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.     

An extended nonparametric homogeneously weighted moving average sign control chart

Parametric (or traditional) control charts are based on the assumption that the quality characteristic of interest follows a specific distribution. However, in many applications, there is a lack of knowledge about the underlying distribution. To this end, nonparametric (or distribution-free) control charts have been developed in recent years. In this article, a nonparametric double homogeneously weighted moving average (DHWMA) control chart based on the sign statistic is proposed for monitoring the location parameter of an unknown and continuous distribution. The performance of the proposed chart is measured through the run-length distribution and its associated characteristics by performing Monte Carlo simulations. The DHWMA sign chart is compared with other nonparametric sign charts, such as the homogeneously weighted moving average, generally weighted moving average (GWMA), double GWMA, and triple exponentially weighted moving average sign charts, as well as the traditional DHWMA chart. The results indicate that the proposed chart performs just as well as and in some cases better than its competitors, especially for small shifts. Finally, two examples are provided to show the application and implementation of the proposed chart.     

Mixed Cumulative Sum–Exponentially Weighted Moving Average Control Charts: An Efficient Way of Monitoring Process Location

Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts are famous statistical tools, to handle special causes and to bring the process back in statistical control. Shewhart charts are useful to detect large shifts, whereas EWMA and CUSUM are more sensitive for small to moderate shifts. In this study, we propose a new control chart, named mixed CUSUM‐EWMA chart, which is used to monitor the location of a process. The performance of the proposed mixed CUSUM‐EWMA control chart is measured through the average run length, extra quadratic loss, relative average run length, and a performance comparison index study. Comparisons are made with some existing charts from the literature. An example with real data is also given for practical considerations. Copyright © 2014 John Wiley & Sons, Ltd.     

Practitioner advice: ERLDAT–A web-based tool to design and analyze EWMA control charts

The performance of a control chart is completely characterized by its run length distribution. Quality practitioners usually do not have access to the run length distribution but rely on the average run length (ARL) to design and evaluate the performance of an exponentially weighted moving average (EWMA) control chart. This article presents a web-based tool that provides users easy access to the Phase 2 (online or monitoring phase) run length distribution for a two-sided EWMA control chart with known parameters. The web-based tool calculates the run length distribution, percentiles of the run length distribution, as well as the mean (ARL) and variance (VRL) of the run length distribution. Additional functionality of the web-based tool includes plotting the run length distribution functions, building tables of the quantiles of the run length distribution, finding the smoothing parameter (λ) for an EWMA control chart for fixed control limit that satisfies ARL, VRL or percentile performance, and finding the control chart limit (k) for an EWMA control chart that satisfies ARL, VRL, or percentile performance. This tool and these techniques enable quality practitioners to better design and evaluate EWMA control charts.     

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 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 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.     

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.     

Mixed Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Monitoring

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart‐type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA‐based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright © 2012 John Wiley & Sons, Ltd.     

A moving average control chart using a robust scale estimator for process dispersion

Control charts are one of the most powerful tools used to detect and control industrial process deviations in statistical process control. In this paper, a moving average control chart based on a robust scale estimator of standard deviation, namely, the sample median absolute deviation (MAD) statistic, for monitoring process dispersion, is proposed. A simulation study is conducted to evaluate the performance of the proposed moving average median absolute deviation (MA‐MAD) chart, in terms of average run length for various distributions. The results show that the moving average MAD chart performs well in detecting small and moderate shifts in process dispersion, especially when the normality assumption is violated. In addition, this chart is very efficient, especially when the quality characteristic follows a skewed distribution. Numerical and simulated examples are given at the end of the paper.     

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

A new hybrid exponentially weighted moving average (HEWMA) control chart has been proposed in the literature for efficiently monitoring the process mean. In that paper, the computed variance of the HEWMA statistic was, unfortunately, not correct! In this discussion, the correct variance of the HEWMA statistic is given, and the run length characteristics of the HEWMA control chart are studied and explored. It is noticed that not only the superiority of the HEWMA control chart remains over the existing (considered before) charts but also the new results based on the corrected control limits are more profound and reflective. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

A sensitive non-parametric EWMA control chart

In practice, we may not always have normally distributed quality characteristics of interest. This leads to the need for non-parametric techniques which are not dependent on the assumptions about the parent distribution. This study develops a non-parametric exponentially weighted moving average (EWMA) chart (namely the NPSS_EWMA chart) for an improved monitoring of process location. The proposal is based on the use of sign statistics on a moving pattern in an EWMA setup. The design structure of the proposed chart is developed and its performance is evaluated in terms of different properties including average run length (ARL), standard deviation run length (SDRL), percentiles, relative ARL (RARL), extra quadratic loss (EQL), and performance comparison index (PCI). The proposal is compared with recently developed non-parametric counterparts namely NPS_EWMA, NPAS_EWMA, and NPS_CUSUM charts. It is observed that the design structure of the proposed NPSS_EWMA chart outshines the existing counterparts. An application example is also included in the study for practical demonstration.     

