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.     

The extended homogeneously weighted moving average control chart

Control charts are widely applied in many manufacturing processes to monitor the quality characteristic of interest. Recently, a homogeneously weighted moving average (HWMA) control chart was proposed as an improvement of the exponentially weighted moving average (EWMA) chart for efficiently monitoring of small shifts in the process mean. In the present article, we extend the HWMA chart by imitating exactly the double EWMA (DEWMA) technique. The proposed scheme is regarded as double HWMA (DHWMA) control chart. The run-length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. A comparison study versus the EWMA, DEWMA, HWMA, mixed EWMA cumulative sum (CUSUM), CUSUM, and GWMA charts indicates that the DHWMA chart is more effective in detecting small to moderate shifts, while it performs similarly with its competitors for large shifts. We also study the robustness of the proposed chart under several nonnormal distributions, and it is shown that the DHWMA chart is in-control robust for small values of the smoothing parameters. Finally, two examples are given to demonstrate the implementation of the proposed chart.     

A sum of squares triple exponentially weighted moving average control chart

Control charts are widely known quality tools used to detect and control industrial process deviations in statistical process control. In the current paper, we propose a new single memory-type control chart, called the sum of squares triple exponentially weighted moving average control chart (referred as SS-TEWMA chart), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed SS-TEWMA control chart is compared with that of the sum of squares EWMA, sum of squares double EWMA, sum of squares generally weighted moving average, and sum of squares double generally weighted moving average, control charts, through Monte Carlo simulations. The comparisons indicate that the proposed chart is more efficient, than the competing ones, in detecting small shifts in the process mean and/or variability for most of the considered scenarios, while it has comparable performance for some others in identifying large shifts in the process mean and small to large shifts in the process variability. Finally, two illustrative examples are provided to explain the application of the SS-TEWMA control chart.     

Monitoring of time between events with a double generally weighted moving average control chart

Monitoring of time between events (TBE) instead of the number of events is used in high‐quality processes where the events occur rarely. This article presents a double generally weighted moving average control chart with a lower time‐varying control limit to monitor the TBE (regarded as DGWMA‐TBE chart). The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the DGWMA‐TBE chart is more effective than the DEWMA and GWMA charts in detecting moderate to large shifts. Furthermore, the DGWMA‐TBE chart is very robust for the same range of shifts when the TBE observations follow a Weibull or a lognormal distribution. Finally, examples are also presented to enhance the performance of the proposed chart.     

Enhanced generally weighted moving average variance charts for monitoring process variance with individual observations

The generally weighted moving average variance (GWMAV) chart is effective in detecting increases in process variance when only individual observations are available. Recently, the combination of exponentially weighted moving average and cumulative sum (CUSUM) charts for the effective detection of small process shifts has emerged. Inspired by the features, we propose the mixed GWMAV-CUSUM chart and its reverse order CUSUM-GWMAV to enhance the detection ability of the GWMAV chart and compare with the existing counterparts. Numerical simulation revealed that the mixed GWMAV-CUSUM and mixed CUSUM-GWMAV charts are sensitive to small upward shifts in the process variance and efficient structures compared with their prototypes and their separate charts, that is, GWMAV and CUSUM charts. An industrial dataset was used to illustrate the application of the proposed mixed charts.     

Novel design of composite generally weighted moving average and cumulative sum charts

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts are popular statistical tools to improve the performance of the Shewhart chart in detecting small process shifts. In this study, we propose the mixed generally weighted moving average (GWMA)‐CUSUM chart and its reverse‐order CUSUM‐GWMA chart to enhance detection ability compared with existing counterparts. The simulation revealed that the mixed GWMA‐CUSUM and mixed CUSUM‐GWMA charts have the sensitivity to detect small process shifts and efficient structures compared with the mixed EWMA‐CUSUM and mixed CUSUM‐EWMA charts, respectively. Moreover, the mixed GWMA‐CUSUM chart with a large design parameter has robust performance, regardless of the high tail t distribution or right skewness gamma distribution.     

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 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.     

Distribution-free triple EWMA control chart for monitoring the process location using the Wilcoxon rank-sum statistic with fast initial response feature

The exponentially weighted moving average (EWMA) control chart is a memory-type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small-to-moderate shifts. This paper proposes a new distribution-free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank-sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real-life illustration is provided to show the application and implementation of the new chart.     

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.     

