The interval-valued kernel PCA (UQ-KPCA) is a variation of the kernel PCA (KPCA) designed for interval-valued data, designed to handle data uncertainty by defining specific similarity measures and kernel functions for interval data. This paper introduces Uncertainty Quantification KPCA (UQ-KPCA) as a novel method to address uncertainties in data. UQ-KPCA converts the traditional KPCA model from single-valued to interval-valued representations, allowing for accurate error and uncertainty quantification. The process modeling using KPCA is then performed on data based on the interval model, followed by the computation of fault detection statistics such as T2, Q, and Φ. The method’s effectiveness is evaluated in the context of the cement rotary kiln process, and compared with the KPCA demonstrating superior performance in accurately identifying faults within a stochastic setting with unknown uncertainties.

This study introduces three novel dynamic interval-valued principal component analysis (DIPCA) methods: dynamic centers PCA (D-CPCA), dynamic vertices PCA (D-VPCA), and dynamic complete information PCA (D-CIPCA). These methods advance traditional interval-valued PCA (IPCA) by integrating dynamic aspects of industrial processes, thus addressing both data uncertainties and temporal correlations. The DIPCA methods were validated using real-world data from the Ain El Kebira cement plant. Results indicate significant improvements in fault detection accuracy, achieving lower false alarm rates and higher reliability compared to classical IPCA methods. Furthermore, an enhanced combined index for interval-valued data was developed, providing a single, comprehensive statistical measure for streamlined process monitoring.