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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 purpose of this paper is to make economic comparison of the proposed X¯ chart with the economic and economic‐statistical design of a multivariate exponentially weighted moving average (MEWMA) control chart proposed by Linderman and Love, using Lorenzen‐Vance cost model.

The economic design of proposed X¯ chart, using Lorenzen‐Vance cost model, is discussed in the paper. It is observed that sampling interval (h) and expected cost/hour (C) depend on various parameters of the chart, used in this model. When there is any change in any parameter of the chart, obviously both sampling interval and expected cost will be different. So it is suggested that one should use Lorenzen and Vance cost model (equation 1) to compute sampling interval and expected cost/hour for the proposed X¯ chart.

The economic design of the proposed X¯ chart has been compared with the economic and economic‐statistical design of the multivariate exponentially weighted moving average (MEWMA) control chart proposed by Linderman and Love. It is found that the proposed X¯ chart performs better than MEWMA chart proposed by Linderman and Love for sample sizes of 7, 9 and 10 for first set of parameters. The proposed X¯ chart also shows lower expected cost/hour than the MEWMA chart for sample size of 2 and 3 and for shifts of 2 and 3 for the second set of parameters.

A lot of effort has been made to develop the proposed X¯ chart for monitoring the process mean. Although optimal sampling intervals are calculated only for two sets of parameters for shifts in the process average of 1, 2 and 3, it can be computed for any set of parameters using the Lorenzen‐Vance cost model.

The research findings could be applied to various manufacturing and service industries, as it is more effective than the Shewhart and EWMA charts.

Control charts are important tools of statistical quality control. In 1956, Duncan first proposed the economic design of x‐control charts to control normal process means and insure that the economic design control chart actually has a lower cost, compared with a Shewhart control chart. An moving average (MA) control chart is more effective than a Shewhart control chart in detecting small process shifts and is considered by some to be simpler to implement than the CUSUM. An economic design of MA control chart has also been proposed in 2005. The weaknesses to only the economic design are poor statistics because it does not consider type I or type II errors and average time to signal when selecting design parameters for control chart. This paper provides a construction of an economic‐statistical model to determine the optimal parameters of an MA control chart to improve economic design. A numerical example is employed to demonstrate the model’s working and its sensitivity analysis is also provided.

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.

The purpose of this paper is to propose a double exponentially weighted moving average control chart using repetitive sampling (RS-DEWMA) for a normally distributed process variable to improve the efficiency of detecting small process mean shift.

The algorithm for the implementation of the proposed chart is developed and the formulae for the in-control and out-of-control average run lengths (ARLs) are derived. Tables of ARLs are presented for various process mean shift. The performance of the proposed chart is investigated in terms of the average run-length for small process mean shift and compared with the existing DEWMA control chart. Numerical examples are given as illustration of the design and implementation of the proposed chart.

The proposed control chart is more efficient than the existing DEWMA control chart in the detection of small process mean shifts as it consistently gives smaller ARL values and quickly detects the process shift. However, the performance of the proposed chart relatively deteriorates for large smoothing constants.

The application of repetitive sampling in the control chart literature is gaining wide acceptability. The design and implementation of the RS-DEWMA control chart offers a new approach in the detection of small process mean shift by process control personnel.

This paper fills a gap in the literature by examining the performance of the repetitive sampling DEWMA control chart. The use of repetitive sampling technique in the control chart is discussed in the literature, however, its use based on the DEWMA statistic has not been considered in this context.

The purpose of this paper is to monitor small shifts in the process mean and/or variance for which observational data meet significant autocorrelation.

A generally weighted moving average (GWMA) control chart for monitoring a process is introduced in which the observations can be modelled as a first‐order autoregressive process with a random error. Using simulation, the average run lengths (ARLs) of control schemes are compared.

The results showed that the GWMA control chart of observations requires less time to detect small shifts in the process mean and/or variance than the EWMA control chart.

The paper presents a useful discussion of a method that enables the detecting ability of the EWMA control chart to be enhanced and shows that when the observations are drawn from an AR(1) process with random error, the EWMA control chart is far more useful than the Shewhart control chart in detecting small shifts. The GWMA control chart of observations is shown to be superior to the EWMA control chart in detecting small shifts in the process mean and variance. The GWMA control chart of observations requires less time to detect small process mean and/or variance shifts as the level of autocorrelation declines. However, the GWMA and EWMA control charts of observations perform poorly for large shifts.

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.

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 economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. An MA control chart is more effective than the Shewhart chart in detecting small process shifts. This paper provides an economic model for determining the optimal parameters of an MA control chart with multiple assignable causes and two failures in the production process. These parameters consist of the sample size, the spread of the control limit and the sampling interval. A numerical example is shown and the sensititivy analysis shows that the magnitude of shift, rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost, meaning that one should more carefully estimate these values when conducting an economic analysis.