On efficient change point detection using a step cumulative sum control chart

Abstract

Control charts are widely used to monitor the stability of processes and Shewhart is the most commonly used type of chart because of the simplicity of its structure. To improve the performance, there are several modifications on control chart suggested since its proposal like cumulative sum and exponentially weighted moving average control charts. The cumulative sum chart accumulates all the deviations from target mean higher than a specific design parameter which can be used to controls the sensitivity of this chart. The optimal choice of this design parameter is half of the target shift size. This results into an optimal performance in terms of quick detection of shift that is equal to the target shift size. For shift sizes other than target, the cumulative sum chart loses its performance and becomes inferior to other control charts in terms of average run length. Since we rarely know the process shift size that is going to occur in future, this study proposes a revision in the structure of cumulative sum chart. The adjusted cumulative sum chart is shown to be very flexible for a wide range of shifts, when designed against a target shift size. The proposed adjusted cumulative sum control chart is compared with cumulative sum, exponentially weighted, combined Shewhart-CUSUM, progressive mean, double progressive mean and mixed EWMA-CUSUM control charts in terms of zero- and steady-state average run lengths. The superiority zones are identified and the results are supported by a real-life implementation of the proposed scheme.

Keywords:

• average run length
• control chart
• cumulative sum
• exponentially weighted moving average
• statistical process control

Acknowledgment

The author would like to express sincere thanks to anonymous reviewers for their constructive comments, which greatly improved the earlier version of this article.

Additional information

Notes on contributors

Nasir Abbas

Nasir Abbas is Associate Professor of Statistics at the Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. His current research interests include mathematical statistics and process monitoring particularly control charting methodologies under parametric and nonparametric environments.