Heteroscedastic latent variable modelling with applications to multivariate statistical process control

Abstract

We present an approach for conducting multivariate statistical process control (MSPC) in noisy environments, i.e., when the signal to noise ratio is low, and, furthermore, noise standard deviation (uncertainty) affecting each collected value can vary over time, and is assumingly known. This approach is based upon a latent variable model structure, HLV (standing for heteroscedastic latent variable model), that explicitly integrates information regarding data uncertainty. Moderate amounts of missing data can also be handled in a coherent and fully integrated way through HLV. Several examples show the added value achieved under noisy conditions by adopting such an approach and a case study illustrates its application to a real industrial context of pulp and paper product quality data analysis.