A parameter-free adaptive EWMA mean chart

ABSTRACT

The adaptive EWMA (AEWMA) chart provides better sensitivity than the EWMA chart when detecting mean shifts that lie within a specific interval. In this paper, we propose a novel AEWMA chart for monitoring the mean of a normally distributed process. The proposed AEWMA chart is parameter-free apart from its decision interval, which makes it very easy to implement, and at the same time, it provides balanced protection against mean shifts of various magnitudes. The idea is to estimate the mean shift using a Shewhart statistic, and then adaptively select a suitable smoothing constant for the EWMA chart based on the estimated mean shift size. The Monte Carlo simulation method is used to compute the zero-state and steady-state run length characteristics. Based on detailed run length comparisons, it is found that the proposed AEWMA chart outperforms the existing AEWMA charts when detecting small, moderate and large shifts simultaneously in the process mean. A real data application is provided to support the theory.

KEYWORDS:

• AEWMA
• average run length
• control chart
• Monte Carlo simulation
• process mean
• zero-state and steady-state
• statistical process control

Acknowledgments

The authors are thankful to the anonymous reviewers for providing useful comments that led to an improved version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

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.

Michael B. C. Khoo

Michael B. C. Khoo is a Professor at the School of Mathematical Sciences, Universiti Sains Malaysia (USM). He received his PhD in Applied Statistics in 2001 from USM. His research interest is in statistical process control. He is a member of the American Society for Quality.