Monitoring and diagnostics of correlated quality variables of different types

Abstract

As data acquisition and processing technologies continue to advance rapidly, new challenges emerge for statistical process monitoring. One such challenge, especially in the era of big data analytics, is monitoring multivariate processes involving a mixture of continuous, categorical, and discrete quality variables. The existing multivariate control charts focus mostly on monitoring correlated variables of the same type. We propose a new Phase II control chart that is based on a modified Holm’s step-down multiple testing procedure (Holm 1979) which achieves two important goals at the same time: (1) it simultaneously monitors correlated variables of different types, while keeping the probability of false alarm under desirable level, and (2) when the process is determined to be out of control, it further provides, without any additional efforts, diagnostics to pinpoint which parameters are out of control. The proposed chart is shown to outperform the existing charts particularly in its ability to provide more accurate diagnostics.

Keywords:

• diagnostics
• Holm’s step-down multiple testing procedure
• multivariate control chart
• phase-II monitoring

Acknowledgments

The authors are grateful to the Editor and the reviewers for their insightful comments and suggestions which help improve the presentation of the article.

Code availability

The code that support the findings of this study are openly available in HMT-chart version 1.0 Zenodo at https://doi.org/10.5281/zenodo.6885370.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first and the third authors were partly supported by the Ministry of Science and Technology, Taiwan (MOST 108-2118-M-035-005-MY3). The second author was partly supported by National Natural Science Foundation of China (NSFC 71672100).

Notes on contributors

Wei-Heng Huang

Dr. Wei-Heng Huang is is an assistant professor in the Department of Statistics at Feng Chia University. He received his Ph.D. degree in the Institute of Statistics at National Chiao Tung University, Hsinchu, Taiwan. His research interests include Statistical Process Control, Bayesian Analysis, and Reliability Analysis. His primary research focuses on developing control charts for different underlying process settings. He has published papers in the following journals, including Quality Technology & Quantitative Management, Quality and Reliability Engineering International, Symmetry, Frontiers in Bioscience-Landmark, Communications in Statistics - Simulation and Computation, and Journal of the Royal Statistical Society, Series A.

Jing Sun

Dr. Jing Sun is an associate professor in the Research Center for Contemporary Management, Department of Management Science and Engineering, School of Economics and Management, Tsinghua University, Beijing, China. She received her PhD from Tianjin University. Her research interests include quality engineering and total quality management, statistical data mining and knowledge discovery. She has published papers in the following journals: Journal of Systems Science and Systems Engineering, Journal of Applied Statistics and Management, Journal of China Mechanical Engineering, Asian Journal on Quality, Dynamical Systems and Control, among others.

Arthur B. Yeh

Dr. Arthur Yeh is Professor of Statistics at the Department of Applied Statistics and Operations Research, Bowling Green State University. Over the years, Dr. Yeh has conducted and published research in several areas of industrial statistics, including, among others, optimal experimental designs, computer experiments, univariate and multivariate control charts, multivariate process capability indices, univariate and multivariate run-by-run process control and statistical profile monitoring. He has published papers in quality engineering and statistics journals, including Journal of Quality Technology, IIE Transactions, International Journal of Production Research, Naval Research Logistics, Journal of Operational Research Society, The American Statistician, Computational Statistics and Data Analysis, The Journal of Applied Statistics, and the Journal of Royal Statistical Society, Series B. He has served as an Associate Editor for The Statistical Papers and The American Statistician in the past. He was the Owens-Illinois Professor of the Schmidthorst College of Business at Bowling Green State University from 2015–2018. He served as department chair from 2007 to 2017, and as Associate Dean for Research and Graduate Programs from 2017 to 2020. He was Co-PI of a two-year $475,000 grant from the Ohio Department of Higher Education for a project entitled “Data-Driven Predictive Models for Identifying Risk Factors Leading to Opiate Abuse”.