New Exponentially Weighted Moving Average Control Charts for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have received considerable attention for detecting small changes in the process mean or the process variability. Several EWMA control charts are constructed using logarithmic and normalizing transformations on unbiased sample variance for monitoring changes in the process dispersion. In this paper, we propose new EWMA control charts for monitoring process dispersion based on the best linear unbiased absolute estimators obtained under simple random sampling (SRS) and ranked set sampling (RSS) schemes, named EWMA‐SRS and EWMA‐RSS control charts. The performance of the proposed EWMA control charts is evaluated in terms of the average run length and standard deviation of run length, estimated by using Monte Carlo simulations. The proposed EWMA control charts are then compared with their existing counterparts for detecting increases and decreases in the process dispersion. It turns out that the EWMA‐RSS control chart performs uniformly better than its analogues for detecting overall changes in process dispersion. Moreover, the EWMA‐SRS chart significantly outperforms the existing EWMA charts for detecting increases in process variability. A real data set is also used to explain the construction and operations of the proposed EWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.     

A Flexible and Generalized Exponentially Weighted Moving Average Control Chart for Count Data

The Conway–Maxwell–Poisson distribution can be used to model under‐dispersed or over‐dispersed count data. This study proposes a flexible and generalized attribute exponentially weighted moving average (EWMA), namely GEWMA, control chart for monitoring count data. The proposed EWMA chart is based on the Conway–Maxwell–Poisson distribution. The performance of the proposed chart is evaluated in terms of run length (RL) characteristics such as average RL, median RL, and standard deviation of the RL distribution. The average RL of the proposed GEWMA chart is compared with Sellers chart. The sensitivity of the standard Poisson EWMA (PEWMA) chart is also studied and compared with the proposed GEWMA chart for under‐dispersed or over‐dispersed data. It has been observed that the PEWMA chart is very sensitive for under‐dispersed or over‐dispersed data while the proposed GEWMA is very robust. Finally, the generalization of the proposed chart to the Bernoulli EWMA, PEWMA, and geometric EWMA charts is also studied using someone simulated data sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Enhancing the Performance of Combined Shewhart‐EWMA Charts

The combination of Shewhart control charts and an exponentially weighted moving average (EWMA) control charts to simultaneously monitor shifts in the mean output of a production process has proven very effective in handling both small and large shifts. To improve the sensitivity of the control chart to detect off‐target processes, we propose a combined Shewhart‐EWMA (CSEWMA) control chart for monitoring mean output using a more structured sampling technique, i.e. ranked set sampling (RSS) instead of the traditional simple random sampling. We evaluated the performance of the proposed charts in terms of different run length (RL) properties including average RL, standard deviation of the RL, and percentile of the RL. Comparisons of these charts with some existing control charts designed for monitoring small, large, or both shifts revealed that the RSS‐based CSEWMA charts are more sensitive and offer better protection against all types of shifts than other schemes considered in this study. Copyright © 2012 John Wiley & Sons, Ltd.     

On developing an exponentially weighted moving average chart under progressive setup: An efficient approach to manufacturing processes

The exponentially weighted moving average (EWMA) control chart is a memory chart that is widely used in process monitoring to spot small and persistent disturbances in the process parameter(s). This chart requires normality of the quality characteristic(s) of interest and a smaller choice of smoothing parameter. Any deviations from these conditions affect its performance in terms of efficiency and robustness. For the said two concerns, this study develops a new mixed EWMA chart under progressive setup (mixed EWMA–progressive mean [MEP] chart). The proposed MEP chart combines the advantages of robustness (under nonnormal scenarios) and high sensitivity to small and persistent shifts in the process mean. The performance of the proposed MEP control chart is evaluated in terms of average run length and some other characteristics of run length distribution. The assessment of the proposed chart is made under standard normal, student's t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed MEP chart is also compared with some existing competitors including the classical EWMA, the classical cumulative sum (CUSUM), the homogenously weighted moving average, the mixed EWMA–CUSUM, the mixed CUSUM–EWMA and the double EWMA charts. The analysis reveals that the proposal of this study offers a superior design structure relative to its competing counterparts. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided in the study.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Nonparametric EWMA Control Chart for Monitoring Process Variability

The exponentially weighted moving average (EWMA) control chart is one of a potentially powerful process monitoring tool of the statistical process control. The EWMA chart has now been widely used because of its excellent ability to detect small to moderate shifts in the process parameter(s). In this study, we propose a new nonparametric/distribution‐free EWMA chart for efficiently monitoring the changes in the process variability. We use extensive Monte Carlo simulations to compute the run length profiles of the proposed EWMA chart. For a better performance comparison, the proposed EWMA chart is compared with a recent existing EWMA chart that has already shown to have better performance than the existing control charts. It turns out that the proposed EWMA chart performs substantially and uniformly better than the existing powerful EWMA chart. The working and implementation of the proposed and existing EWMA charts with the help of an illustrative example are also included in this study. Copyright © 2017 John Wiley & Sons, Ltd.     

