An Improved Distribution-free EWMA Mean Chart

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used here. In this article, we propose an improved asymmetric EWMA mean chart based on a simple statistic to monitor process mean shift. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed asymmetric EWMA mean chart. We recommend the proposed improved asymmetric EWMA mean chart because the average run lengths of the modified charts are more accurate and reasonable than those of the five existed mean charts. A numerical example of service times with a right skewed distribution from a service system of a bank branch is used to illustrate the application of the improved asymmetric EWMA mean chart and to compare it with the five existing mean charts. The proposed chart showed better detection performance than those of the five existing mean charts in monitoring and detecting shifts in the process mean.     

A new approach for monitoring process variance

ABSTRACT

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used in such circumstances. In this paper, we propose a new variance chart based on a simple statistic to monitor process variance shifts. We explore the sampling properties of the new monitoring statistic and calculate the average run lengths (ARLs) of the proposed variance chart. Furthermore, an arcsine transformed exponentially weighted moving average (EWMA) chart is proposed because the ARLs of this modified chart are more intuitive and reasonable than those of the variance chart. We compare the out-of-control variance detection performance of the proposed variance chart with that of the non-parametric Mood variance (NP-M) chart with runs rules, developed by Zombade and Ghute [Nonparametric control chart for variability using runs rules. Experiment. 2014;24(4):1683–1691], and the nonparametric likelihood ratio-based distribution-free exponential weighted moving average (NLE) chart and the combination of traditional exponential weighted moving average (EWMA) mean and EWMA variance (CEW) control chart proposed by Zou and Tsung [Likelihood ratio-based distribution-free EWMA control charts. J Qual Technol. 2010;42(2):174–196] by considering cases in which the critical quality characteristic has a normal, a double exponential or a uniform distribution. Comparison results showed that the proposed chart performs better than the NP-M with runs rules, and the NLE and CEW control charts. A numerical example of service times with a right-skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the application of the proposed variance chart and of the arcsine transformed EWMA chart and to compare them with three existing variance (or standard deviation) charts. The proposed charts show better detection performance than those three existing variance charts in monitoring and detecting shifts in the process variance.     

A New Adaptive Variable Sample Size Approach in EWMA Control Chart

Adaptive control charts have been developed for improving the capability of control charts in detecting small shifts. In this article, we propose a new exponential weighted moving average control chart with variable sample size, in which the sample size is determined as an integer linear function by EWMA statistic value. The performance of the proposed VSS EWMA control chart is compared with FSS EWMA as well as traditional VSS EWMA control charts. The results show the better performance of the proposed VSS strategy respect to the traditional one and fixed sample size.     

An EWMA chart for monitoring process mean

In the statistical process control literature, there exists several improved quality control charts based on cost-effective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-effective RSS scheme has been recently introduced for efficiently estimating the population mean, namely varied L RSS (VLRSS). In this article, we propose a new exponentially weighted moving average (EWMA) control chart for monitoring the process mean using VLRSS, named the EWMA-VLRSS chart, under both perfect and imperfect rankings. The EWMA-VLRSS chart encompasses the existing EWMA charts based on RSS and MRSS (named the EWMA-RSS and EWMA-MRSS charts). We use extensive Monte Carlo simulations to compute the run length characteristics of the EWMA-VLRSS chart. The proposed chart is then compared with the existing EWMA charts. It is found that, with either perfect or imperfect rankings, the EWMA-VLRSS chart is more sensitive than the EWMA-RSS and EWMA-MRSS charts in detecting small to large shifts in the process mean. A real dataset is also used to explain the working of the EWMA-VLRSS chart.     

