The Shewhart-type RZ control chart for monitoring the ratio of autocorrelated variables

Abstract

In many industrial manufacturing processes, the quality of products can depend on the relative amount between two quality characteristics X and Y. Often, this calls for the on-line monitoring of the ratio Z = X/Y as a quality characteristic itself by means of a control chart. A large number of control charts monitoring the ratio have been investigated in the literature under the assumption of independent normal observations of the two quality characteristics. In practice, due to the high frequency in sensor data collection, both autocorrelation and cross-correlation between consecutive observations can exist for X and Y and should be modelled to protect against the false alarm rate inflation when implementing a control chart for monitoring the ratio Z = X/Y. In this paper, we tackle this problem by investigating the performance of the Phase II Shewhart-type RZ control chart monitoring the ratio of two normal variables whose relationship is captured by a bivariate time series autoregressive model VAR(1), which can also account for the cross-correlation between the two quality characteristics. With the numerical study, we discuss how the design and the statistical performance of the Shewhart-type RZ control chart change with the VAR(1) model's parameters. We also provide an example to illustrate the use of the Shewhart-type RZ control chart with bivariate time series of observations in a furnace process.

Keywords:

• Quality control
• multivariate autoregressive model
• control charts
• anomaly detection
• autocorrelated data

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data analysed during this study are included in this paper.

Additional information

Notes on contributors

Huu Du Nguyen

Dr Huu Du Nguyen is a member of School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam. He obtained a PhD in Mathematics, Science and Information Technology and Communication at the Université de Bretagne-Sud, Vannes, France. His research is related to Reliability, Statistical Process Control, Machine Learning and Deep Learning.

Adel Ahmadi Nadi

Adel Ahmadi Nadi is currently a postdoctoral fellow of Statistics at the University of Waterloo, Canada. He finished his Ph.D. in Statistics on May 2021 at the Ferdowsi University of Mashhad, Iran. His research mainly focusses on developing Statistical techniques to deal with industrial and health problems.

Kim Duc Tran

Kim Duc Tran is currently a researcher and permanent Vice Director of the International Research Institute for Artificial Intelligence and Data Science at Dong A University, Danang, Vietnam. His research is focussed on advanced statistical process monitoring techniques, machine learning, and anomaly detection techniques.

Philippe Castagliola

Philippe Castagliola is graduated (PhD 1991) from the UTC (Université de Technologie de Compiégne, France). He is currently full professor at Nantes Université, Nantes, France, and he is also a member of the LS2N (Laboratoire des Sciences du Numérique de Nantes), UMR CNRS 6004. He is an associate editor for Quality Engineering (QE), Communications in Statistics (LSTA, LSSP, UCAS), the International Journal of Reliability, Quality and Safety Engineering (IJRQSE) and Quality Technology & Quantitative Management (QTQM). His research activity includes developments of new Statistical Process Monitoring techniques.

Giovanni Celano

Giovanni Celano is an associate professor at the University of Catania (Italy). He holds a PhD in production engineering from the University of Palermo (Italy). His current research is focussed on developing and implementing statistical process monitoring techniques for on-line quality control with a particular focus on small production runs. He has authored/coauthored about 135 papers in international journals and in proceedings of national and international conferences. He is a member of the ENBIS (European Network of Business and Industrial Statistics). He is an Advisory Editor of the Engineering Reports journal and an Associate Editor of the Quality Technology and Quantitative Management journal.

Kim Phuc Tran

Kim Phuc Tran is currently a Senior Associate Professor (Maître de Conférences HDR, equivalent to a UK Reader) of Artificial Intelligence and Data Science at the ENSAIT and the GEMTEX laboratory, University of Lille, France. He received an Engineer's degree and a Master of Engineering degree in Automated Manufacturing. He obtained a Ph.D. in Automation and Applied Informatics at the University of Nantes, and an HDR (Doctor of Science or Dr. habil.) in Computer Science and Automation at the University of Lille, France. His research deals with Real-time Anomaly Detection with Machine Learning with applications, Decision Support Systems with Artificial Intelligence, and Enabling Smart Manufacturing with IIoT, Federated learning, and Edge computing. He has published more than 64 papers in peer-reviewed international journals and proceedings of international conferences. He edited 3 books with Springer Nature and Taylor & Francis. He is the Associate Editor, Editorial Board Member, and Guest Editor for several international journals such as IEEE Transactions on Intelligent Transportation Systems and Engineering Applications of Artificial Intelligence. He has supervised 9 Ph.D. students and 3 Postdocs. In addition, as the project coordinator (PI), he is conducting 1 regional research project about Healthcare Systems with Federated Learning. He has been or is involved (co-PI or member) in 8 national and European projects. He is an expert and evaluator for the Research and Innovation program of the Government of the French Community, Belgium. He received the Award for Scientific Excellence (Prime d'Encadrement Doctoral et de Recherche) given by the Ministry of Higher Education, Research and Innovation, France for 4 years from 2021 to 2025 in recognition of his outstanding scientific achievements. From 2017 until now, he has been the Senior Scientific Advisor at Dong A University and the International Research Institute for Artificial Intelligence and Data Science (IAD), Danang, Vietnam where he has held the International Chair in Data Science and Explainable Artificial Intelligence.