###### Abstract  
Fault monitoring is often employed for the secure functioning of industrial systems. To assess performance and enhance product quality, statistical process control (SPC) charts such as Shewhart, CUSUM, and EWMA statistics have historically been utilized. When implemented to multivariate procedures, unfortunately, such univariate control charts demonstrate low fault sensing ability. Due to some limitations of univariate charts, numerous process monitoring techniques dependent on multivariate statistical approaches such as principal component analysis (PCA) and partial least squares (PLS) have been designed. Yet, in some challenging scenarios in industrial chemical and biological processes with notably nonlinear properties, PCA works poorly, according to its presumption that the dataset generally be linear. However, Kernel Principal Component Analysis (KPCA) is a reliable and precise nonlinear process control methodology, but the interaction mainly through upper control limits (UCLs) dependent on the Gaussian distribution may weaken its output. This article introduces time-varying statistical error tracking through Kernel Principal Component Analysis (KPCA) based on Generalized Likelihood Ratio statistics (GLR) using a sequential sampling scheme named KPCA-SSGLR for nonlinear fault detection. The main issue of employing just T\({}^{2}\) and Q statistic in KPCA is that they cannot correctly give practitioners the change point of the system fault, preventing practitioners from diagnosing the issue. Based on this perspective, this study attempts to incorporate KPCA with sequential sampling Generalized Likelihood Ratio (SSGLR) for monitoring the nonlinear fault in multivariate systems. The KPCA is utilized for dimension reduction, while the SSGLR is employed as a tracking statistic. The kernel density estimation (KDE) was employed to approximate UCLs for variational system operation relying on KPCA. The testing efficiency of the corresponding KPCA-KDE-SSGLR technique was then analyzed and competed with KPCA and kernel locality preserving projection (KLPP), the UCLs of which were focused on the Gaussian distribution. The purpose of this analysis is to enhance the development of KPCA-KDE-SSGLR to accomplish future enhancements and to advance the practical use of the established model by implementing the sequential sampling GLR approach. The fault monitoring efficiency is demonstrated through different simulation scenarios, one utilizing synthetic data, the other from the Tennessee Eastman technique, and lastly through a hot strip mill. The findings indicate the applicability of the KPCA-KDE-based SSGLR system over the KLPP and KPCA-KDE methods by its two T\({}^{2}\) and Q charts to recognize the faults. generalized likelihood ratio chart multivariate statistics; kernel principal component analysis; kernel density estimation; fault detection and identification; kernel locality preserving projections +
Footnote †: journal: Applied sciences  
time periods. The generated data points are strongly linked and contain a significant amount of distortion. Relatively very less information can be retrieved in the absence of an adequate mechanism for analyzing relevant inputs, and as a result, maintenance crews have an inadequate grasp of the mechanism. Because of this misunderstanding, the operation becomes unsteady. Statistical process control (SPC) provides the most potent mechanism for detecting imperfection scope. Control charts are widely employed to describe modifications in systems that can react to a degradation of the commodity's output and track the function of industrial output. Statistical process control (SPC) charts, notably Shewhart, CUSUM, and EWMA, have been applied to analyze procedures and enrich product performance in the previous era. Consequently, experiments have demonstrated that these approaches are ineffective in identifying significant variations in the system. Establishing a valuable detection framework for identifying means shifts is becoming a critical problem in a simple operation.