The Performance of the Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

The adaptive exponentially weighted moving average (AEWMA) control chart has the advantage of detecting balance mixed range of mean shifts. Its performance has been studied under the assumption that the process parameters are known. Under this assumption, previous studies have shown AEWMA to provide superior statistical performance when compared with other different types of control charts. In practice, however, the process parameters are usually unknown and are required to be estimated. Using a Markov Chain approach, we show that the performance of the AEWMA control chart is affected when parameters are estimated compared with the known‐parameter case. In addition, we show the effect of different standard deviation estimators on the chart performance. Finally, a performance comparison is conducted between the exponentially weighted moving average (EWMA) chart and the AEWMA chart when the process parameters are unknown. We recommend the use of the AEWMA chart over the ordinary EWMA chart especially when a small number of Phase I samples is available to estimate the unknown parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

The performance of control charts can be adversely affected when based on parameter estimates instead of known in‐control parameters. Several studies have shown that a large number of phase I observations may be needed to achieve the desired in‐control statistical performance. However, practitioners use different phase I samples and thus different parameter estimates to construct their control limits. As a consequence, there would be in‐control average run length (ARL) variation between different practitioners. This kind of variation is important to consider when studying the performance of control charts with estimated parameters. Most of the previous literature has relied primarily on the expected value of the ARL (AARL) metric in studying the performance of control charts with estimated parameters. Some recent studies, however, considered the standard deviation of the ARL metric to study the performance of control charts. In this paper, the standard deviation of the ARL metric is used to study the in‐control and out‐of‐control performance of the adaptive exponentially weighted moving average (AEWMA) control chart. The performance of the AEWMA chart is then compared with that of the Shewhart and EWMA control charts. The simulation results show that the AEWMA chart might represent a good solution for practitioners to achieve a reasonable amount of ARL variation from the desired in‐control ARL performance. In addition, we apply a bootstrap‐based design approach that provides protection against frequent false alarms without deteriorating too much the out‐of‐control performance. Copyright © 2014 John Wiley & Sons, Ltd.     

Design Strategies for the Multivariate Exponentially Weighted Moving Average Control Chart

The multivariate exponentially weighted moving average (MEWMA) control chart has received significant attention from researchers and practitioners because of its desirable properties. There are several different approaches to the design of MEWMA control charts: statistical design; economic–statistical design; and robust design. In this paper a review and comparison of these design strategies is provided.Copyright © 2004 John Wiley & Sons, Ltd.     

A Multivariate Exponentially Weighted Moving Average Control Chart

A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ² and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ² charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.     

The Negative Binomial Exponentially Weighted Moving Average Chart with Estimated Control Limits

The control chart based on the compound Poisson distribution (the negative binomial exponentially weighted moving average (EWMA) chart) has been shown to be more effective than the c‐chart to monitor the wafer nonconformities in semiconductor production process. The performance of the negative binomial EWMA chart is generally evaluated with the assumption that the process parameters are known. However, in many control chart applications, the process parameters are usually unknown and are required to be estimated. For an accurate parameter estimate, a very large sample size may be required, which is seldom available in the applications. This article investigates the effect of parameter estimation on the run length properties of the negative binomial EWMA charts. Using a Markov chain approach, we show that the performance of the negative binomial EWMA chart is affected when parameters are estimated compared with the known‐parameter case. We also provide recommendations regarding phase I sample sizes, smoothing constant and clustering parameter. The sample size must be quite large for the in‐control chart performance to be close to that for the known‐parameter case. Finally, a wafer process example has been used to highlight the practical implications of estimation error and to offer advice to practitioners when constructing/analysing a phase I sample. Copyright © 2013 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.     

An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

We evaluate the performance of the Crosier's cumulative sum (C‐CUSUM) control chart when the probability distribution parameters of the underlying quality characteristic are estimated from Phase I data. Because the average run length (ARL) under estimated parameters is a random variable, we study the estimation effect on the chart performance in terms of the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL). Previous evaluations of this control chart were conducted while assuming known process parameters. Using the Markov chain and simulation approaches, we evaluate the in‐control performance of the chart and provide some quantiles for its in‐control ARL distribution under estimated parameters. We also compare the performance of the C‐CUSUM chart to that of the ordinary CUSUM (O‐CUSUM) chart when the process parameters are unknown. Our results show that large number of Phase I samples are required to achieve a quite reasonable performance. Additionally, the performance of the C‐CUSUM chart is found to be superior to that of the O‐CUSUM chart. Finally, we recommend the use of a recently proposed bootstrap procedure in designing the C‐CUSUM chart to guarantee, at a certain probability, that the in‐control ARL will be of at least the desired value using the available amount of Phase I data. Copyright © 2015 John Wiley & Sons, Ltd.     

