An adaptive exponentially weighted moving average control chart for poisson processes

Abstract

The Adaptive Exponentially Weighted Moving Average (AEWMA) control chart is known to be effective in detecting range of shifts simultaneously. Moreover, the AEWMA chart is known to diminish the inertia effect. The AEWMA chart is usually investigated while assuming that the monitored process follows a continuous distribution; commonly the normal distribution. In practice, however, monitored data could be of a discrete-type. We aim in this study to propose a discrete-version from the AEWMA chart; namely the Poisson AEWMA chart. The chart is compared with its counterparts; the Poisson EWMA chart and Poisson CUSUM chart using the ARL and RMI metrics. Our results show that the Poisson AEWMA chart performs more efficiently in detecting shifts of various sizes with an RMI value approaching zero. The Poisson CUSUM chart has the worst performance. Moreover, the proposed Poisson AEWMA chart is capable of detecting shifts faster than an approach based on normal approximation even for large values of the mean defects. In addition, the superiority of the Poisson AEWMA chart in diminishing the inertia effect is illustrated through a numerical example. The example shows that the Poisson AEWMA chart is capable of detecting out of control situations very fast even if the chart statistic is in a disadvantageous position before a shift occurs.

Keywords:

• Statistical quality control
• control charts
• process monitoring and control
• ARL
• Poisson distribution

Acknowledgments

The authors would like to thank the Editor and the anonymous referees for their helpful and insightful comments.

Additional information

Notes on contributors

Aya A. Aly

Aya A. Aly is an Assistant Professor of Statistics at the Faculty of Economics and Political Science, Cairo University. She graduated from the same faculty in 2004 with a Bachelor of Statistics. She received her master's degree in statistics in 2009 and her PhD in 2015 from the Faculty of Economics and Political Science, Cairo University. Her main research area of interest is statistical quality control.

Nesma A. Saleh

Nesma A. Saleh is an Assistant Professor of Statistics at the Department of Statistics, Faculty of Economics and Political Science, Cairo University. She holds her BSc (2009), MSc (2012), and PhD (2016) in statistics from Cairo University. Her main area of interest is statistical quality control.

Mahmoud A. Mahmoud

Mahmoud A. Mahmoud is Dean of the Faculty of Economics and Political Science, Cairo University. Prior to becoming Dean, he was the Vice Dean for Education and Students’ Affairs, and a Professor of Statistics at Cairo University, Faculty of Economics and Political Science. He holds his BS (1992) and MS (1997) in statistics from Cairo University, and PhD (2004) in statistics from Virginia Tech - USA. His primary area of interest is statistical quality control and improvement. He is a member of the Editorial Board of Quality and Reliability Engineering International, and Review of Economics and Political Science (REPS). He is a Deputy Editor-in-Chief in Journal of Humanities and Applied Social Sciences (JHASS).