A data-driven monitoring scheme for multivariate multimodal data

Abstract

Multivariate multimodal data, obtained from complex processes with multiple correlated quality characteristics and multiple operating modes, are commonly used in many applications. Online monitoring of multivariate multimodal data has been receiving increasing attention because timely detection of process problems is important. However, existing statistical process monitoring methods are often inadequate for addressing the challenges of multivariate multimodal data monitoring. For example, they may require the process data to be unimodal or identically distributed or may assume the information regarding the multimodal processes to be known a priori. Therefore, a data-driven monitoring scheme is proposed in this paper. First, the Dirichlet process Gaussian mixture model is adopted, which can depend entirely on data characteristics and automatically cluster the data without any prior knowledge. On this basis, an exponentially weighted moving average scheme is then constructed by incorporating the negative log-likelihood statistic. Using thorough simulations and a real example, we analyse and compare the performance of the model estimation and online monitoring for detecting various out-of-control scenarios. Extensive results show that our proposed monitoring scheme is sensitive to not only model parameter shifts but also model order changes. Moreover, the proposed scheme generally performs better and more robustly than existing methods.