Incorporating principal component analysis into Hotelling [formula omitted] control chart for compositional data monitoring

Abstract

In the manufacturing industry, compositional data (CoDa) is a vital quality characteristic to be monitored. The proposed study has introduced a Hotelling T2 control chart using principal component analysis to monitor CoDa explicitly. The proposed method overcomes the limitations of previous approaches by utilizing isometric log-ratio transformation to map the CoDa into unrestricted real space. A Monte Carlo simulation procedure is employed to evaluate the performance of the proposed multivariate control chart. The simulation involves varying combinations of the number of variables (p) and subgroup sizes to obtain metrics such as the average run length when the process is out-of-control (OOC) and the upper control limit. The article presents a comprehensive analysis of the proposed control chart’s statistical performance. These visual aids facilitate a deeper understanding of the method’s effectiveness in detecting OOC conditions in CoDa. Furthermore, two illustrative examples using synchronous machines and components of electronic scrap are provided to illustrate the practical implementation and effectiveness of the Hotelling T2-based principal component control chart for p=5-part and p=12-part CoDa in real-world scenarios.