How do you implement multivariate statistical process monitoring?

Multivariate process monitoring uses statistical models to detect abnormal process behavior. Implementation: historical batch alignment (dynamic time warping, indicator variables), model building using PCA or PLS on normal operating condition (NOC) data, establishing control limits (Hotelling T2, SPE/DModX statistics), real-time scoring of new batches. Advanced methods: multi-way PCA for batch processes, batch evolution modeling (BEM), contribution plots for fault diagnosis. Challenges include handling batch-to-batch variation, process drift, sensor faults, and missing data. Integration with PAT enables multivariate regression models predicting quality attributes. Golden batch analysis identifies optimal trajectories. Multivariate monitoring detects subtle deviations missed by univariate charts and supports deviation investigation through variable contribution analysis.