  High dimensional data has introduced challenges that are difficult to address
when attempting to implement classical approaches of statistical process
control. This has made it a topic of interest for research due in recent years.
However, in many cases, data sets have underlying structures, such as in
advanced manufacturing systems. If extracted correctly, efficient methods for
process control can be developed. This paper proposes a robust sparse
dimensionality reduction approach for correlated high-dimensional process
monitoring to address the aforementioned issues. The developed monitoring
technique uses robust sparse probabilistic PCA to reduce the dimensionality of
the data stream while retaining interpretability. The proposed methodology
utilizes Bayesian variational inference to obtain the estimates of a
probabilistic representation of PCA. Simulation studies were conducted to
verify the efficacy of the proposed methodology. Furthermore, we conducted a
case study for change detection for in-line Raman spectroscopy to validate the
efficiency of our proposed method in a practical scenario.