A mixed GWMA–CUSUM control chart for monitoring the process mean

The memory-type control charts are widely used in the process and service industries for monitoring the production processes. The reason is their sensitivity to quickly react against the small process disturbances. Recently, a new cumulative sum (CUSUM) chart has been proposed that uses the exponentially weighted moving average (EWMA) statistic, called the EWMA–CUSUM chart. Similarly, in order to further enhance the sensitivity of the EWMA–CUSUM chart, we propose a new CUSUM chart using the generally weighted moving average (GWMA) statistic, called the GWMA–CUSUM chart, for efficiently monitoring the process mean. The GWMA–CUSUM chart encompasses the existing CUSUM and EWMA–CUSUM charts. Extensive Monte Carlo simulations are used to explore the run length profiles of the GWMA–CUSUM chart. Based on comprehensive run length comparisons, it turns out that the GWMA–CUSUM chart performs substantially better than the CUSUM, EWMA, GWMA, and EWMA–CUSUM charts when detecting small shifts in the process mean. An illustrative example is also presented to explain the implementation and working of the EWMA–CUSUM and GWMA–CUSUM charts.     

Robustness to non-normality and autocorrelation of individuals control charts

This paper studies the effects of non-normality and autocorrelation on the performances of various individuals control charts for monitoring the process mean and/or variance. The traditional Shewhart X chart and moving range (MR) chart are investigated as well as several types of exponentially weighted moving average (EWMA) charts and combinations of control charts involving these EWMA charts. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts, and that the performana of the X and MR charts is very sensitive to the normality assumption. It is also shown that certain combinations of EWMA charts can be designed to be robust to non-normality and very effective at detecting small and moderate shifts in the process mean and/or variance. Although autocorrelation can have a significant effect on the in-control performances of these combinations of EWMA charts, their relative out-of-control performances under independence are generally maintained for low to moderate levels of autocorrelation.     

Non parametric double generally weighted moving average sign charts based on process proportion

Non parametric control charts have received increasing attention in the field of statistical process control. This paper presents a non parametric double generally weighted moving average (DGWMA) sign chart for monitoring small deviations when the quality characteristics of a process are unknown. The statistical performance of the non parametric DGWMA sign chart is evaluated and compared with those of other charts, including the exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double EWMA (DEWMA) sign charts. Simulation studies indicate that the non parametric DGWMA sign chart with a large design and median adjustment parameters is always more sensitive than other charts in detecting small changes.     

A Double Moving Average Control Chart

The double exponentially weighted moving average (DEWMA) technique has been investigated in recent years for detecting shifts in the process mean and has been shown to be more efficient than the corresponding exponentially weighted moving average (EWMA) technique. In this article, we extend the DEWMA technique of performing exponential smoothing twice to the double moving average (DMA) technique by computing the moving average twice. Using simulation, we show that our proposed DMA chart improves upon the ARL performance of the moving average (MA) chart in detecting mean shifts of small to moderate magnitudes. It is also shown through simulation that, generally, the DMA charts with spans, w = 10 and 15 provide comparable average run length (ARL) performances to the EWMA and cumulative sum (CUSUM) charts, designed for detecting small shifts.     

Robustness of the EWMA and the combined X¯–EWMA control charts with variable sampling intervals to non-normality

The exponentially weighted moving average (EWMA) control charts with variable sampling intervals (VSIs) have been shown to be substantially quicker than the fixed sampling intervals (FSI) EWMA control charts in detecting process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true for some processes. In the present paper, the performances of the EWMA and combined X¯–EWMA control charts with VSIs are evaluated under non-normality. It is shown that adding the VSI feature to the EWMA control charts results in very substantial decreases in the expected time to detect shifts in process mean under both normality and non-normality. However, the combined X¯–EWMA chart has its false alarm rate and its detection ability is affected if the process data are not normally distributed.     

A new adaptive EWMA control chart using auxiliary information for monitoring the process mean

The adaptive memory-type control charts, including the adaptive exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, have gained considerable attention because of their excellent speed in providing overall good detection over a range of mean shift sizes. In this paper, we propose a new adaptive EWMA (AEWMA) chart using the auxiliary information for efficiently monitoring the infrequent changes in the process mean. The idea is to first estimate the unknown process mean shift using an auxiliary information based mean estimator, and then adaptively update the smoothing constant of the EWMA chart. Using extensive Monte Carlo simulations, the run length profiles of the AEWMA chart are computed and explored. The AEWMA chart is compared with the existing control charts, including the classical EWMA, CUSUM, synthetic EWMA and synthetic CUSUM charts, in terms of the run length characteristics. It turns out that the AEWMA chart performs uniformly better than these control charts when detecting a range of mean shift sizes. An illustrative example is also presented to demonstrate the working and implementation of the proposed and existing control charts.     

