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.     

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.     

A New Cumulative Sum Quality Control Scheme for Monitoring the Process Mean

A control chart is a powerful statistical process monitoring tool that is frequently used in many industrial and service organizations to monitor in‐control and out‐of‐control performances of the manufacturing processes. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recognized as potentially powerful tool in quality and management control. These control charts are sensitive to both small and moderate changes in the process. In this paper, we propose a new CUSUM (NCUSUM) quality control scheme for efficiently monitoring the process mean. It is shown that the classical CUSUM control chart is a special case of the proposed controlling scheme. The NCUSUM control chart is compared with some of the recently proposed control charts by using characteristics of the distribution of run length, i.e. average run length, median run length and standard deviation of run length. It is worth mentioning that the NCUSUM control chart detects the random shifts in the process mean substantially quicker than the classical CUSUM, fast initial response‐based CUSUM, adaptive CUSUM with EWMA‐based shift, adaptive EWMA and Shewhart–CUSUM control charts. An illustrative example is given to exemplify the implementation of the proposed quality control scheme. 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.     

Monitoring Process Variance Using an ARL‐unbiased EWMA‐p Control Chart

Control charts are effective tools for signal detection in manufacturing processes. As much of the data in industries come from processes having non‐normal or unknown distributions, the commonly used Shewhart variable control charts cannot be appropriately used, because they depend heavily on the normality assumption. The average run length (ARL) is generally used to measure the detection performance of a process when using a control chart, but it is biased for the monitoring statistic with an asymmetric distribution. That is, the ARL‐biased control chart leads to take longer to detect the shifts in parameter than to trigger a false alarm. To overcome this problem, we herein propose an ARL‐unbiased exponentially weighted moving average proportion (EWMA‐p) chart to monitor the process variance for process data with non‐normal or unknown distributions. We further explore the procedure to determine the control limits and to investigate the out‐of‐control variance detection performance of the ARL‐unbiased EWMA‐p chart. With a numerical example involving non‐normal service times from a bank branch in Taiwan, we illustrate the applications of the proposed ARL‐unbiased EWMA‐p chart and also compare the out‐of‐control detection performance of the ARL‐unbiased EWMA‐p chart, the arcsin transformed symmetric EWMA variance, and other existing variance charts. The proposed ARL‐unbiased EWMA‐p chart shows superior detection performance. Thus, we recommend the ARL‐unbiased EWMA‐p chart for process data with non‐normal or unknown distributions. Copyright © 2015 John Wiley & Sons, Ltd.     

A double sampling scheme for process variability monitoring

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries come from processes exhibiting nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. This paper thus proposes a standardized asymmetric exponentially weighted moving average (EWMA) variance chart with a double sampling scheme (SDS EWMA‐AV chart) for monitoring process variability. We further explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using the proposed SDS EWMA‐AV chart. The performance of the SDS EWMA‐AV chart and that of the single sampling EWMA variance (SS EWMA‐V) chart are then compared, with the former showing superior out‐of‐control detection performance versus the latter. We also compare the out‐of‐control variance detection performance of the proposed chart with those of nonparametric variance charts, the nonparametric Mood variance chart (NP‐M chart) with runs rules, and the nonparametric likelihood ratio‐based distribution‐free EWMA (NLE) chart and the combination of traditional EWMA (CEW) and the SS EWMA‐V control charts by considering cases in which the critical quality characteristic presents normal, double exponential, uniform, chi‐square, and exponential distributions. Comparison results show that the proposed chart always outperforms the NP‐M with runs rules, the NLE, CEW, and the SS EWMA‐V control charts. We hence recommend employing the SDS EWMA‐AV chart. Finally, a numerical example of a service system for a bank branch in Taiwan is used to illustrate the application of the proposed variability control chart.     

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 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 EWMA Control Chart for Exponential Distributed Quality Based on Moving Average Statistics

We propose an exponentially weighted moving average (EWMA) control chart for monitoring exponential distributed quality characteristics. The proposed control chart first transforms the sample data to approximate normal variables, then calculates the moving average (MA) statistic for each subgroup, and finally constructs the EWMA statistic based on the current and the previous MA statistics. The upper and the lower control limits are derived using the mean and the variance of EWMA statistics. The in‐control and the out‐of‐control average run lengths are derived and tabularized according to process shift parameters and smoothing constants. It is shown that the proposed control chart outperforms the MA control chart for all shift parameters. Copyright © 2015 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.     

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.     

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.     

Design of a Control Chart Using a Modified EWMA Statistic

In this paper, the design of a control chart is given using a modified exponentially weighted moving average statistic under the assumption that the quality characteristic of interest follows the normal distribution. The structure of the proposed control chart is developed, and the necessary measures are derived to find the average run length for in‐control and out‐of‐control processes. The efficiency of the proposed chart is compared with two existing control charts in terms of the average run length. The results are explained with the help of industrial example. Copyright © 2016 John Wiley & Sons, Ltd.     

A mixed cumulative sum homogeneously weighted moving average control chart for monitoring process mean

The homogeneously weighted moving average (HWMA) control chart is famous to identify small deviations in the process mean. The plotting statistic of the HWMA chart assigns equal weight among the previous samples as compared to the plotting statistic of the exponentially weighted moving average chart. We propose a new HWMA chart that uses the plotting statistic of the cumulative sum chart. The run length performance of the proposed chart is measured in terms of the average, the standard deviation, some percentile points, and compared with some existing counterparts' charts. The comparison shows that the proposed chart performs superior to their existing counterparts. An application based on a real-life dataset is also presented.     

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 new non‐parametric CUSUM mean chart

Not all data in practice came from a process with normal distribution. When the process distribution is non‐normal or unknown, the commonly used Shewhart control charts are not suitable. In this paper, a new non‐parametric CUSUM Mean Chart is proposed to monitor the possible small mean shifts in the process. The sampling properties of the new monitoring statistics are examined and the average run lengths of the proposed chart are examined. Two numerical examples are used to illustrate the proposed chart and compare with the two existing charts, assuming normality and Beta distribution, respectively. The CUSUM Mean Chart showed better detection ability than those two charts in monitoring and detecting small process mean shifts. Copyright © 2010 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.     

The effects of violations of the multivariate normality assumption in multivariate Shewhart and MEWMA control charts

A multivariate Shewhart and a multivariate exponentially weighted moving average control charts are types of multivariate control charts for monitoring the mean vector. For those control charts, a multivariate normal distribution is an important assumption that is used to describe a behavior of a set of quality characteristics of interest. This research explores the sensitivity of average run lengths and standard deviation of run lengths for the multivariate Shewhart and the multivariate exponentially weighted moving average control charts when the normality assumption is incorrect.     

A new nonparametric double exponentially weighted moving average control chart

There are many practical situations where the underlying distribution of the quality characteristic either deviates from normality or it is unknown. In such cases, practitioners often make use of the nonparametric control charts. In this paper, a new nonparametric double exponentially weighted moving average control chart on the basis of the signed-rank statistic is proposed for monitoring the process location. Monte Carlo simulations are carried out to obtain the run length characteristics of the proposed chart. The performance comparison of the proposed chart with the existing parametric and nonparametric control charts is made by using various performance metrics of the run length distribution. The comparison showed the superiority of the suggested chart over its existing parametric and nonparametric counterparts. An illustrative example for the practical implementation of the proposed chart is also provided by using the industrial data set.     

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.