A variable-selection control chart via penalized likelihood and Gaussian mixture model for multimodal and high-dimensional processes

Abstract

With the development of the sensor network and manufacturing technology, multivariate processes face a new challenge of high-dimensional data. However, traditional statistical methods based on small- or medium-sized samples such as T-2 monitoring statistics may not be suitable because of the "curse of dimensionality" problem. To overcome this shortcoming, some control charts based on the variable-selection (VS) algorithms using penalized likelihood have been suggested for process monitoring and fault diagnosis. Although there has been much effort to improve VS-based control charts, there is usually a common distributional assumption that in-control observations should follow a single multivariate Gaussian distribution. However, in current manufacturing processes, processes can have multimodal properties. To handle the high-dimensionality and multimodality, in this study, a VS-based control chart with a Gaussian mixture model (GMM) is proposed. We extend the VS-based control chart framework to the process with multimodal distributions, so that the high-dimensionality and multimodal information in the process can be better considered.