Effective Control Charts for Monitoring the NGINAR(1) Process

In recent years, there has been a growing interest in the control of autocorrelated count data. Existing results focus on the Poisson integer‐valued autoregressive (INAR) process, but this process cannot deal with overdispersion (variance is greater than mean), which is a common phenomenon in count data. We propose to control the autocorrelated count data based on a new geometric INAR (NGINAR) process, which is an alternative to the Poisson one. In this paper, we use the combined jumps chart, the cumulative sum chart, and the combined exponentially weighted moving average chart to detect the shift of parameters in the process. We compare the performance of these charts for the case of an underlying NGINAR(1) process in terms of the average run lengths. One real example is presented to demonstrate good performances of the charts. Copyright © 2015 John Wiley & Sons, Ltd.     

Poisson progressive mean control chart

In real life applications, many process‐monitoring problems in statistical process control are based on attribute data resulting from quality characteristics that cannot be measured on numerical or quantitative scales. For the monitoring of such data, a new attribute control chart has been proposed in this study, namely, the Poisson progressive Mean (PPM) control chart. The performance of the PPM chart is compared with the existing charts used for the monitoring of Poisson processes such as the Shewhart c‐chart, Poisson Exponentially Weighted Moving Average chart, Poisson double Exponentially Weighted Moving Average chart and the Poisson Cumulative Sum charts. The average run length comparison indicated the superior performance of the PPM chart in terms of shift detection ability. This study will help quality practitioners to choose an efficient attribute control 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.     

Improved CUSUM monitoring of Markov counting process with frequent zeros

There has been a growing interest in monitoring processes featuring serial dependence and zero inflation. The phenomenon of excessive zeros often occurs in count time series because of the advancement of quality in manufacturing process. In this study, we propose three control charts, such as the cumulative sum chart with delay rule (CUSUM‐DR), conforming run length (CRL)‐CUSUM chart, and combined Shewhart CRL‐CUSUM chart, to enhance the performance of monitoring Markov counting processes with excessive zeros. Numerical experiments are conducted based on integer‐valued autoregressive time series models, for example, zero‐inflated Poisson INAR and INARCH, to evaluate the performance of the proposed charts designed for the detection of mean increase. A real example is also illustrated to demonstrate the usability of our proposed charts.     

Should observations be grouped for effective monitoring of multivariate process variability?

A multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability on the basis of individual and grouped multivariate observations. We compare one of the most well-known methods for monitoring individual observations—a multivariate exponentially weighted mean squared deviation (MEWMS) chart—with various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using charts based on overlapping subgroups when monitoring with subgroup data. The effect of subgroup size is also investigated. Steady-state average time to signal is used as the performance measure. We show that monitoring methods based on individual observations are the quickest in detecting sustained shifts in the process variability. We use a simulation study to obtain our results and illustrated these with a case study.     

Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length

The average run length (ARL) is usually used as a sole measure of performance of a multivariate control chart. The Hotelling's T², multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts are commonly optimally designed based on the ARL. Similar to the case of univariate quality control, in multivariate quality control, the shape of the run length distribution changes in accordance to the magnitude of the shift in the mean vector, from highly skewed when the process is in‐control to nearly symmetric for large shifts. Because the shape of the run length distribution changes with the magnitude of the shift in the mean vector, the median run length (MRL) provides additional and more meaningful information about the in‐control and out‐of‐control performances of multivariate charts, not given by the ARL. This paper provides a procedure for optimal designs of the multivariate synthetic T² chart for the process mean, based on MRL, for both the zero and steady‐state modes. Two Mathematica programs, each for the zero state and steady‐state modes are given for a quick computation of the optimal parameters of the synthetic T² chart, designed based on MRL. These optimal parameters are provided in the paper, for the bivariate case with sample sizes, nin{4, 7, 10}. The MRL performances of the synthetic T², MEWMA and Hotelling's T² charts are also compared. Copyright © 2011 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.     

Deviance residual-based control charts for monitoring the beta-distributed processes

Beta-distributed process outputs are common in manufacturing industry because they range from 0 to 1 based on inputs like yield. Under the normality assumption, Shewarts control charts and Hotelling's control charts based on the deviance residual have been applied to monitor the process mean of the beta-distributed process outputs. The normality assumption can be violated according to the shape of the beta distribution. Therefore, without the normality assumption, we propose antirank control charts, exponentially weighted moving average (EWMA) control charts and cumulative sum (CUSUM) control charts. The proposed control charts outperform the existing control charts in the experimental results. The previous research has been focused on monitoring the process mean only. For the first time, in order to monitor the process variance of the beta-distributed process outputs, we propose the multivariate exponentially weighted mean squared deviation (MEWMS) chart, the first norm distance of the MEWMS deviation from its expected value (MEWMSL₁) chart, the chart based on MEWMS deviation with the approximated distribution of trace (MEWMS_AT), the multivariate trace sum squared deviation (MTSSD) chart and the multivariate matrix sum squared deviation (MMSSD) chart based on the deviance residual. The proposed control charts are compared and recommended in terms of the experimental results. This research can be a guideline for practitioners who monitor the deviance residual.     

