Modeling multivariate profiles using Gaussian process-controlled B-splines

Due to the increasing presence of profile data in manufacturing, profile monitoring has become one of the most popular research directions in statistical process control. The core of profile monitoring is how to model the profile data. Most of the current methods deal with univariate profile modeling where only within-profile correlation is considered. In this article, a linear mixed-effect model framework is adopted for dealing with multivariate profiles, having both within- and between-profile correlations. For better flexibility yet reduced computational cost, we propose to construct the random component of the linear mixed effects model using B-splines, whose control points are governed by a multivariate Gaussian process. Extensive simulations have been conducted to compare the model with classic models. In the case study, the proposed model is applied to the transmittance profiles from the low-emittance glasses.