Improved Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Dispersion Abdul Haq, a,b * † Jennifer Brown, a Elena Moltchanova a and Amer Ibrahim Al-Omari c Exponentially weighted moving average (EWMA) control charts are mostly used to monitor the manufacturing processes. In this paper, we propose some improved EWMA control charts for detecting the random shifts in the process mean and process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS), named EWMA-ORSS and EWMA-OIRSS charts, respectively. Monte Carlo simulations are used to estimate the average run length, median run length and standard deviation of run length of the proposed EWMA control charts. It is observed that the EWMA-ORSS mean control chart is able to detect the random shifts in the process mean substantially quicker than the Shewhart-cumulative sum and the Shewhart- EWMA control charts based on the RSS scheme. Both EWMA-ORSS and EWMA-OIRSS location charts perform better than the classical EWMA, hybrid EWMA, Shewhart-EWMA and fast initial response-EWMA charts. The EWMA-ORSS dispersion control chart performs better than the simple random sampling based CS-EWMA and other EWMA control charts in efficient detection of the random shifts that occur in the process variability. An application to real data is also given to explain the implementation of the proposed EWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd. Keywords: average run length; control chart; cumulative sum; dispersion; ordered ranked set sampling; perfect ranking and imperfect rankings 1. Introduction C ontrol chart is a powerful statistical process monitoring tool that is frequently used to identify the unusual variations of the production processes. In manufacturing industries, the most commonly used control charts are Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA). The Shewhart-type control charts are based on the current information due to which they remain insensitive to small shifts that occur in the process parameters. Roberts 1 was the first to introduce the EWMA or geometric moving average control chart for monitoring the process mean. The Shewhart control chart becomes a special case of the EWMA control chart. This makes the EWMA control chart at least as effective as the Shewhart control chart. It is well known that the EWMA control charts are superior to the Shewhart control charts for detecting random shifts of smaller magnitudes. In recent years, these control charts have gained considerable attention in various fields such as signal segmentation, navigation system monitoring, nuclear engineering, health care and education (see 2–7 and references therein). In the last decades, there have been substantial advancements and improvements in the control charting methodologies. Recently, Abbas et al. 8 suggested a mixed EWMA-CUSUM control chart for monitoring the process mean. It is shown that for detection of small shifts in the process location, this control chart performs better than its competitors. Riaz et al. 9 and Abbas et al. 10 increased the efficiency of CUSUM and EWMA control charts by applying several run rules, respectively. Haq 11 proposed a hybrid EWMA control chart for monitoring the process mean by mixing plotting statistics of the EWMA control charts. It is shown that both Shewhart and EWMA control charts are its special cases. Riaz et al. 12 suggested some Shewhart’s type control charts based on auxiliary information. Some important literature in the direction of location control charts may be seen in 13–24 and references cited therein. a Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand b Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan c Department of Mathematics, Al al-Bayt University, Mafraq, Jordan *Correspondence to: Abdul Haq, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand. † E-mail: aaabdulhaq@yahoo.com Copyright © 2013 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2013 Research Article (wileyonlinelibrary.com) DOI: 10.1002/qre.1573 Published online in Wiley Online Library