Mixed EWMA-CUSUM and mixed CUSUM-EWMA modified control charts for monitoring first order autoregressive processes

Abstract

In practice most processes are known to produce autocorrelated observations. Autocorrelation degrades the performance of control charts by producing frequent false alarms when the process is stable or makes the charts respond slowly to the detection of out-of-control states. The effects due to autocorrelation can be eliminated by using modified charts. In this procedure, the control limits of the traditional charts are adjusted to account for the autocorrelation. In this paper, we present the Mixed EWMA-CUSUM and Mixed CUSUM-EWMA modified charts for monitoring correlated data. The performance of these charts are compared to existing modified charts such as the Shewhart, CUSUM, EWMA, combined Shewhart-CUSUM and combined Shewhart-EWMA schemes using the average run length, extra quadratic loss and relative average run length measures. Examples are given to illustrate how the charts perform.

Keywords:

• Autocorrelation
• average run length
• mean shift
• mixed CUSUM-EWMA
• mixed EWMA-CUSUM
• statistical process control

Acknowledgement

The author Saddam Akber Abbasi acknowledges the research support provided by Qatar University, Doha Qatar. Moreover, the authors Richard Osei-Aning and Muhammad Riaz acknowledge the Information Technology Centre at King Fahd University of Petroleum and Minerals for providing high performance computing resources that have contributed to the research results reported within this paper.