Multivariate statistical process control using mixture modelling

When performing process monitoring, the classical approach of multivariate statistical process control (MSPC) explicitly assumes the normal operating conditions (NOC) to be distributed normally. If this assumption is not met, usually severe out‐of‐control situations are missed or in‐control situations can falsely be seen as out‐of‐control. Combining mixture modelling with MSPC (MM‐MSPC) leads to an approach in which non‐normally distributed NOC regions can be described accurately. Using the expectation maximization (EM) algorithm, a mixture of Gaussian functions can be defined that, together, describe the data well. Using the Bayesian information criterion (BIC), the optimal set of Gaussians and their specific parametrization can be determined easily. Artificial and industrial data sets have been used to test the performance of the combined MM‐MSPC approach. From these applications it has been shown that MM‐MSPC is very promising: (1) a better description of the process data is given compared with standard MSPC and (2) the clusters found can be used for a more detailed process analysis and interpretation.