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The proposed exponentially weighted moving average combined Shewhart cumulative score (EWMA‐CUSCORE) procedure for controlling the process mean cumulate scores of ‐1, 0, 1 or 2h assigned to each moving average of the current and past sample mean values depending on a preassigned interval in which its value falls. It will be shown by average run length (ARL) comparisons that the proposed scheme performs better than the Shewhart type schemes, the combined Shewhart cumulative score type schemes, the cusum type schemes and the standard EWMA type schemes for detecting shifts in the process mean when the underlying process control variable is normal.

The double exponentially weighted moving average (DEWMA), which is known in the literature as Brown′s one‐parameter linear method for forecasting is proposed as a control tool for process monitoring and detecting shifts in the process mean. Obtains a closed‐form expression for the asymptotic standard deviation of the proposed DEWMA control statistic and discusses the determination of its average run length. Provides examples and comparisons between the proposed DEWMA and the standard EWMA. The results reveal that the proposed DEWMA control scheme performs much better than a Shewhart scheme for small and moderate shifts in the process mean and it has average run length properties similar to those for EWMA control schemes. However, DEWMA has smaller variability and it allows more smoothing of the data with no compromise in the sensitivity of detecting shifts in the process mean. It also shifts the range of the design parameters for optimal ARL to larger values as compared with EWMA schemes. Such properties are more desirable for some industrial processes.

Exponentially weighted moving average (EWMA) control chart can be designed to quickly detect small shifts in the mean of a sequence of independent normal observations. But this chart cannot perform well for skewed distribution. The main goal of this article is to suggest an EWMA control chart method that can be used to monitoring small shifts in a skewed distribution. Weighted variance method is introduced to construct a kind of EWMA chart for skewed distribution and the optimization design of this chart is given by using average run length as a performance assessment criteria. Pair of asymmetry control limits could be evaluated by sample dates in skewed distribution. The advantage of this method in detecting little drift for skewed distribution was illustrated by comparing with others control charts.

This study aims to focus on proposing a new memory-type chart called progressive mean exponentially weighted moving average (PMEWMA) control chart. This memory-type chart is an improvement on the existing progressive mean control chart, to detect small and moderate shifts in a process.

The PMEWMA control chart is developed by using a cumulative average of the exponentially weighted moving average scheme known as the progressive approach. This scheme is designed based on the assumption that data follow a normal distribution. In addition, the authors investigate the robustness of the proposed chart to the normality assumption.

The variance and the mean of the scheme are computed, and the mean is found to be an unbiased estimator of the population mean. The proposed chart's performance is compared with the existing charts in the literature by using the average run-length as the performance measure. Application examples from the petroleum and bottling industry are also presented for practical considerations. The comparison shows that the PMEWMA chart is quicker in detecting small shifts in the process than the other memory-type charts covered in this study. The authors also notice that the PMEWMA chart is affected by higher kurtosis and skewness.

A new memory-type scheme is developed in this research, which is efficient in detecting small and medium shifts of a process mean.

The exponentially weighted moving average (EWMA) control charts are widely used in industries for monitoring small and moderate process shifts. The purpose of this paper is to develop an algorithm for the optimization design of the EWMA chart (known as MD‐EWMA chart).

The design algorithm adjusts the sample size n, sampling interval h, lower and upper control limits LCL and UCL, and the EWMA weight factor λ of the chart in an optimal manner in order to minimize the mean number of defective units (denoted as MD) produced per out‐of‐control case. The probability distribution of the random process shift (e.g. mean shift δ) is taken into account that may be modeled by a Rayleigh distribution based on the sample data acquired during the operation of the control chart.

The results of the comparison studies and an example show that the proposed MD‐EWMA chart is significantly superior to the Shewhart‐type MD‐X¯ chart and the other EWMA charts in terms of the overall mean defective MD.

As the economic charts, the proposed MD‐EWMA chart aims at reducing the quality cost. But the design of this chart only requires limited number of specifications that can be easily determined. Consequently, the MD chart provides the control chart designers with an alternative choice between the statistical design and the economic design. Specifically, the mean shift δ is handled as a random variable by using a parametric or nonparametric approach to manipulate the sample data of δ acquired during the operation of the control chart. The MD counts the number of defective units produced per out of control case; so the design of control chart based on MD is more realistic from a practical viewpoint. In addition, the design of MD‐EWMA chart combines forecasting with controlling methods of quality management.

This work aims to focuse on improving the performance of the new exponentially weighted moving average (NEWMA) scheme for monitoring process dispersion. The authors use the generalized time-varying fast initial response (GFIR) to further enhance the detection ability of variability NEWMA control charts at the process startup. The performance of the proposed chart and other schemes discussed in this article are evaluated; and compared using the average run length (ARL) and standard deviation run length (SDRL) measures. It is observed that the ARL of the proposed scheme is quicker in detecting small and moderate shifts in the process dispersion than its counterparts. The real-life application of the proposed scheme is presented.

The dynamic parameter of GFIR is used to enhance the detection ability of variability NEWMA control charts. The authors apply GFIR to the control limit of variability NEWMA scheme. This further narrows the control limit, hence enabling it to swiftly detect small and moderate changes in process dispersion.

