Multivariate control charts based on Mahalanobis distance for bivariate quality monitoring in petrochemical and pharmaceutical analyses

This study evaluates the practical implementation of a covariance-adjusted monitoring procedure based on the squared Mahalanobis distance (D2) for routine bivariate quality control data. The approach was assessed using four small datasets generated in petrochemical and pharmaceutical laboratories, representing paired analytical measurements commonly monitored in routine practice. Rather than proposing a new multivariate statistical process control statistic, the study focuses on a transparent, spreadsheet-compatible implementation of D2-based monitoring and on the empirical characterization of control-threshold variability under small sample conditions. The D2 chart was compared with conventional univariate charts and with chi-square-based upper thresholds. In most datasets, both univariate and multivariate charts indicated stable process behavior with no action-level signals, reflecting the predominantly in-control nature of the available data. One ritonavir–lopinavir dataset provided an illustrative action-level exceedance, suggesting how a covariance-adjusted statistic may flag localized joint deviations; however, this single event should not be interpreted as definitive validation of fault-detection capability. A permutation-based resampling strategy was used to examine the variability of control thresholds and signal probabilities across alternative historical-monitoring partitions. Overall, the results support the feasibility, interpretability, and reproducibility of the proposed bivariate workflow as a complementary tool for routine analytical monitoring, while indicating that more rigorous validation with independent datasets containing known deviations is required before broader claims regarding fault-detection performance can be made. Graphical abstract