Optimum variable-dimension EWMA chart for multivariate statistical process control

ABSTRACT

The variable-dimension T² control chart (VDT² chart) was recently proposed for monitoring the mean of multivariate processes in which some of the quality variables are easy and inexpensive to measure while other variables require substantially more effort or expense. The chart requires most of the times that only the inexpensive variables be sampled, switching to sampling all the variables only when a warning is triggered. It has good ARL performance compared with the standard T² chart, while significantly reducing the sampling cost. However, like the T² chart, it has limited sensitivity to small and moderate mean shifts. To detect such shifts faster, we developed an exponentially weighted moving average (EWMA) version of the VDT² chart, along with Markov chain models for ARL calculation, and software (made available) for optimizing the chart design. The optimization software, which is based on genetic algorithms, runs in Windows^© and has a friendly user interface. The performance analysis shows the great gain in performance achieved by the incorporation of the EWMA procedure.

KEYWORDS:

• exponentially weighted moving average
• genetic algorithms
• multivariate process control
• optimization
• T² control chart
• variable dimension

Acknowledgments

We want to thank two anonymous reviewers and the editor, whose comments and suggestions contributed to improve the final quality of this article.

Funding

This work was partly supported by the CNPq, Ministry of Science and Technology, Brazil, through research fellowship grants for the first author (projects number 307453/2011-1 and 308677/2015-3) and a visiting professor short-term support for the second author (project number 453054/2014-5); and by the SENESCYT-Ecuador (National Secretary of Higher Education, Science, Technology and Innovation of Equator).

Additional information

Notes on contributors

Eugenio K. Epprecht

Eugenio K. Epprecht is an Associate Professor at the Dept of Industrial Engineering of PUC-Rio. He holds a PhD in Computer Science by the University of Namur, Belgium. His major research interest is in Statistical Process Control. He is a member of ASQ.

Francisco Aparisi

Francisco Aparisi is a full professor at Universidad Politécnica de Valencia (UPV), Spain. He holds a PhD in Statistics and Operational Research by UPV. His major research interest is in Statistical Process Control and optimization by Genetic Algorithms.

Omar Ruiz

Omar Ruiz is a Professor in Instituto de Ciencias Matemáticas of the Escuela Superior Politécnica del Litoral (ESPOL), Ecuador. He holds a PhD in Statistics and Operational Research by UPV, Spain. His main research interests are in Biostatistics and Statistical Process Control.