Statistical monitoring of multiple profiles simultaneously using Gaussian processes

Profile monitoring is the application of control charts to monitor the stability of a process over time when the process can be characterized by a functional relationship between a response variable and 1 or more explanatory variables. Most of the research in profile monitoring has been focused on monitoring univariate profiles, while multivariate profile data are widely observed in practice. In this paper, a monitoring approach based on a multivariate Gaussian process (MGP) model is proposed to monitor multivariate profiles simultaneously. In this regard, using a non‐separable covariance function, a MGP model is fitted to represent the baseline in‐control multivariate profile. Then, the stability of the process is tracked by monitoring a distance measure between the new observations of the multivariate profile and the baseline in‐control model. A key advantage of this method is that it considers correlations both within profiles and between profiles. We also introduce, as a benchmark, a univariate Gaussian process‐based profile monitoring scheme modified for multivariate profiles. The performance of the proposed approaches is investigated and compared through numerical studies and a real‐world case study. The analysis confirms the effectiveness of the MGP‐based monitoring scheme for multivariate profiles.