The authors present the performance comparisons by examining the ARL properties of the proposed chart and its counterparts. The performance comparison shows that the proposed chart is highly sensitive in detecting small and intermediate process shifts. The real-life application presented also supports the study’s conclusion from the simulation studies. The performance comparison of the proposed chart and its counterparts shows that the proposed scheme is efficient in detecting process abnormalities, especially at the startup.

In terms of the control limits, the proposed chart is the generalized variability NEWMA control chart in which all the previously proposed NEWMA variant schemes can be obtained. Also, the newly proposed control scheme is more efficient in detecting small or moderate persistent shifts in the process dispersion.

This paper presents economic and economic–statistical designs of the adaptive exponentially weighted moving average (AEWMA) control chart for monitoring the process mean. It also aims to compare the effect of estimated process parameters on the economic performance of three charts, which are Shewhart, exponentially weighted moving average and AEWMA control charts with economic–statistical design.

The optimal parameters of the control charts are obtained by applying the Lorenzen and Vance’s (1986) cost function. Comparisons between the economic–statistical and economic designs of the AEWMA control chart in terms of expected cost and statistical measures are performed. Also, comparisons are made between the economic performance of the three competing charts in terms of the average expected cost and standard deviation of expected cost.

This paper concludes that taking into account the economic factors and statistical properties in designing the AEWMA control chart leads to a slight increase in cost but in return the improvement in the statistical performance is substantial. In addition, under the estimated parameters case, the comparisons reveal that from the economic point of view the AEWMA chart is the most efficient chart when detecting shifts of different sizes.

The importance of the study stems from designing the AEWMA chart from both economic and statistical points of view because it has not been tackled before. In addition, this paper contributes to the literature by studying the effect of the estimated parameters on the performance of control charts with economic–statistical design.

The purpose of this paper is to develop a new control chart using two EWMA statistics called the hybrid exponentially weighted moving average (HEWMA) chart to improve the sensitivity of EWMA chart proposed by Zhang et al. (2014). When mean and variance of process are not constants, the use of control chart using coefficient of variation (CV) is a successful approach.

The control chart using EWMA statistics has ability to detect moderate and small shifts in the process. The authors present the designing of the proposed HEWMA statistics control chart called the HEWMA_CV chart based on two hybrid EWMA (HEWMA) statistics. The proposed control chart utilizes the current information and previous information to make decision about the state of control chart.

In this paper, the authors will present the designing of HEWMA statistics control chart called the HEWMA_CV chart. The efficiency of the proposed control chart is shown using the simulated data and real data from the industry. The application of proposed chart on the real data shows that the proposed chart has ability to detect shift in the process and it is superior than existing chart in terms of average run length (ARL).

The design and implementation of the proposed control chart on a real data shows that it can be applied in several industries, such as chemical industry, biological assays, etc.

The practical application of HEWMA chart using coefficient variation is gaining extensive adequacy. The design and implementation of the HEWMA chart offers a new approach in the detection of small process mean shift.

In practice, when mean and variance of process are not constants, the use of control chart using CV is a successful approach. In this paper, the authors designed a new control chart using two EWMA statistics called the HEWMA chart to improve the sensitivity of EWMA chart. The comparison shows that the proposed chart is superior than the existing chart in terms of ARL.

This study aims to assess the effect of updating the Phase I data – to enhance the parameters' estimates – on the control charts' detection power designed to monitor social networks.

A dynamic version of the degree corrected stochastic block model (DCSBM) is used to model the network. Both the Shewhart and exponentially weighted moving average (EWMA) control charts are used to monitor the model parameters. A performance comparison is conducted for each chart when designed using both fixed and moving windows of networks.

Our results show that continuously updating the parameters' estimates during the monitoring phase delays the Shewhart chart's detection of networks' anomalies; as compared to the fixed window approach. While the EWMA chart performance is either indifferent or worse, based on the updating technique, as compared to the fixed window approach. Generally, the EWMA chart performs uniformly better than the Shewhart chart for all shift sizes. We recommend the use of the EWMA chart when monitoring networks modeled with the DCSBM, with sufficiently small to moderate fixed window size to estimate the unknown model parameters.

This study shows that the excessive recommendations in literature regarding the continuous updating of Phase I data during the monitoring phase to enhance the control chart performance cannot generally be extended to social network monitoring; especially when using the DCSBM. That is to say, the effect of continuously updating the parameters' estimates highly depends on the nature of the process being monitored.

When there is a change in a process, the MaxMin exponentially weighted moving average (EWMA) control chart shows which parameters have increased or decreased. The MaxMin EWMA may also be viewed as smoothed tolerance limits. Tolerance limits are limits that include a specific proportion of the population at a given confidence level. In the context of process control, they are used to make sure that production will not be outside specifications. In this article, we provide useful coverages for the MaxMin EWMA chart, when also used as tolerance limits. The proposed EWMA smoothed tolerance limits require relatively small sample sizes to attain useful coverages at high confidence levels. The MaxMin EWMA chart has already been successfully field‐tested and subsequently implemented with 100 multi‐stream processes.