Detection of linear trends in process mean

Abstract

In this paper, we develop a process control approach to detect linear trends in the process mean. A statistic based on the deviation between the target mean and the expected mean of the process is used in the development of the new approach. The statistic is shown to have a chi-square distribution. The approach is described and its performance is compared with cumulative sum (CUSUM), exponentially weighted moving average (EWMA), Shewhart, and generalized likelihood ratio (GLR) charts in detecting linear trends in the process mean. The results indicate that proposed approach is effective in detecting small to large trends. We also investigate the run length properties of the proposed approach under linear trends and compare its values with simulation results. Finally, we analyse the performance of the proposed approach in detecting the time when a drift occurs in the process and compare it with CUSUM and EWMA estimators. The results show that the proposed approach is more effective in detecting drift time for moderate and large trends.

Keywords:

• Control charts
• Linear trend
• Change time detection

Acknowledgements

The authors would like to thank the referees for their helpful comments that greatly improved this paper.