Monitoring the Coefficient of Variation Using the Side Sensitive Group Runs Chart

Many quality characteristics have means and standard deviations that are not independent. Instead, the standard deviations of these quality characteristics are proportional to their corresponding means. Thus, monitoring the coefficient of variation (CV), for these quality characteristics, using a control chart has gained remarkable attention in recent years. This paper presents a side sensitive group runs chart for the CV (called the SSGR CV chart). The implementation and optimization procedures of the proposed chart are presented. Two optimization procedures are developed, i.e. (i) by minimizing the average run length (ARL) when the shift size is deterministic and (ii) by minimizing the expected average run length (EARL) when the shift size is unknown. An application of the SSGR CV chart using a real dataset is also demonstrated. Additionally, the SSGR CV chart is compared with the Shewhart CV, runs rules CV, synthetic CV and exponentially weighted moving average CV charts by means of ARLs and standard deviation of the run lengths. The performance comparison is also conducted using EARLs when the shift size is unknown. In general, the SSGR CV chart surpasses the other charts under comparison, for most upward and downward CV shifts. Copyright © 2015 John Wiley & Sons, Ltd.     

A new dual CUSUM mean chart

The conventional cumulative sum (CUSUM) chart is usually designed based on a known shift size. In usual practice, shift size is often unknown and can be assumed to vary within an interval. With such a range of shift size, the dual CUSUM (DCUSUM) chart provides more sensitivity than the CUSUM chart. In this paper, we propose dual Crosier CUSUM (DCCUSUM) charts with and without fast initial response features to efficiently monitor the infrequent changes in the mean of a normally distributed process. Monte Carlo simulations are used to compute the run length characteristics of one‐sided and two‐sided DCCUSUM charts. These run length characteristics are compared with those of the CUSUM, Crosier CUSUM, Shewhart‐CUSUM, and DCUSUM charts in terms of the integral relative average run length. It turns out that the proposed chart shows better performance when detecting a range of mean shift sizes. A real dataset is considered to illustrate the implementation of existing and proposed charts.     

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 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.     

Side-sensitive modified group runs charts with and without measurement errors for monitoring the coefficient of variation

The coefficient of variation (CV) is used in process monitoring when the process mean and standard deviation are proportional to each other. In this work, a side-sensitive modified group runs CV (SSMGR CV) chart is proposed for monitoring the process CV. The run length performance of the SSMGR CV chart is compared to those of the existing CV charts in terms of the average and standard deviation of the run length criteria. The SSMGR CV chart is found to outperform the existing CV charts. In addition, the run length performance of the SSMGR CV chart is also evaluated in the presence of measurement errors, as these errors are not only unavoidable in practice but they also affect the sensitivity of a control chart in detecting an out-of-control situation. The results obtained show that the accuracy and precision errors affect the performance of the SSMGR CV chart in detecting an out-of-control situation.     

A Kullback-Leibler information control chart for linear profiles monitoring

Profile monitoring is referred to as monitoring the functional relationship between the response and explanatory variables. Traditionally, process control charts monitor the mean and/or the variance of a univariate quality characteristic. For several correlated quality characteristics, multivariate process control charts monitor the mean vector and/or the covariance matrix. However, monitoring the functional relationship between variables is sometimes more beneficial. One example is the power output of a Diesel engine and the amount of fuel injected should be related. In this paper, we propose a Kullback-Leibler information (KLI) control chart for linear profiles monitoring in Phase II. The plotted statistics of the KLI chart are calculated based on a backward procedure. The functional relationship is described by linear regression. The performance of the proposed KLI control chart is compared with those of other existing control charts, especially the Generalized Likelihood Ratio (GLR) chart for both KLI and GLR charts do not require design parameters. The results show that (1) the KLI control chart is better than the GLR control chart in detecting the shift of variance in terms of Average Time to Signal, and (2) if the shift of the regression coefficient is small, the GLR chart outperforms the KLI chart, but if the size of shift is large, the KLI chart outperforms the GLR chart. The plotted statistics of KLI are compared to that of GLR. Their similarity is discussed.     

Run length quantiles of EWMA control charts monitoring normal mean or/and variance

Exponentially weighted moving average (EWMA) control charts are well-established devices for monitoring process stability. Typically, control charts are evaluated by considering their Average Run Length (ARL), that is the expected number of observations or samples until the chart signals. Because of the limitations of an average, various papers also dealt with the run length distribution and quantiles. Going beyond these papers, we develop algorithms for and evaluate the quantile performance of EWMA control charts with variance adjusted control limits and with fast initial response features, of EWMA charts based on the sample variance, and of EWMA charts simultaneously monitoring mean and variance. Additionally, for the mean charts we consider medium, late and very late process changes and their impact on appropriately conditioned run length quantiles. It is demonstrated that considering run length quantiles can protect from constructing distorted EWMA designs while optimising their zero-state ARL performance. The implementation of all the considered measures in the R package ‘spc’ allows any control chart user to consider EWMA schemes from the run length quantile prospective in an easy way.     