A new nonparametric synthetic EWMA control chart for monitoring process mean

The exponentially weighted moving average (EWMA) control charts are widely used in chemical and process industries because of their excellent speed in catching small to moderate shifts in the process target. In usual practice, many data come from a process where the monitoring statistic is non-normally distributed or it follows an unknown probability distribution. This necessitates the use of distribution-free/nonparametric control charts for monitoring the deviations from the process target. In this paper, we integrate the existing EWMA sign chart with the conforming run length chart to propose a new synthetic EWMA (SynEWMA) sign chart for monitoring the process mean. The SynEWMA sign chart encompasses the synthetic sign and EWMA sign charts. Monte Carlo simulations are used to compute the run length profiles of the SynEWMA sign chart. Based on a comprehensive comparison, it turns out that the SynEWMA sign chart is able to perform substantially better than the existing EWMA sign chart. Both real and simulated data sets are used to explain the working and implementation of existing and proposed control charts.     

Monitoring the mean of autocorrelated observations with one generally weighted moving average control chart

Traditionally, using a control chart to monitor a process assumes that process observations are normally and independently distributed. In fact, for many processes, products are either connected or autocorrelated and, consequently, obtained observations are autocorrelative rather than independent. In this scenario, applying an independence assumption instead of autocorrelation for process monitoring is unsuitable. This study examines a generally weighted moving average (GWMA) with a time-varying control chart for monitoring the mean of a process based on autocorrelated observations from a first-order autoregressive process (AR(1)) with random error. Simulation is utilized to evaluate the average run length (ARL) of exponentially weighted moving average (EWMA) and GWMA control charts. Numerous comparisons of ARLs indicate that the GWMA control chart requires less time to detect various shifts at low levels of autocorrelation than those at high levels of autocorrelation. The GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in a process mean.     

A non parametric CUSUM control chart based on the Mann–Whitney statistic

We consider a novel univariate non parametric cumulative sum (CUSUM) control chart for detecting the small shifts in the mean of a process, where the nominal value of the mean is unknown but some historical data are available. This chart is established based on the Mann–Whitney statistic as well as the change-point model, where any assumption for the underlying distribution of the process is not required. The performance comparisons based on simulations show that the proposed control chart is slightly more effective than some other related non parametric control charts.     

A multivariate exponentially weighted moving average control chart for monitoring process variability

This paper introduces a new multivariate exponentially weighted moving average (EWMA) control chart. The proposed control chart, called an EWMA V-chart, is designed to detect small changes in the variability of correlated multivariate quality characteristics. Through examples and simulations, it is demonstrated that the EWMA V-chart is superior to the |S|-chart in detecting small changes in process variability. Furthermore, a counterpart of the EWMA V-chart for monitoring process mean, called the EWMA M-chart is proposed. In detecting small changes in process variability, the combination of EWMA M-chart and EWMA V-chart is a better alternative to the combination of MEWMA control chart (Lowry et al. , 1992) and |S|-chart. Furthermore, the EWMA M- chart and V-chart can be plotted in one single figure. As for monitoring both process mean and process variability, the combined MEWMA and EWMA V-charts provide the best control procedure.     

A HEWMA-CUSUM control chart for the Weibull distribution

The Weibull distribution is one of the most popular distributions for lifetime modeling. However, there has not been much research on control charts for a Weibull distribution. Shewhart control is known to be inefficient to detect a small shift in the process, while exponentially weighted moving average (EWMA) and cumulative sum control chart (CUSUM) charts have the ability to detect small changes in the process. To enhance the performance of a control chart for a Weibull distribution, we introduce a new control chart based on hybrid EWMA and CUSUM statistic, called the HEWMA-CUSUM chart. The performance of the proposed chart is compared with the existing chart in terms of the average run length (ARL). The proposed chart is found to be more sensitive than the existing chart in ARL. A simulation study is provided for illustration purposes. A real data is also applied to the proposed chart for practical use.     

