Recursive PCA for adaptive process monitoring

While principal component analysis (PCA) has found wide application in process monitoring, slow and normal process changes often occur in real processes, which lead to false alarms for a ®xed-model monitoring approach. In this paper, we propose two recursive PCA algorithms for adaptive process monitoring. The paper starts with an ecient approach to updating the correlation matrix recursively. The algorithms, using rank-one modi®cation and Lanczos tridiagonalization, are then proposed and their computational complexity is compared. The number of principal components and the con®dence limits for process monitoring are also determined recursively. A complete adaptive monitoring algorithm that addresses the issues of missing values and outlines is presented. Finally, the proposed algorithms are applied to a rapid thermal annealing process in semiconductor processing for adaptive monitoring.