On the design and performance of upper one-sided Shewhart charts for zero-inflated Poisson processes with estimated parameters

ABSTRACT

In this work we study the performance of the upper one-sided Shewhart-type control charts for monitoring a zero-inflated Poisson process, in the case of estimated process parameters. In practice, the process parameters are unknown and must be estimated from a Phase I dataset. However, this affects the theoretical performance of a control chart and further investigation is needed to assess how much the performance of the chart is affected. Moreover, practical guidelines are necessary regarding the size of the Phase I sample so as the performance of the control chart in the case of estimated parameters is close to the known parameters case. In this work we use Monte Carlo simulation and evaluate various performance measures that provide useful information on chart’s performance in the case of estimated parameters. Both the in-control and the out-of-control performance are investigated. Moreover, we suggest adjustments to obtain the desired in-control performance, when the size of the Phase I sample is prespecified. The results show that very large Phase I samples are needed in order to make the chart’s performance, in the case of estimated parameters, close to the theoretical one. Using the suggested adjustments, these differences can be significantly reduced.

KEYWORDS:

• Conditional average run length distribution
• estimation effect
• false alarm rate
• maximum likelihood
• statistical process control

Acknowledgements

The authors would like to express their gratitude to the Associate Editor and the three anonymous reviewers for their constructive comments which improved significantly the content and the presentation of this article. Also, we would like to thank the Editor-in-Chief Prof. C.-W. Wu for the generous extension of the submission deadline.

Disclosure statement

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

Additional information

Notes on contributors

Eftychia Mamzeridou

Eftychia Mamzeridou received a BSc in Mathematics from the Aristotle University of Thessaloniki, Greece and a MSc in Statistics from the University of Sheffield, UK. At this moment, she is a PhD candidate at the University of the Aegean, Department of Statistics & Actuarial-Financial Mathematics. Also, she works as a Teaching Laboratory Staff at the same department. Her main research interest is statistical process/quality control.

Αthanasios Rakitzis

Athanasios C. Rakitzis received a PhD in statistics from the University of Piraeus, Greece. He is an assistant professor at the Department of Statistics and Insurance Science, University of Piraeus, Greece. He served as an assistant professor in the University of the Aegean (Department of Statistics & Actuarial-Financial Mathematics). He has also worked as a postdoctoral researcher (Marie Curie Fellow) at the Universite de Nantes, Institute Universitaire de Technologie de Nantes, France. His research interests include statistical process control and applied probability.