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.     

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.     

New control charts for monitoring the Weibull percentiles under complete data and Type‐II censoring

In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type‐II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA‐SEV‐Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM‐SEV‐Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA‐YP and CUSUM‐YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA‐YP and CUSUM‐YP control charts perform better than the EWMA‐SEV‐Q and CUSUM‐SEV‐Q control charts in terms of average run length. In Type‐II censoring, the EWMA‐SEV‐Q chart is slightly better than the CUSUM‐SEV‐Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.     

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.     

Mixed Cumulative Sum–Exponentially Weighted Moving Average Control Charts: An Efficient Way of Monitoring Process Location

Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts are famous statistical tools, to handle special causes and to bring the process back in statistical control. Shewhart charts are useful to detect large shifts, whereas EWMA and CUSUM are more sensitive for small to moderate shifts. In this study, we propose a new control chart, named mixed CUSUM‐EWMA chart, which is used to monitor the location of a process. The performance of the proposed mixed CUSUM‐EWMA control chart is measured through the average run length, extra quadratic loss, relative average run length, and a performance comparison index study. Comparisons are made with some existing charts from the literature. An example with real data is also given for practical considerations. Copyright © 2014 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.     

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.     

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.     

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.     

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.     

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 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.     

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 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.     

Detecting mean increases in zero truncated INAR(1) processes

Count data with zero truncation are common in the production process. It's essential to monitor these data during production flow, production quality control and market management. Most of the previous studies were based on the independent observations assumption. In fact, serial dependence of count data which significantly affects the performance of the control charts exists extensively in practice. Motivated by this, several important first-order integer-valued autoregressive time series processes are used to model the autocorrelated count data with zero truncation. We investigate the effectiveness of three following charts, the combined jumps chart, the exponentially weighted moving average chart and the cumulative sum chart, to detect the upward shifts of the process mean based on these models. A bivariate Markov chain approach could be used to obtain the average run length of these charts. Design recommendations for achieving robustness are provided based on the computation study. An application to product quality complaints data is presented to demonstrate good performances of the charts.     

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.     

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.     

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 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.     

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.