A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

A New Synthetic Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as a potentially powerful process monitoring tool of the statistical process control because of their excellent speed in detecting small to moderate shifts in the process parameters. Recently, new EWMA and synthetic control charts have been proposed based on the best linear unbiased estimator of the scale parameter using ordered ranked set sampling (ORSS) scheme, named EWMA‐ORSS and synthetic‐ORSS charts, respectively. In this paper, we extend the work and propose a new synthetic EWMA (SynEWMA) control chart for monitoring the process dispersion using ORSS, named SynEWMA‐ORSS chart. The SynEWMA‐ORSS chart is an integration of the EWMA‐ORSS chart and the conforming run length chart. Extensive Monte Carlo simulations are used to estimate the run length performances of the proposed control chart. A comprehensive comparison of the run length performances of the proposed and the existing powerful control charts reveals that the SynEWMA‐ORSS chart outperforms the synthetic‐R, synthetic‐S, synthetic‐D, synthetic‐ORSS, CUSUM‐R, CUSUM‐S, CUSUM‐ln S², EWMA‐ln S² and EWMA‐ORSS charts when detecting small shifts in the process dispersion. A similar trend is observed when the proposed control chart is constructed under imperfect rankings. An application to a real data is also provided to demonstrate the implementation and application of the proposed control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

Use of ranked set sampling in nonparametric control charts

Control charts are widely used to identify changes in a production process. Nonparametric or distribution-free charts can be useful when there is a lack of underlying process distribution. A nonparametric exponentially weighted moving average (EWMA) control chart based on sign test using ranked set sampling (RSS) is proposed to monitor the possible small shifts in the process mean. The performance of the proposed chart is evaluated in terms of average run length, median run length, and standard deviation of the run length distribution. It has been observed that the proposed version of the EWMA sign chart, using RSS shows better detection ability than that version of the EWMA sign chart and the parametric EWMA control chart using simple random sampling scheme. An application with real data-set is also provided to explain the proposal for practical considerations.     

New EWMA control charts for monitoring process dispersion using auxiliary information

The exponentially weighted moving average (EWMA) control chart is a well‐known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary‐information–based (AIB) EWMA (AIB‐EWMA) charts. These AIB‐EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB‐EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB‐Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB‐EWMA charts.     

New memory‐type dispersion control charts

The exponentially weighted moving average (EWMA) control chart is a memory‐type process monitoring tool that is frequently used to monitor small and moderate disturbances in the process mean and/or process dispersion. In this study, we propose 2 new memory‐type control charts for monitoring changes in the process dispersion, namely, the generally weighted moving average and the hybrid EWMA charts. We use Monte Carlo simulations to compute the run length profiles of the proposed control charts. The run length comparisons of the proposed and existing charts reveal that the generally weighted moving average and hybrid EWMA charts provide better protection than the existing EWMA chart when detecting small to moderate shifts in the process dispersion. An illustrative dataset is also used to show the superiority of the proposed charts over the existing chart.     

Progressive Mean Control Chart for Monitoring Process Location Parameter

Control charts are widely used for process monitoring. They show whether the variation is due to common causes or whether some of the variation is due to special causes. To detect large shifts in the process, Shewhart‐type control charts are preferred. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are generally used to detect small and moderate shifts. Shewhart‐type control charts (without additional tests) use only current information to detect special causes, whereas CUSUM and EWMA control charts also use past information. In this article, we proposed a control chart called progressive mean (PM) control chart, in which a PM is used as a plotting statistic. The proposed chart is designed such that it uses not only the current information but also the past information. Therefore, the proposed chart is a natural competitor for the classical CUSUM, the classical EWMA and some recent modifications of these two charts. The conclusion of this article is that the performance of the proposed PM chart is superior to the compared ones for small and moderate shifts, and its performance for large shifts is better (in terms of the average run length). Copyright © 2012 John Wiley & Sons, Ltd.     

Improving the Performance of Exponentially Weighted Moving Average Control Charts

A control chart is a graphical tool used for monitoring a production process and quality improvement. One such charting procedure is the Shewhart‐type control chart, which is sensitive mainly to the large shifts. For small shifts, the cumulative sum (CUSUM) control charts and exponentially weighted moving average (EWMA) control charts were proposed. To further enhance the ability of the EWMA control chart to quickly detect wide range process changes, we have developed an EWMA control chart using the median ranked set sampling (RSS), median double RSS and the double median RSS. The findings show that the proposed median‐ranked sampling procedures substantially increase the sensitivities of EWMA control charts. The newly developed control charts dominate most of their existing counterparts, in terms of the run‐length properties, the Average Extra Quadratic Loss and the Performance Comparison Index. These include the classical EWMA, fast initial response EWMA, double and triple EWMA, runs‐rules EWMA, the max EWMA with mean‐squared deviation, the mixed EWMA‐CUSUM, the hybrid EWMA and the combined Shewhart–EWMA based on ranks. An application of the proposed schemes on real data sets is also given to illustrate the implementation and procedural details of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.     

