Weakly correlated profile monitoring based on sparse multi-channel functional principal component analysis

Although several works have been proposed for multi-channel profile monitoring, two additional challenges are yet to be addressed: (i) how to model complex correlations of multi-channel profiles when different profiles have different features (i.e., weakly or sparsely correlated); (ii) how to efficiently detect sparse changes occurring in only a small segment of a few profiles. To fill this research gap, our contributions are twofold. First, we propose a novel Sparse Multi-channel Functional Principal Component Analysis (SMFPCA) to model multi-channel profiles. SMFPCA can not only flexibly describe the correlation structure of multiple, or even high-dimensional, profiles with distinct features, but also achieve sparse PCA scores which are easily interpretable. Second, we propose an efficient convergence-guaranteed optimization algorithm to solve SMFPCA in real time based on the block coordinate descent algorithm. Third, as the SMFPCA scores can naturally identify sparse out-of-control (OC) patterns, we use the scores to construct a monitoring scheme which provides increased sensitivity to sparse OC changes. Numerical studies together with a real case study in a manufacturing system demonstrate the effectiveness of the developed methodology.