Auxiliary information-based maximum generally weighted moving average chart for simultaneously monitoring process mean and variability

An auxiliary information-based (AIB) maximum exponentially weighted moving average (MaxEWMA) chart has been proposed to simultaneously monitor both increases and decreases in the process mean and/or variability, called the AIB-MaxEWMA chart, which is superior to the existing MaxEWMA chart. In this paper, we propose the AIB maximum generally weighted moving average chart, called the AIB-MaxGWMA chart, to further enhance the sensitivity of the AIB-MaxEWMA chart. Numerical simulation studies indicate that the AIB-MaxGWMA chart is sensitive to small shifts in the process mean and/or variability. The performance of the AIB-MaxGWMA chart based on average run lengths (ARLs) also outperforms than its counterparts including AIB-MaxEWMA, MaxGWMA and MaxEWMA charts. An example is used to illustrate the efficiency of the proposed AIB-MaxGWMA chart in detecting small process shifts.     

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 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.     

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.     

Optimal one- and two-sided adaptive EWMA scheme for monitoring Poisson count data

The Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one- and two-sided performance of a new adaptive EWMA (exponentially weighted moving average)-type chart for monitoring Poisson count data. An appropriate discrete-state Markov chain technique is provided to compute the exact ARL (average run length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.     

An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location

The statistical performance of traditional control charts for monitoring the process shifts is doubtful if the underlying process will not follow a normal distribution. So, in this situation, the use of a nonparametric control charts is considered to be an efficient alternative. In this paper, a nonparametric exponentially weighted moving average (EWMA) control chart is developed based on Wilcoxon signed‐rank statistic using ranked set sampling. The average run length and some other associated characteristics were used as the performance evaluation of the proposed chart. A major advantage of the proposed nonparametric EWMA signed‐rank chart is the robustness of its in‐control run length distribution. Moreover, it has been observed that the proposed version of the EWMA signed‐rank chart using ranked set sampling shows better detection ability than some of the competing counterparts including EWMA sign chart, EWMA signed‐rank chart, and the usual EWMA control chart using simple random sampling scheme. An illustrative example is also provided for practical consideration. Copyright © 2016 John Wiley & Sons, Ltd.     

Monitoring of zero-inflated Poisson processes with EWMA and DEWMA control charts

The zero-inflated Poisson (ZIP) distribution is an extension of the ordinary Poisson distribution and is used to model count data with an excessive number of zeros. In ZIP models, it is assumed that random shocks occur with probability p, and upon the occurrence of random shock, the number of nonconformities in a product follows the Poisson distribution with parameter λ. In this article, we study in more detail the exponentially weighted moving average control chart based on the ZIP distribution (regarded as ZIP-EWMA) and we also propose a double EWMA chart with an upper time-varying control limit to monitor ZIP processes (regarded as ZIP-DEWMA chart). The two charts are studied to detect upward shifts not only in each parameter individually but also in both parameters simultaneously. The steady-state performance and the performance with estimated parameters are also investigated. The performance of the two charts has been evaluated in terms of the average and standard deviation of the run length, and compared with Shewhart-type and CUSUM schemes for ZIP distribution, it is shown that the proposed chart is very effective especially in detecting shifts in p when λ remains in control (IC) and in both parameters simultaneously. Finally, one real example is given to display the application of the ZIP charts on practitioners.     

Modified calibrated control charts for monitoring the population mean under stratified sampling

In this research paper, we discuss the use of calibration technique to propose some new estimators under stratified sampling design and its use in reliability engineering. We first proposed the estimators using the calibration technique and then modify the already existing control charts such as Shewhart, exponentially weighted moving average and hybrid exponentially weighted moving averages using these calibration estimators. We also have studied the use of the proposed control charts in detail by showing their efficiency in terms of average run length. We find out that a hybrid control chart is more effective to detect the early shifts in the mean of the process.     

The performance of EWMA median and CUSUM median control charts for a normal process with measurement errors

Measurement error is often occurred in statistical process control. The effect of a linearly covariate error model on the exponentially weighted moving average (EWMA) median and cumulative sum (CUSUM) median charts is investigated. The results indicate that the EWMA median and CUSUM median charts are significantly affected in the presence of measurement errors. We compared the performance of the EWMA median and CUSUM median charts by using Markov chain method in the average run length and the standard deviation of the run length. We concluded that the CUSUM median chart for small shifts and the EWMA median chart for larger shifts are recommended. Two examples are provided to illustrate the application of the EWMA and CUSUM median charts with measurement errors.     

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.