A Robust Phase I Exponentially Weighted Moving Average Chart for Dispersion

A Phase I estimator of the dispersion should be efficient under in‐control data and robust against contaminations. Most estimation methods proposed in the literature are either efficient or robust against either sustained shifts or scattered disturbances. In this article, we propose a new estimation method of the dispersion parameter, based on exponentially weighted moving average charting, which is efficient and robust to both types of unacceptable observations in Phase I. We compare the method with various existing estimation methods and show that the proposed method has the best overall performance if it is unknown what type of contaminations are present in Phase I. We also study the effect of the robust estimator from Phase I on the Phase II exponentially weighted moving average control chart performance. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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 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 Exponentially Weighted Moving Average Charts: Discussion

Abbas et al. (Abbas N, Riaz M, Does RJMM. Enhancing the performance of EWMA charts. Quality and Reliability Engineering International 2011; 27(6):821–833) proposed the use of signaling schemes with exponentially weighted moving average charts (named as 2/2 and modified ? 2/3 schemes) for their improved design structures. A two‐sided control structure of these schemes is given in the paper. The computational results in some of the tables of that paper for modified ? 2/3 are mistakenly given for the one‐sided control structure. The corrected two‐sided results are provided here. It is noticed that the superiority of the proposed scheme over the classical exponentially weighted moving average chart remains but is less pronounced. Copyright © 2014 John Wiley & Sons, Ltd.     

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

Maximum exponentially weighted moving average (MaxEWMA) control charts have attracted substantial interest because of their ability to simultaneously detect increases and decreases in both the process mean and the process variability. In this paper, we propose new MaxEWMA control charts based on ordered double ranked set sampling (ODRSS) and ordered imperfect double ranked set sampling (OIDRSS) schemes, named MaxEWMA‐ODRSS and MaxEWMA‐OIDRSS control charts, respectively. The proposed MaxEWMA control charts are based on the best linear unbiased estimators obtained under ODRSS and OIDRSS schemes. Extensive Monte Carlo simulations are used to estimate the average run length and standard deviation of the run length of the proposed MaxEWMA control charts. The run length performances and the diagnostic abilities of the proposed MaxEWMA control charts are compared with that of their counterparts based on simple random sampling (SRS), ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling schemes (OIRSS) schemes, that is, MaxEWMA‐SRS, maximum generally weighted moving average (MaxGWMA‐SRS), MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts. It turns out that the proposed MaxEWMA‐ODRSS and MaxEWMA‐OIDRSS control charts perform uniformly better than the MaxEWMA‐SRS, MaxGWMA‐SRS, MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts in simultaneous detection of shifts in the process mean and variability. An application to real data is also provided to illustrate the implementations of the proposed and existing MaxEWMA control charts. Copyright © 2014 John Wiley & Sons, Ltd.     

An Improved Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

Maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for detecting changes in both process mean and process variability. In this paper, we propose an improved MaxEWMA control charts based on ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS) schemes for simultaneous detection of both increases and decreases in the process mean and/or variability, named MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts. These MaxEWMA control charts are based on the best linear unbiased estimators of location and scale parameters obtained under ORSS and OIRSS methods. Extensive Monte Carlo simulations have been used to estimate the average run length and standard deviation of run length of the proposed MaxEWMA control charts. These control charts are compared with their counterparts based on simple random sampling (SRS), that is, MaxEWMA‐SRS and MaxGWMA‐SRS control charts. The proposed MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts are able to perform better than the MaxEWMA‐SRS and MaxGWMA‐SRS control charts for detecting shifts in the process mean and dispersion. An application to real data is provided to illustrate the implementation of the proposed MaxEWMA control charts. Copyright © 2013 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.     

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.     

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.     

A Control Chart for COM–Poisson Distribution Using Resampling and Exponentially Weighted Moving Average

In this paper, we propose a control chart using exponentially weighted moving average (EWMA) statistic for count data based on the Conway–Maxwell–Poisson (called COM–Poisson) distribution. Repetitive sampling is considered by constructing two pairs of control limits for the proposed control chart. The performance of the proposed control chart is evaluated using the average run length (ARL) for various values of specified parameters. It has been observed that the proposed control chart is more efficient in terms of ARLs as compared to the existing control charts. The tables are provided and explained with the help of example. Copyright © 2015 John Wiley & Sons, Ltd.     

Progressive Mean as a Special Case of Exponentially Weighted Moving Average

In the category of memory‐type control charts, progressive mean control chart was proposed recently, for monitoring the process location. Here we show, through the derivation, that the plotting statistic for the progressive mean control chart becomes a special case of exponentially weighted moving average when the sensitivity parameter becomes reciprocal of the sample number. Copyright © 2014 John Wiley & Sons, Ltd.