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.     

A comparison of control charts from the viewpoint of change-point estimation

ISO/DIS 7870 has presented the cumulative sum chart, the moving average chart, and the exponentially weighted moving average chart as control charts using accumulated data. In this paper, we compare the three control charts in terms of change-point estimation. We show the probability distribution, the bias and the mean square error of the change-point estimators using a Markov process and Monte Carlo simulation. These control charts have almost equivalent performances based on average run length considerations when parameters of each control chart are set appropriately. However, from the viewpoint of change-point estimation we recommend the CUSUM chart.     

Control charts for the shape parameter of reflected power function distribution under classical estimators

The reflected power function distribution (RPFD) has applications in the fields of reliability engineering and survival analysis. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows RPFD, we develop control charts to keep the process in control. A memory less control chart like a Shewhart control chart, and two memory-based control charts like an exponentially weighted moving average (EWMA) control chart and a hybrid exponentially weighted moving average (HEWMA) control chart are discussed and compared with each other. Proposal of these control charts is based on two different estimators, the percentile estimator (PE) and the modified maximum likelihood estimator (MMLE). This study shows that an HEWMA control chart based on PE performs better than PE-based Shewhart and EWMA control charts, as well as MMLE-based Shewhart, EWMA, and HEWMA control charts.     

An enhanced approach for the progressive mean control charts

To maintain and improve the quality of the processes, control charts play an important role for reduction of variation. To detect large shifts in the process parameters, Shewhart control charts are commonly applied but for small shifts, exponentially weighted moving averages (EWMA), cumulative sum (CUSUM), double exponentially weighted moving average (DEWMA), double CUSUM, moving average (MA), double moving average (DMA), and progressive mean (PM) control charts, are used. This study proposes double progressive mean (DPM) and optimal DPM control charts to enhance the performance of the PM chart. As the proposed DPM control charts use information sequentially, hence their performance is compared with natural competitors EWMA, CUSUM, DEWMA, double CUSUM, MA, DMA, and PM control charts. Run length and its different properties are evaluated to compare the performance of the proposed charts and counterparts. Results reveal that proposed optimal DPM outperforms the other charts. An example related to voltage on fixed capacitance level is also provided to illustrate the proposed charts.     

Control charts for monitoring the mean and percentiles of Weibull processes with variance components

In this article, we study Shewhart and exponentially weighted moving average control charts for monitoring the mean or, equivalently, the percentiles of a Weibull process when additional sources of variation, also known as variance components, are present. We adopt a frailty model to describe the monitored process. We derive analytical properties for this model and use them to develop control charts. We consider charts for the sample mean and exponentially weighted moving averages. We compare their average run length performances to their traditional counterparts when they do not account for variance components.     

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.     

A comparison study of control charts for Weibull distributed time between events

Monitoring decreases in the mean of Weibull time between events data to address process quality deteriorations is an important task in reliability analysis. Two new control charts such as Weibull exponentially weighted moving average and mixed cumulative sum‐exponentially weighted moving average by transforming the Weibull data to the exponential data are proposed and compared with 2 existing control charts such as Weibull cumulative sum and mixed exponentially weighted moving average‐cumulative sum. The performance comparison provides a way to select a specific control chart in a given situation. The average run length and the standard deviation of the run length are used as performance measures. The relative mean index is also utilized to measure the overall performance. The smaller the value of the relative mean index, the better the performance of the control chart and vice versa. Two illustrative examples are provided to show the applications of the proposed control charts.     

The modified control charts for monitoring the shape parameter of weighted power function distribution under classical estimator

Zaka et al provided a new distribution called the Weighted Power function distribution (WPFD), which has application in reliability engineering and survival analysis. They used different estimation methods to estimate the unknown parameters of WPFD and proved that modified maximum likelihood estimator (MMLE) is best to consider for the estimation of parameters. We have constructed the memoryless and memory-based control charts based on the assumption that the distribution of the underlying process does not follow the normal distribution. In this paper, we provide modified control charts using MMLE of the shape parameter for WPFD. We develop control charts to keep the process in control when the distribution of errors of underlying process follows WPFD. We propose the modified memoryless control chart, that is, Shewhart control chart and modified memory-based control chart, that is, Exponentially weighted moving average (EWMA) and Hybrid exponentially weighted moving average (HEWMA) control charts. We have made the comparison of the proposed control charts using Monte Carlo simulation and the real-life application for both and the memoryless control charts and memory-based control charts. We see that HEWMA based on MMLE performs better as compared to other proposed control charts.     

