Predictive ratio CUSUM (PRC): A Bayesian approach in online change point detection of short runs

Abstract

The online quality monitoring of a process with low volume data is a very challenging task and the attention is most often placed in detecting when some of the underline (unknown) process parameter(s) experience a persistent shift. Self-starting methods, both in the frequentist and the Bayesian domain aim to offer a solution. Adopting the latter perspective, we propose a general closed-form Bayesian scheme, where the testing procedure is built on a memory-based control chart that relies on the cumulative ratios of sequentially updated predictive distributions. The theoretic framework can accommodate any likelihood from the regular exponential family and the use of conjugate analysis allows closed form modeling. Power priors will offer the axiomatic framework to incorporate into the model different sources of information, when available. A simulation study evaluates the performance against competitors and examines aspects of prior sensitivity. Technical details and algorithms are provided as supplementary material.

Keywords:

• control chart
• phase I analysis
• regular exponential family
• self-starting
• statistical process control and monitoring

Acknowledgments

We are grateful to the Editor and all reviewers for their excellent work. Their constructive criticism and suggestions, improved significantly the quality of this manuscript. This research was partially funded by the international company Instrumentation Laboratory (IL), Bedford, Massachusetts, USA and the Research Center of the Athens University of Economics and Business (AUEB).

Additional information

Funding

This work was supported by Research Center of the Athens University of Economics and Business (RC/AUEB) and Instrumentation Laboratory (IL), Bedford, Massachusetts, USA.

Notes on contributors

Konstantinos Bourazas

Dr. Konstantinos Bourazas received his Ph.D. from the Department of Statistics, at the Athens University of Economics and Business, Greece. He is currently a postdoctoral researcher at the Department of Mathematics & Statistics at the University of Cyprus, as well as participating in an interdepartmental research project at the University of Ioannina, Greece. His research interests are in the areas of Statistical Process Control and Monitoring, Bayesian Statistics, Change Point Models, Replication Studies and Applied Statistics.

Frederic Sobas

Dr. Frederic Sobas is specialized in hemostasis. He is a clinical chemist graduated from Claude Bernard University Lyon I, France. He is a Quality Manager focusing in medical laboratories accreditation issues with respect to ISO 15189 norm.

Panagiotis Tsiamyrtzis

Panagiotis Tsiamyrtzis is an Associate Professor at the Department of Mechanical Engineering, Politecnico di Milano and his email is [email protected].