Adaptive cumulative sum charts with the adaptive runs rule

Abstract

Adaptive cumulative sum (ACUSUM) charts, which adjust the reference value dynamically based on estimated shift size, provide good performance in detecting a range of mean shifts. However, when the range is wide, ACUSUM may not perform well for small shifts over the range. An adaptive runs rule, which is motivated by the concept of supplementary runs rule, is proposed, in order to make control charts more sensitive to small mean shifts. The adaptive runs rule assigns scores to consecutive runs based on the estimated shift size of the mean. The ACUSUM chart is supplemented with the adaptive runs rule to enhance its sensitivity in detecting small mean shifts. The average run length performance of the ACUSUM chart with the adaptive runs rule is compared with those of cumulative sum and variants of adaptive charts including ACUSUM. The experimental results reveal that the ACUSUM chart with the adaptive runs rule achieves superior detection performance over a wide range of mean shifts.

Keywords:

• adaptive cumulative sum
• average run length
• cumulative sum
• exponentially weighted moving average
• statistical process control
• supplementary runs rule

Acknowledgments

The authors are very grateful to the editor and two anonymous referees for their valuable and constructive comments and suggestions which greatly improved the final version of the paper. This paper was made possible by the support of NPRP 08-323-2-116 grant from Qatar National Research Fund (QNRF). The statements made herein are solely the responsibility of the authors.