A comparative study of memory‐type control charts under normal and contaminated normal environments

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used to detect small changes in the parameters of production processes. Recently, a new control structure was introduced, named as mixed EWMA–CUSUM control chart, which combined both charts. The current study provides a detailed comparison of these three types of control charts when the process parameters are unknown under normal and contaminated normal environments. Performance measures average run length and different percentiles of run length distribution are used for comparison purposes. We investigate six different location estimators with the structures of the three memory charts and study their robustness properties. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonparametric Progressive Mean Control Chart for Monitoring Process Target

Nonparametric control charts are widely used when the parametric distribution of the quality characteristic of interest is questionable. In this study, we proposed a nonparametric progressive mean control chart, namely the nonparametric progressive mean chart, for efficient detection of disturbances in process location or target. The proposed chart is compared with the recently proposed nonparametric exponentially weighted moving average and nonparametric cumulative sum charts using different run length characteristics such as the average run length, standard deviation of the run length, and the percentile points of the run length distribution. The comparisons revealed that the proposed chart outperformed recent nonparametric exponentially weighted moving average and nonparametric cumulative sum charts, in terms of detecting the shifts in process target. A real life example concerning the fill heights of soft drink beverage bottles is also provided to illustrate the application of the proposed nonparametric control chart. Copyright © 2012 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.     

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.     

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Recently, the monitoring of compositional data by means of control charts has been investigated in the statistical process control literature. In this article, we develop a Phase II multivariate exponentially weighted moving average control chart, for the continuous surveillance of compositional data based on a transformation into coordinate representation. We use a Markov chain approximation to determine the performance of the proposed multivariate control chart. The optimal multivariate exponentially weighted moving average smoothing constants, control limits, and out‐of‐control average run lengths have been computed for different combinations of the in‐control average run lengths and the number of variables. Several tables are presented and enumerated to show the statistical performance of the proposed control chart. An example illustrates the use of this chart on an industrial problem from a plant in Europe.     

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.     

Error Detection and Pattern Prediction Through Phase II Process Monitoring

The continuous monitoring of the machine is beneficial in improving its process reliability through reflected power function distribution. It is substantial for identifying and removing errors at the early stages of production that ultimately benefit the firms in cost-saving and quality improvement. The current study introduces control charts that help the manufacturing concerns to keep the production process in control. It presents an exponentially weighted moving average and extended exponentially weighted moving average and then compared their performance. The percentiles estimator and the modified maximum likelihood estimator are used to constructing the control charts. The findings suggest that an extended exponentially weighted moving average control chart based on the percentiles estimator performs better than exponentially weighted moving average control charts based on the percentiles estimator and modified maximum likelihood estimator. Further, these results will help the firms in the early detection of errors that enhance the process reliability of the telecommunications and financing industry.     

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.     

Distribution‐free mixed cumulative sum‐exponentially weighted moving average control charts for detecting mean shifts

In this paper, we propose distribution‐free mixed cumulative sum‐exponentially weighted moving average (CUSUM‐EWMA) and exponentially weighted moving average‐cumulative sum (EWMA‐CUSUM) control charts based on the Wilcoxon rank‐sum test for detecting process mean shifts without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured through the average run‐length, relative mean index, average extra quadratic loss, and average ratio of the average run‐length and performance comparison index. It is found that the proposed charts perform better than its counterparts considered in this paper under non‐normal distributions and outperform the classical mixed CUSUM‐EWMA and EWMA‐CUSUM charts in many cases under the normal distribution. The effect of the phase I sample size is also investigated on the phase II performance of the proposed charts. A numerical illustration is given to demonstrate the implementation and simplicity of the proposed charts.     

A New Chart for Monitoring Service Process Mean

Control charts are demonstrated effective in monitoring not only manufacturing processes but also service processes. In service processes, many data came from a process with nonnormal distribution or unknown distribution. Hence, the commonly used Shewhart variable control charts are not suitable because they could not be properly constructed. In this article, we proposed a new mean chart on the basis of a simple statistic to monitor the shifts of the process mean. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed chart. Furthermore, an arcsine transformed exponentially weighted moving average chart was proposed because the average run lengths of this modified chart are more intuitive and reasonable than those of the mean chart. We would recommend the arcsine transformed exponentially weighted moving average chart if we were concerned with the proper values of the average run length. A numerical example of service times with skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the proposed charts. Copyright © 2011 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.     

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.