A maximum adaptive exponentially weighted moving average control chart for monitoring process mean and variability

ABSTRACT

The maximum exponentially weighted moving average (MaxEWMA) chart is widely recognized as an efficient statistical process monitoring tool because of its ability to respond quickly against small-to-moderate shifts in the process parameters. In this article, we propose a maximum adaptive exponentially weighted moving average (MaxAEWMA) chart for simultaneously monitoring the mean and/or variance of a normally distributed process. Unlike the MaxEWMA chart, the MaxAEWMA chart provides an overall good performance for detecting a range of the mean and dispersion shift sizes rather than a single value. The run length characteristics of the MaxAEWMA chart are computed using extensive Monte Carlo simulations. The MaxAEWMA chart is comprehensively compared with the MaxEWMA chart in terms of the average and standard deviation of the run length. It is found that the MaxAEWMA chart performs substantially and uniformly better than the MaxEWMA chart. An example is given to explain the implementation of the MaxEWMA and MaxAEWMA charts.

KEYWORDS:

• Average run length
• maximum adaptive EWMA
• maximum EWMA
• Monte Carlo simulation
• process mean and dispersion
• statistical process control

Acknowledgments

The author wishes to thank the referees for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Abdul Haq

Abdul Haq graduated (PhD) from the School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand. He is an assistant professor at the Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan. His research interest is in statistical process control.