Bayesian multivariate control charts for multivariate profiles monitoring

ABSTRACT

In many topical applications, the product’s quality can be well described in terms of statistical regression relationships between one or more response and a set of explanatory variables. In the literature, various types of regression models have been proposed for profile monitoring applications, and each of those regression models can be implemented and applied in its standard frequentist’s and its Bayesian variant. We formulate two popular Phase II multivariate cumulative sum control charts for monitoring multivariate linear profiles in terms of Bayesian regression models, and we show empirically that the resulting new Bayesian control charts perform better than the corresponding non-Bayesian control charts. For the comparative evaluation of the control charts we employ the average run length criterion. Moreover, we propose a new Bayesian approach, which we refer to as the informative prior generation method. The key idea of this method is to make use of historical datasets to generate informative prior distributions. The advantage of this method is that we do not ignore the historical data from Phase I. Instead we re-use it to construct informative prior distributions for Phase II monitoring. The applicability and the superiority of the proposed Bayesian control charts are illustrated through extensive simulation studies.

KEYWORDS:

• Profile monitoring
• statistical process monitoring
• multivariate linear profile
• Bayesian modelling
• Phase II

Disclosure statement

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

Additional information

Notes on contributors

Ahmad Ahmadi Yazdi

Ahmad Ahmadi Yazdi is an Assistant Professor of Industrial Engineering at the department of industrial engineering of Yazd University (Iran). He received his PhD degree of industrial Engineering from Isfahan University of Technology (IUT). His research interests are Statistical Quality Monitoring (SPM), Profile Monitoring, Data Mining, Productivity management and Bayesian Statistics.

Mahdi Shafiee Kamalabad

Mahdi Shafiee Kamalabad is an assistant professor of Data Science at Utrecht University’s Department of Methodology & Statistics. He is a member of the Centre for Complex Systems Studies and specializes in developing statistical and machine learning models to analyze complex data and uncover patterns, particularly in network science, including network inference, learning, and social network analysis.

Daniel L. Oberski

Daniel L. Oberski is full professor of health and social data science, with a joint appointment at Utrecht University’s Department of Methodology & Statistics, and the department of Biostatistics and Data Science at the Julius Center, University Medical Center Utrecht (UMCU).

Marco Grzegorczyk

Marco Grzegorczyk is currently an Associate Professor for Computational Statistics at the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence of Groningen University (Netherlands). He received a PhD degree in Statistics from TU Dortmund University (Germany) in 2006. His main research interests are Computational Statistics, Bayesian Statistics and Bayesian networks.