A moving average S control chart for monitoring process variability

An efficient alternative to the S control chart for detecting shifts of small magnitude in the process variability using a moving average based on the sample standard deviation s statistic is proposed. Control limit factors are derived for the chart for different values of sample size and span w. The performance of the moving average S chart is compared to the S chart in terms of average run length. The result shows that the performance of moving average S chart for varying values of w outweigh those of the S chart for small and moderate shifts in process variability.     

New GWMA‐CUSUM control chart for monitoring the process dispersion

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely accepted because of their fantastic speed in identifying small‐to‐moderate unusual variations in the process parameter(s). Recently, a new CUSUM chart has been proposed that uses the EWMA statistic, called the CS‐EWMA chart, for monitoring the process variability. On similar lines, in order to further improve the detection ability of the CS‐EWMA chart, we propose a CUSUM chart using the generally weighted moving average (GWMA) statistic, named the GWMA‐CUSUM chart, for monitoring the process dispersion. Monte Carlo simulations are used to compute the run length profiles of the GWMA‐CUSUM chart. On the basis of the run length comparisons, it turns out that the GWMA‐CUSUM chart outperforms the CUSUM and CS‐EWMA charts when identifying small variations in the process variability. A simulated dataset is also used to explain the working and implementation of the CS‐EWMA and GWMA‐CUSUM charts.     

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

Exponentially weighted moving average (EWMA) quality control schemes have been recognized as a potentially powerful process monitoring tool because of their superior speed in detecting small to moderate shifts in the underlying process parameters. In quality control literature, there exist several EWMA charts that are based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. Recently, a mixed RSS (MxRSS) scheme has been introduced, which encompasses both SRS and RSS schemes, and is a cost‐effective alternative to the RSS scheme. In this paper, we propose new EWMA control charts for efficiently monitoring the process mean based on MxRSS and imperfect MxRSS (IMxRSS) schemes, named EWMA–MxRSS and EWMA–IMxRSS charts, respectively. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed EWMA charts. The run length performances of the suggested EWMA charts are compared with the classical EWMA chart based on SRS (EWMA–SRS). It turns out that both EWMA–MxRSS and EWMA–IMxRSS charts perform uniformly better than the EWMA–SRS chart when detecting all different shifts in the process mean. An application to a real data set is provided as an illustration of the design and implementation of the proposed EWMA chart. Copyright © 2014 John Wiley & Sons, Ltd.     

An exponentially weighted moving average chart based on likelihood‐ratio test for monitoring Weibull mean and variance with subgroups

Monitoring changes in the Weibull mean and variance simultaneously is of interest in quality control. The mean and variance of a Weibull process are determined by its shape and scale parameters. Most studies are focused on monitoring the Weibull scale parameter with fixed shape parameter or the Weibull shape parameter with fixed scale parameter. In this paper, we propose an exponentially weighted moving average chart based on the likelihood‐ratio test and an inverse error function called ELR chart to monitor changes in the Weibull mean and variance simultaneously. The simulation approach is used to derive the average run length. We compare our proposed chart with other existing control charts for 3 cases, including scale parameter changes with fixed shape parameter, shape parameter changes with fixed scale parameter, and both parameters changes. The results show that the ELR chart outperforms the other control charts in terms of average run length in most cases. Two numerical examples are used to illustrate the applications of the proposed control chart.     

The Generally Weighted Moving Average Control Chart for Detecting Small Shifts in the Process Mean

A generalization of the exponentially weighted moving average (EWMA) control chart is proposed and analyzed. The generalized control chart we have proposed is called the generally weighted moving average (GWMA) control chart. The GWMA control chart, with time-varying control limits to detect start-up shifts more sensitively, performs better in detecting small shifts of the process mean. We use simulation to evaluate the average run length (ARL) properties of the EWMA control chart and GWMA control chart. An extensive comparison reveals that the GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in the mean of a process. To enhance the detection ability of the GWMA control chart, we submit the composite Shewhart-GWMA scheme to monitor process mean. The composite Shewhart-GWMA control chart with/without runs rules is more sensitive than the GWMA control chart in detecting small shifts of the process mean. The resulting ARLs obtained by the GWMA control chart when the assumption of normality is violated are discussed.     

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.     

Simultaneous Use of Runs Rules and Auxiliary Information With Exponentially Weighted Moving Average Control Charts

Quality has become a key determinant of success in all aspects of industry. Exponentially weighted moving average control chart is an important tool of statistical process control used to monitor and improve quality of industrial processes. To enhance the performance of control charts, there are many strategies including the choice of an efficient plotting statistic, the choice of an efficient sampling design, the application of runs rules, and the use auxiliary information among many others. In this study, we propose nine different signaling schemes to enhance the performance of an exponentially weighted moving average control chart for location parameter, which is based on the exploitation of auxiliary information. Performance evaluation of the proposed schemes is carried out in terms of average run length. Comparisons of proposals are made with the classical as well as the auxiliary based exponentially weighted moving average and cumulative sum charts, which indicate that the proposed schemes perform better than the comparative counterparts under discussion. Copyright © 2016 John Wiley & Sons, Ltd.