challenging. The stochastic nature of SPS is exacerbated by external factors such as inputs, environmental conditions, and equipment state, all of which influence the final product's quality and performance. Moreover, the lack of precise in-situ measurements introduces additional noise into the available data. Consequently, effective process monitoring for SPS is indispensable. Over the past few decades, several methods have been developed for SPS process monitoring. Multiway Principal Component Analysis (PCA) has been widely used due to its simplicity, low-dimensional computing space, and fast processing of high-dimensional data. However, it is limited by its linearity and cannot handle nonlinear dynamics. To address this limitation, the kernel method has been employed to map data into a high-dimensional feature space, making data linearly separable. Other methods, including an improved Independent Component Analysis (ICA), a kernel ICAPCA method, and a multiway kernel entropy ICA method, have been developed to capture nonlinear and non-Gaussian features in SPS data. Support Vector Machines (SVM) integrated with PCA or fuzzy reasoning have been used for anomaly detection in SPS. However, these methods struggle to handle the common characteristics of SPS data, such as nonlinearity, heavy-tailed distributions, and multimodality. Additionally, the tuning of hyperparameters in these methods can be cumbersome.