CS‐EWMA Chart for Monitoring Process Dispersion

Control charts are the most extensively used technique to detect the presence of special cause variations in processes. They can be classified into memory and memoryless control charts. Cumulative sum and exponentially weighted moving average control charts are memory‐type control charts as their control structures are developed in such a way that the past information is not ignored as it is done in the case of memoryless control charts, like the Shewhart‐type control charts. The present study is based on the proposal of a new memory‐type control chart for process dispersion. This chart is named as CS‐EWMA chart as its plotting statistic is based on a cumulative sum of the exponentially weighted moving averages. Comparisons with other memory charts used to monitor the process dispersion are done by means of the average run length. An illustration of the proposed technique is done by applying the CS‐EWMA chart on a simulated dataset. Copyright © 2012 John Wiley & Sons, Ltd.     

Multivariate EWMA control charts using individual observations for process mean and variance monitoring and diagnosis

Most multivariate control charts in the literature are designed to detect either mean or variation shifts rather than both. A simultaneous use of the Hotelling T ² and |S| control charts has been proposed but the Hotelling T ² reacts to mean shifts, dispersion changes, and changes of correlations among responses. The combination of two multivariate control charts into one chart sometimes loses the ability to provide detailed diagnostic information when a process is out-of-control. In this research a new multivariate control chart procedure based on exponentially weighted moving average (EWMA) statistics is proposed to monitor process mean and variance simultaneously to identify proper sources of variations. Two multivariate EWMA control charts using individual observations are proposed to achieve a quick detection of mean or variance shifts or both. Simulation studies show that the proposed charts are capable of identifying appropriate types of shifts in terms of correct detection percentages. A manufacturing example is used to demonstrate how the proposed charts can be properly set-up based on average run length values via simulations. In addition, correct detection rates of the proposed charts are explored.     

An efficient adaptive EWMA control chart for monitoring the process mean

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.     

Memory‐Type Control Charts for Monitoring the Process Dispersion

Control charts have been broadly used for monitoring the process mean and dispersion. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are memory control charts as they utilize the past information in setting up the control structure. This makes CUSUM and EWMA‐type charts good at detecting small disturbances in the process. This article proposes two new memory control charts for monitoring process dispersion, named as floating T ? S² and floating U ? S² control charts, respectively. The average run length (ARL) performance of the proposed charts is evaluated through a simulation study and is also compared with the CUSUM and EWMA charts for process dispersion. It is found that the proposed charts are better in detecting both positive as well as negative shifts. An additional comparison shows that the floating U ? S² chart has slightly smaller ARLs for larger shifts, while for smaller shifts, the floating T ? S² chart has better performance. An example is also provided which shows the application of the proposed charts on simulated datasets. Copyright © 2013 John Wiley & Sons, Ltd.     

New Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely accepted because of their excellent performance in detecting small to moderate shifts in the process parameters. In this paper, we propose new EWMA control charts for monitoring the process mean and the process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered double ranked set sampling (ODRSS) and ordered imperfect double ranked set sampling (OIDRSS) schemes, named EWMA‐ODRSS and EWMA‐OIDRSS charts, respectively. We use Monte Carlo simulations to estimate the average run length, median run length, and standard deviation of run length of the proposed EWMA charts. We compare the performances of the proposed EWMA charts with the existing EWMA charts when detecting shifts in the process mean and in the process variability. It turns out that the EWMA‐ODRSS mean chart performs uniformly better than the classical EWMA, fast initial response‐based EWMA, Shewhart‐EWMA, and hybrid EWMA mean charts. The EWMA‐ODRSS mean chart also outperforms the Shewhart‐EWMA mean charts based on ranked set sampling (RSS) and median RSS schemes and the EWMA mean chart based on ordered RSS scheme. Moreover, the graphical comparisons of the EWMA dispersion charts reveal that the proposed EWMA‐ODRSS and EWMA‐OIDRSS charts are more sensitive than their counterparts. We also provide illuminating examples to illustrate the implementation of the proposed EWMA mean and dispersion charts. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean

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.     

On mixed memory control charts based on auxiliary information for efficient process monitoring

Control charts are popular monitoring tools in statistical process control toolkit. These are used to identify assignable causes in the process parameters (location and/or dispersion). These assignable causes result in a shift in the process parameter(s). The shift can be categorized into three sizes (small, moderate, and large). Memory control charts such as the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are effective for identifying small-to-moderate shift(s) in the process. Likewise, mixed memory control charts are useful for efficient process monitoring. In this study, we have proposed two new mixed memory control charts based on auxiliary information named MxMEC and MxMCE control charts to improve the efficiency of these mixed charts. The MxMEC chart is a merger of the auxiliary information based MxEWMA chart and the classical CUSUM chart. Likewise, the MxMCE chart integrates the auxiliary information based MxCUSUM with the classical EWMA chart. The proposed MxMEC and MxMCE charts are evaluated through famous performance measures including average run length, extra quadratic loss, relative average run length, and performance comparison index. The performance of the study proposals is compared with the existing counterparts such as the classical CUSUM and EWMA, MxCUSUM, MxEWMA, MEC, MCE, and runs rules-based CUSUM charts. The comparisons revealed the superiority of the proposed charts against other competing charts particularly for small-to-moderate shifts in the process location. Finally, a real-life data is used to show the implementation procedure of the proposed charts in practical situations.