Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used for monitoring the process mean. In this paper, a new hybrid EWMA (HEWMA) control chart is proposed by mixing two EWMA control charts. An interesting feature of the proposed control chart is that the traditional Shewhart and EWMA control charts are its special cases. Average run lengths are used to evaluate the performances of each of the control charts. It is worth mentioning that the proposed HEWMA control chart detects smaller shifts substantially quicker than the classical CUSUM, classical EWMA and mixed EWMA–CUSUM control charts. Copyright © 2012 John Wiley & Sons, Ltd.

In recent years, the memory‐type control charts—exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)—along with the adaptive and dual control‐charting structures have received considerable attention because of their excellent ability in providing an overall good detection over a range of mean‐shift sizes. These adaptive memory‐type control charts include the adaptive exponentially weighted moving average (AEWMA), dual CUSUM, and adaptive CUSUM charts. In this paper, we propose a new AEWMA chart for efficiently monitoring the process mean. The idea is to first design an unbiased estimator of the mean shift using the EWMA statistic and then adaptively update the smoothing constant of the EWMA chart. The run length profiles of the proposed AEWMA chart are computed using extensive Monte Carlo simulations. Based on a comprehensive comparative study, it turns out that the proposed AEWMA chart performs better than the existing AEWMA, adaptive CUSUM, dual CUSUM, and Shewhart‐CUSUM charts, in terms of offering more balanced protection against mean shifts of different sizes. An example is also used to explain the working of the existing and proposed control charts.

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The maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for simultaneously detecting both increases and decreases in the mean and/or dispersion of a process. In this paper, we propose a new auxiliary information-based (AIB) MaxEWMA control chart, called the AIB-MaxEWMA chart. The AIB-MaxEWMA chart encompasses the existing MaxEWMA chart. Extensive Monte Carlo simulations are performed to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the AIB-MaxEWMA chart. An extensive comparison reveals that the AIB-MaxEWMA chart performs uniformly better than the MaxEWMA chart. An example is also used to explain the implementation and working of the AIB-MaxEWMA chart.A. HAQ research papers on the AIB control charts now exist in the literature. Riaz 10 constructed a new AIB Shewhart chart using the regression estimator for improved process mean monitoring, and it has been shown that the AIB Shewhart chart surpasses the classical Shewhart chart. On similar lines, Riaz and Does 11 suggested a Shewhart-type dispersion chart using a ratio-type variance estimator for phase-I quality control. It turned out that the AIB dispersion chart is more powerful than the existing Shewhart unbiased sample variance chart. Ahmad et al. 12 compared the performances of several AIB Shewhart-type dispersion charts-based on the ratio-type variance estimators-with that of the existing process variance control charts, and have suggested using AIB dispersion charts for precisely monitoring the process dispersion. The AIB EWMA chart for monitoring the process mean was suggested by Abbas et al. 13 -the AIB EWMA chart is at least as sensitive as the classical EWMA chart. For efficiently monitoring the process median, Ahmad et al. 14 have suggested several improved AIB Shewhart charts using different ratio-type estimators. Recently, Riaz 15 has proposed improved Shewhart-type charts using AIB location estimators. For more interesting works on the AIB charts, we refer to Haq and Khoo, Abbasi and Riaz, Arshad et al., Riaz et al., Riaz, and Riaz et al.,[16][17][18][19][20][21] to name a few.In this paper, we propose a new MaxEWMA chart for simultaneously monitoring the process mean and dispersion of a normally distributed process using the auxiliary information on a single correlated auxiliary variable, named the AIB-MaxEWMA chart. Monte Carlo simulations are used to compute the run length profiles, including the average run length (ARL) and standard deviation of the run length (SDRL) of the proposed control chart. We show that the AIB-MaxEWMA chart encompasses the existing MaxEWMA chart. In addition, the AIB-MaxEWMA chart turns out to be as sensitive as the MaxEWMA chart.The rest of the paper is organized as follows: the MaxEWMA chart is reviewed in Section 2. Section 3 suggests an AIB-MaxEWMA chart. The performance and comparative studies are conducted in Section 4. An illustrative example is given in Section 5 to explain the working and implementation of ...