Alternative parameter learning schemes for monitoring process stability

Abstract

In statistical process control, accurately estimating in-control (IC) parameters is crucial for effective monitoring. This typically requires a Phase I analysis to obtain estimates before monitoring commences. The traditional “fixed” estimate (FE) approach uses these estimates exclusively, while the “adaptive” estimate (AE) approach updates the estimates with each new observation. Such extreme criteria reflect the traditional bias-variance tradeoff in the framework of the sequential parameter learning schemes. This paper proposes an intermediate update rule that generalizes two ad hoc criteria for monitoring univariate Gaussian data, by giving a lower probability to parameter updates when an out-of-control (OC) situation is likely, therefore updating more frequently when there is no evidence of an OC scenario. The simulation study shows that this approach improves the detection power for small and early shifts, which are commonly regarded as a weakness of control charts based on fully online adaptive estimation. The paper also shows that the proposed method performs similarly to the fully adaptive procedure for larger or later shifts. The proposed method is illustrated by monitoring the sudden increase in ICU counts during the 2020 COVID outbreak in New York.

Keywords:

• Adaptive estimation
• window of opportunity
• estimation effects
• statistical process control

Acknowledgments

The authors thank the editor and the reviewers for their constructive comments and suggestions, which improved the quality of the paper.

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work was supported by UNIPD under Grant DOR2021.

Notes on contributors

Daniele Zago

Daniele Zago is a current Ph.D. student in Statistics at the University of Padua since 2021. He obtained his bachelor's degree in Statistics for Technology and Science and his master's degrees in Statistical Sciences from the University of Padua. His main research interests revolve around fundamental issues in practical applications of statistical process control and optimization.

Giovanna Capizzi

Dr. Giovanna Capizzi is a full Professor of Statistics at the University of Padua. She earned her Ph.D. in Statistics from the University of Padua in 1992. Dr. Capizzi's main research interest is in statistical process monitoring, and she has made significant contributions to the field. she has published extensively in several international peer-reviewed journals, including Statistics and Computing, Technometrics, Journal of Quality Technology, IIE Transactions, and Quality Engineering. Dr. Capizzi serves as an associate editor of Technometrics since 2013, and she is a member of the editorial board of the Journal of Quality Technology since 2014.