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.     

The design of geometric generalized likelihood ratio control chart

This paper develops a control chart, named generalized likelihood ratio (GLR) control chart, based on a GLR statistic to monitor the parameter of geometrically distributed process. The GLR statistic is obtained based on window of the past samples. The performance of the GLR control chart is compared with the cumulative sum (CUSUM) and two combinations of CUSUM charts, in terms of the steady state average time to signal. Simulation results show that the GLR control chart outperforms the CUSUM and two combinations of CUSUM charts in detecting a wide range of parameter shifts in the geometrically distributed process. A real data set is used to demonstrate the performance and effectiveness of the proposed control chart.     

Robust kernel distance multivariate control chart using support vector principles

It is important to monitor manufacturing processes in order to improve product quality and reduce production cost. Statistical Process Control (SPC) is the most commonly used method for process monitoring, in particular making distinctions between variations attributed to normal process variability to those caused by ‘special causes’. Most SPC and multivariate SPC (MSPC) methods are parametric in that they make assumptions about the distributional properties and autocorrelation structure of in-control process parameters, and, if satisfied, are effective in managing false alarms/-positives and false-negatives. However, when processes do not satisfy these assumptions, the effectiveness of SPC methods is compromised. Several non-parametric control charts based on sequential ranks of data depth measures have been proposed in the literature, but their development and implementation have been rather slow in industrial process control. Several non-parametric control charts based on machine learning principles have also been proposed in the literature to overcome some of these limitations. However, unlike conventional SPC methods, these non-parametric methods require event data from each out-of-control process state for effective model building. The paper presents a new non-parametric multivariate control chart based on kernel distance that overcomes these limitations by employing the notion of one-class classification based on support vector principles. The chart is non-parametric in that it makes no assumptions regarding the data probability density and only requires ‘normal’ or in-control data for effective representation of an in-control process. It does, however, make an explicit provision to incorporate any available data from out-of-control process states. Experimental evaluation on a variety of benchmarking datasets suggests that the proposed chart is effective for process monitoring.     

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.     

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 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 double exponentially weighted moving average chart based on likelihood ratio for monitoring an inflated Pareto process

In this paper, we present a new chart called a likelihood ratio based double exponentially weighted moving average (LR_DEWMA) chart to monitor the shape parameter of the inflated Pareto process. Three other control charts such as the Shewhart type, the classical cumulative sum (CUSUM), and the likelihood ratio based EWMA (LR_EWMA) charts are also investigated. The performance of the control charts is evaluated by the average run length (ARL) and standard deviation of run lengths (SDRL) computed through the Monte Carlo simulation approach. Moreover, the median run length (MRL) and some other run length (RL) percentiles are also considered in some cases. Different charts have shown the best performance in different cases. In detecting smaller shifts, while the LR_DEWMA chart outperformed the other charts in terms of ARL and MRL, the CUSUM chart has shown the best performance in terms of SDRL and IQR of RLs. The application of the proposed control charts is illustrated using a chromatography analyses data from the food industry.     

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg–Fisher–Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.     

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.     

Joint Monitoring of Process Mean and Variability with a Single Moving Average Control Chart

Memory based control charts are developed as alternatives to the Shewhart charts for the detection of small sustaining process shifts. Among the widely used memory control charts are the EWMA (Exponentially Weighted Moving Average), CUSUM (Cumulative Sum), and moving average schemes. Relative to the CUSUM chart, the EWMA and moving average charts are quite basic. The EWMA chart uses a weighted average as the chart statistic while the time-weighted moving average chart is based on unweighted moving average. The moving average statistic of width w is simply the average of the w most recent observations. In this article, the use of one moving average control chart to monitor both process mean and variability. This new moving average chart is efficient in detecting both increases and decreases in mean and/or variability.     

Monitoring type‐2 censored reliability data in multistage processes

In this paper, we propose control charts to monitor the Weibull scale parameter of type‐2 censored reliability data in multistage processes. A cumulative sum control chart and 2 exponentially weighted moving average control charts based on conditional expected values are devised to detect decreases in the mean level of reliability‐related quality characteristic. The proposed control schemes are based on standard smallest extreme value distributions derived from Weibull processes to effectively account for the cascade property, which is the main characteristic of multistage processes. Subsequently, simulation study is conducted to evaluate the performance of the control charts using average run length criterion. Extra quadratic loss, performance comparison index, and relative average run length are also used to compare the detect ability of our proposed monitoring procedures. Moreover, sensitivity analysis is done to study the impact of failure number in the sample size and to investigate the robustness of the proposed monitoring procedures against the shift in the previous stage. Finally, a real case study in a glass bottle–making company is investigated to illustrate the performance of the competing control charts. The results reveal the superiority of the cumulative sum control chart.     

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.