Dual multivariate CUSUM charts with auxiliary information for process mean

It is customary to increase the sensitivity of a control chart using an efficient estimator of the underlying process parameter which is being monitored. In this paper, using an auxiliary information-based (AIB) mean estimator, we propose dual multivariate CUSUM (DMCUSUM) and mixed DMCUSUM (MDMCUSUM) charts, called the AIB-DMCUSUM and AIB-MDMCUSUM charts, with and without fast initial response features for monitoring the mean vector of a multivariate normally distributed process. The DMCUSUM chart combines two similar-type multivariate CUSUM (MCUSUM) charts while the MDMCUSUM chart combines two different-type MCUSUM charts, into a single chart. The objective of two multivariate subcharts in the DMCUSUM/MDMCUSUM chart is to simultaneously detect small-to-moderate and moderate-to-large shifts in the process mean vector. Monte Carlo simulations are used to compute the run length characteristics, including the average run length (ARL), extra quadratic loss, and integral of the relative ARL. Based on detailed run length comparisons, it turns out that the AIB-DMCUSUM and AIB-MDMCUSUM charts uniformly and substantially outperform the DMCUSUM and MDMCUSUM charts when detecting different sizes of shift in the process mean vector. A real dataset is used to explain the implementation of proposed AIB multivariate charts.     

New Exponentially Weighted Moving Average Control Charts for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have received considerable attention for detecting small changes in the process mean or the process variability. Several EWMA control charts are constructed using logarithmic and normalizing transformations on unbiased sample variance for monitoring changes in the process dispersion. In this paper, we propose new EWMA control charts for monitoring process dispersion based on the best linear unbiased absolute estimators obtained under simple random sampling (SRS) and ranked set sampling (RSS) schemes, named EWMA‐SRS and EWMA‐RSS control charts. The performance of the proposed EWMA control charts is evaluated in terms of the average run length and standard deviation of run length, estimated by using Monte Carlo simulations. The proposed EWMA control charts are then compared with their existing counterparts for detecting increases and decreases in the process dispersion. It turns out that the EWMA‐RSS control chart performs uniformly better than its analogues for detecting overall changes in process dispersion. Moreover, the EWMA‐SRS chart significantly outperforms the existing EWMA charts for detecting increases in process variability. A real data set is also used to explain the construction and operations of the proposed EWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.     

A synthetic double sampling control chart for process mean using auxiliary information

A control chart is a simple yet powerful tool that is extensively adopted to monitor shifts in the process mean. In recent years, auxiliary‐information–based (AIB) control charts have received considerable attention as these control charts outperform their counterparts in monitoring changes in the process parameter(s). In this article, we integrate the conforming run length chart with the existing AIB double sampling (AIB DS) chart to propose an AIB synthetic DS chart for the process mean. The AIB synthetic DS chart also encompasses the existing synthetic DS chart. A detailed discussion on the construction, optimization, and evaluation of the run length profiles is provided for the proposed control chart. It is found that the optimal AIB synthetic DS chart significantly outperforms the existing AIB Shewhart, optimal AIB synthetic, and AIB DS charts in detecting various shifts in the process mean. An illustrative example is given to demonstrate the implementation of the existing and proposed AIB control charts.     

An overview of synthetic‐type control charts: Techniques and methodology

In this paper, we provide an overview of a class of control charts called the synthetic charts. Synthetic charts are a combination of a traditional chart (such as a Shewhart, CUSUM, or EWMA chart) and a conforming run‐length (CRL) chart. These charts have been considered in order to maintain the simplicity and improve the performance of small and medium‐sized shift detection of the traditional Shewhart charts. We distinguish between different types of synthetic‐type charts currently available in the literature and highlight how each is designed and implemented in practice. More than 100 publications on univariate and multivariate synthetic‐type charts are reviewed here. We end with some concluding remarks and a list of some future research ideas.     

