In many industrial plants with multiple parallel production lines manufacturing products with different technical characteristics (e.g., battery production lines), it is necessary to monitor these lines simultaneously with respect to whether the quality characteristic is in control. In such cases, one effective approach is to collect and monitor the data in panel form, because panel monitoring leads one to the real condition of the manufacturing line. Monitoring variations in panel data is challenging due to the simultaneous observation of multiple cross-sectional units; however, the literature does not address this contribution. This study introduces two new eigenvalue-based methods: 1) Eigenvalue CUSUM, and 2) Eigenvalue EWMA. In these proposed methods, a moving window is applied directly to the raw panel data, and the maximum eigenvalue of each window is calculated.
The performance of the proposed methods is evaluated through extensive simulations under various mean shift sizes (in terms of standard deviation). Simulation results show that the Eigenvalue EWMA scheme provides stable and sensitive detection, while the Eigenvalue CUSUM scheme responds faster to moderate and large shifts. Finally, the proposed methods are evaluated on real data collected from an automobile battery manufacturing line. The case study results indicate that both proposed methods detect process changes faster compared to traditional methods.
The proposed eigenvalue-based moving-window approach differs from conventional multivariate methods, including Hotelling’s T², MCUSUM, MEWMA, and Dynamic PCA, which require panel observations to be restructured into a single multivariate vector. Comparisons showed faster detection of small and moderate shifts.