A penalized likelihood-based quality monitoring via L2-norm regularization for high-dimensional processes

Abstract

Technological advances have resulted in the introduction of new products and manufacturing processes that have a large number of characteristics and variables to be monitored to ensure the product quality. Simultaneous monitoring of variables under such a high-dimensional environment is quite challenging. Traditional approaches are less sensitive to the out-of-control signals in high-dimensional processes, especially when only a few variables are responsible for abnormal changes in the process output. Recently, variable selection-based charts are proposed to overcome the drawbacks of the traditional approaches. These approaches adopt diagnosis procedures to identify a small subset of potentially changed variables. However, the detection capability of these charts may be low in cases when the size of the shift is relatively small in a highly correlated data structure, which is critical in modern industry. Moreover, the complexity of computation would dramatically increase as the dimension of the process parameters increases due to the diagnosis procedure, which is inappropriate for online monitoring. This article proposes a new penalized likelihood-based approach via norm regularization, which does not select variables but rather “shrinks” all process mean estimates toward zero. A closed-form solution of the proposed approach along with probability distributions of the monitoring statistic under null and alternative hypotheses are obtained, which makes the proposed chart significantly efficient to monitor high-dimensional processes. In addition, we explore theoretical properties of the approach and present several extensions of the proposed chart and its integration with other existing charts. Finally, we compare the performance of the approach with existing methods and present a case study of a high-speed milling process.