SUBJECTS INDEX

Exponentially weighted moving average (EWMA) control charts are very widely used for the detection of small shifts. Another similar charting structure is double EWMA (DEWMA) control chart for the improved detection of the shifts. Many interesting features of EWMA and DEWMA have been described in the literature. This study intends to investigate EWMA and DEWMA control charts under Type-I censoring for gamma-distributed lifetimes. The idea of conditional expected values is used to monitor the mean level. The performance evaluations are carried out using average run length as a measure in this study. The optimum sample size comparisons for the specified and unspecified parameter are also part of the study. To assess the overall performance of the control charts, we also used extra quadratic loss and it is found DEWMA is an efficient chart for the detection of shift in scale parameter. Moreover, an illustrative example for practical considerations is included in the study. It is observed that varying censoring rates affect the performance of the chart depending upon the type of chart, the method of estimation, and the amount of shift.     

Weighted adaptive multivariate CUSUM control charts

An adaptive multivariate cumulative sum (AMCUSUM) control chart has received considerable attention because of its ability to dynamically adjust the reference parameter whereby achieving a better performance over a range of mean shifts than the conventional multivariate cumulative sum (CUSUM) charts. In this paper, we introduce a progressive mean–based estimator of the process mean shift and then use it to devise new weighted AMCUSUM control charts for efficiently monitoring the process mean. These control charts are easy to design and implement in a computerized environment compared with their existing counterparts. Monte Carlo simulations are used to estimate the run‐length characteristics of the proposed control charts. The run‐length comparison results show that the weighted AMCUSUM charts perform substantially and uniformly better than the classical multivariate CUSUM and AMCUSUM charts in detecting a range of mean shifts. An example is used to illustrate the working of existing and proposed multivariate CUSUM control charts.     

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.     

A progressive approach for the detection of the coefficient of variation

A progressive average chart usually triggers initial out-of-control (OC) signals more simply and quickly than other memory-type charts . In this paper, two progressive average control procedures are proposed for monitoring the coefficient of variation (CV) of a normally distributed process variable, namely, the progressive CV (PCV) and progressive resetting CV (PRCV) control charts , respectively. The implementation of the proposed charts is presented, and the necessary design parameters are provided. Through extensive numerical simulations, it is shown that the proposed PCV and PRCV charts outperform several existing control charts to detect the initial OC signals, especially for the small and moderate CV shifts, under each combination of the shift size, the sample size, and the in-control target value of the CV. In addition, the application of the proposed control charts is illustrated by a detection example for a spinning process.     

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.     

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.     

On increasing the sensitivity of moving average control chart using auxiliary variable

In the statistical process control, the most useful tool to monitor the manufacturing processes in the industries is the control chart. Quality practitioners always desire the charting structure that identifies sustainable changes in the monitoring processes. The sensitivity of the control chart is improved when additional correlated auxiliary information about the study variable is introduced. The regression estimate in the form of auxiliary and supporting variables presents an unbiased and efficient statistic of the mean of the process variable. In this study, auxiliary information-based moving average (AB-MA) control chart is designed for efficient monitoring of shifts in the process location parameter. The performance of the AB-MA control chart is evaluated and compared with existing charts using average run length and other run length characteristics. The comparison reveals that the AB-MA control chart outperforms the competitors in detecting the small and medium changes in the process location parameter. The application of the proposal is also provided to implement it in real situation.     

A new adaptive CUSUM control chart for detecting the multivariate process mean

We propose a new multivariate CUSUM control chart, which is based on self adaption of its reference value according to the information from current process readings, to quickly detect the multivariate process mean shifts. By specifying the minimum magnitude of the process mean shift in terms of its non‐centrality parameter, our proposed control chart can achieve an overall performance for detecting a particular range of shifts. This adaptive feature of our method is based on two EWMA operators to estimate the current process mean level and make the detection at each step be approximately optimal. Moreover, we compare our chart with the conventional multivariate CUSUM chart. The advantages of our control chart detection for range shifts over the existing charts are greatly improved. The Markovian chain method, through which the average run length can be computed, is also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Dispersion

Exponentially weighted moving average (EWMA) control charts are mostly used to monitor the manufacturing processes. In this paper, we propose some improved EWMA control charts for detecting the random shifts in the process mean and process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS), named EWMA‐ORSS and EWMA‐OIRSS charts, respectively. Monte Carlo simulations are used to estimate the average run length, median run length and standard deviation of run length of the proposed EWMA control charts. It is observed that the EWMA‐ORSS mean control chart is able to detect the random shifts in the process mean substantially quicker than the Shewhart‐cumulative sum and the Shewhart‐EWMA control charts based on the RSS scheme. Both EWMA‐ORSS and EWMA‐OIRSS location charts perform better than the classical EWMA, hybrid EWMA, Shewhart‐EWMA and fast initial response‐EWMA charts. The EWMA‐ORSS dispersion control chart performs better than the simple random sampling based CS‐EWMA and other EWMA control charts in efficient detection of the random shifts that occur in the process variability. An application to real data is also given to explain the implementation of the proposed EWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.