Maximum Chi-Square Generally Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

In this article, we propose a new control chart called the maximum chi-square generally weighted moving average (MCSGWMA) control chart. This control chart can effectively combine two generally weighted moving average (GWMA) control charts into a single one and can detect both increases as well as decreases in the process mean and/or variability simultaneously. The average run length (ARL) characteristics of the MCSGWMA and maximum exponentially weighted moving average (MaxEWMA) charts are evaluated by performing computer simulations. The comparison of the ARLs shows that the MCSGWMA control chart performs better than the MaxEWMA control chart.     

Monitoring simple linear profiles using variable sample size schemes

ABSTRACT

Profile monitoring is one of the new research areas in statistical process control. Most of the control charts in this area are designed with fixed sampling rate which makes the control chart slow in detecting small to moderate shifts. In order to improve the performance of the conventional fixed control charts, adaptive features are proposed in which, one or more design parameters vary during the process. In this paper the variable sample size feature of EWMA₃ and MEWMA schemes are proposed for monitoring simple linear profiles. The EWMA₃ method is based on the combination of three exponentially weighted moving average (EWMA) charts for monitoring three parameters of a simple linear profile separately and the Multivariate EWMA (MEWMA) chart is based on the using a single chart to monitor the coefficients and variance of a general linear profile. Also a two-sided control chart is proposed for monitoring the standard deviation in the EWMA₃ method. The performance of the proposed charts is compared in terms of the average time to signal. Numerical examples show that using adaptive features increase the power of control charts in detecting the parameter shifts. Finally, the performance of the proposed variable sample size schemes is illustrated through a real case in the leather industry.     

Multivariate process dispersion monitoring without subgrouping

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.     

Control charts based on linear combinations of order statistics

The last 20 years have seen an increasing emphasis on statistical process control as a practical approach to reducing variability in industrial applications. Control charts are used to detect problems such as outliers or excess variability in subgroup means that may have a special cause. We describe an approach to the computation of control limits for exponentially weighted moving average control charts where the usual statistics in classical charts are replaced by linear combinations of order statistics; in particular, the trimmed mean and Gini's mean difference instead of the mean and range, respectively. Control limits are derived, and simulated average run length experiments show the trimmed control charts to be less influenced by extreme observations than their classical counterparts, and lead to tighter control limits. An example is given that illustrates the benefits of the proposed charts. parameters; see, for example, Hunter (1986) and Montgomery (1996). On the other hand, EWMA charts have been shown to be more efficient than Shewharttype charts in detecting small shifts in the process mean; see, for example, Ng & Case (1989), Crowder (1989), Lucas & Saccucci (1990), Amin & Searcy (1991) and Wetherill & Brown (1991). In fact, the EWMA control chart has become popular for monitoring a process mean; see Hunter (1986) for a good discussion. More recently, EWMA charts have been developed for monitoring process variability;     

Control charts based on linear combinations of order statistics

The last 20 years have seen an increasing emphasis on statistical process control as a practical approach to reducing variability in industrial applications. Control charts are used to detect problems such as outliers or excess variability in subgroup means that may have a special cause. We describe an approach to the computation of control limits for exponentially weighted moving average control charts where the usual statistics in classical charts are replaced by linear combinations of order statistics; in particular, the trimmed mean and Gini's mean difference instead of the mean and range, respectively. Control limits are derived, and simulated average run length experiments show the trimmed control charts to be less influenced by extreme observations than their classical counterparts, and lead to tighter control limits. An example is given that illustrates the benefits of the proposed charts. parameters; see, for example, Hunter (1986) and Montgomery (1996). On the other hand, EWMA charts have been shown to be more efficient than Shewharttype charts in detecting small shifts in the process mean; see, for example, Ng & Case (1989), Crowder (1989), Lucas & Saccucci (1990), Amin & Searcy (1991) and Wetherill & Brown (1991). In fact, the EWMA control chart has become popular for monitoring a process mean; see Hunter (1986) for a good discussion. More recently, EWMA charts have been developed for monitoring process variability;