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Memory-type control charts are widely used for monitoring small to moderate shifts in the process parameter(s). In the present article, we present an exponentiated exponentially weighted moving average (Exp-EWMA) control chart that weights the past observations of a process using an exponentiated function. We evaluated the run-length characteristics of the Exp-EWMA chart via Monte Carlo simulations. A comparison study versus the CUSUM, EWMA and extended EWMA (EEWMA) charts under similar in-control (IC) run-length properties demonstrates that the Exp-EWMA chart is more effective for detecting small and, under certain circumstances, moderate shifts for both the zero-state and steady-state cases. Moreover, the Exp-EWMA chart has better zero-state out-of-control (OOC) performance than an EWMA chart with smoothing parameter equal to the limit to the infinity of the exponentiated function, while the two charts perform similarly for the steady-state case. Finally, it is shown that the Exp-EWMA chart is more IC robust than its competitors under several non-normal distributions. Two examples are provided to explain the implementation of the proposed chart [ABSTRACT FROM AUTHOR]

Distribution-free or nonparametric control charts are used for monitoring the process parameters when there is a lack of knowledge about the underlying distribution. In this paper, we investigate a single distribution-free triple exponentially weighted moving average control chart based on the Lepage statistic (referred as TL chart) for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous distribution. The design and implementation of the proposed chart are discussed using time-varying and steady-state control limits for the zero-state case. The run-length distribution of the TL chart is evaluated by performing Monte Carlo simulations. The performance of the proposed chart is compared to those of the existing EWMA-Lepage (EL) and DEWMA-Lepage (DL) charts. It is observed that the TL chart with a time-varying control limit is superior to its competitors, especially for small to moderate shifts in the process parameters. We also provide a real example from a manufacturing process to illustrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

Control charts based on the sample mean X ¯ are used for monitoring shifts in the process mean under the assumption that the process standard deviation is stable or well estimated. However, in many applications, this assumption is violated. In this case, t control charts are preferred as they are robust to changes in the process standard deviation. In this article, a generally weighted moving average chart based on the t statistic (referred as GWMA t chart) is proposed for monitoring shifts in the process mean. Its performance is studied using Monte Carlo simulation. It is shown that the proposed chart is more effective than the Shewhart t and EWMA t charts. Moreover, it is found more robust than the GWMA X ¯ chart to changes in the process standard deviation. Finally, two illustrative examples are given to display the application of the proposed chart. [ABSTRACT FROM AUTHOR]

The modified exponentially weighted moving average (MEWMA) control chart has been proposed in the literature in an effort to improve the performance of the classical EWMA chart. In this article, we study in more detail the MEWMA chart using various values of its additional design parameter and we also propose the double MEWMA (DMEWMA) chart for monitoring shifts in the process mean, under the assumption that the underlying process follows a normal distribution. The statistical performance of the two charts has been evaluated on the basis of the average and standard deviation of run-length performing Monte Carlo simulations. A comparison study versus the EWMA and DEWMA charts indicate that the modified schemes have better detection ability for the range of shifts where a classical chart is not optimal designed. Finally, one real example is given to demonstrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

The exponentially weighted moving average (EWMA) control chart is a very popular memory-type chart and also effective in detecting small shifts in the process mean. Several modifications of the EWMA chart, such as the double and triple EWMA charts (regarded as DEWMA and TEWMA charts, respectively) have been developed to enhance its performance in detecting small shifts. In the present article, we propose the quadruple EWMA chart (regarded as QEWMA chart) in order to improve much more the detection ability of the EWMA chart. The run-length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. Comparing with the EWMA, DEWMA and TEWMA charts, it is found that the QEWMA chart outperforms its competitors for small shifts. Moreover, it is shown that the proposed chart is more in-control (IC) robust under several non-normal distributions than the other charts, especially for a medium value of the smoothing parameter. The effect of inertia on the performance of the QEWMA chart is also investigated as a part of this article. Finally, two examples are provided to demonstrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

Parametric (or traditional) control charts are based on the assumption that the quality characteristic of interest follows a specific distribution. However, in many applications, there is a lack of knowledge about the underlying distribution. To this end, nonparametric (or distribution-free) control charts have been developed in recent years. In this article, a nonparametric double homogeneously weighted moving average (DHWMA) control chart based on the sign statistic is proposed for monitoring the location parameter of an unknown and continuous distribution. The performance of the proposed chart is measured through the run-length distribution and its associated characteristics by performing Monte Carlo simulations. The DHWMA sign chart is compared with other nonparametric sign charts, such as the homogeneously weighted moving average, generally weighted moving average (GWMA), double GWMA, and triple exponentially weighted moving average sign charts, as well as the traditional DHWMA chart. The results indicate that the proposed chart performs just as well as and in some cases better than its competitors, especially for small shifts. Finally, two examples are provided to show the application and implementation of the proposed chart. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Nonparametric (or distribution‐free) control charts are used for monitoring processes where there is a lack of knowledge about the underlying distribution. In this article, a triple exponentially weighted moving average control chart based on the signed‐rank statistic (referred as TEWMA‐SR chart) is proposed for monitoring shifts in the location parameter of an unknown, but continuous and symmetric, distribution. The run‐length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. A comparison study with other existing nonparametric control charts based on the signed‐rank statistic, the TEWMA sign chart, and the parametric TEWMA‐X¯ chart indicates that the proposed chart is more effective in detecting small shifts, while it is comparable with the other charts for moderate and large shifts. Finally, two illustrative examples are provided to demonstrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

Control charts are widely applied in many manufacturing processes to monitor the quality characteristic of interest. Recently, a homogeneously weighted moving average (HWMA) control chart was proposed as an improvement of the exponentially weighted moving average (EWMA) chart for efficiently monitoring of small shifts in the process mean. In the present article, we extend the HWMA chart by imitating exactly the double EWMA (DEWMA) technique. The proposed scheme is regarded as double HWMA (DHWMA) control chart. The run‐length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. A comparison study versus the EWMA, DEWMA, HWMA, mixed EWMA cumulative sum (CUSUM), CUSUM, and GWMA charts indicates that the DHWMA chart is more effective in detecting small to moderate shifts, while it performs similarly with its competitors for large shifts. We also study the robustness of the proposed chart under several nonnormal distributions, and it is shown that the DHWMA chart is in‐control robust for small values of the smoothing parameters. Finally, two examples are given to demonstrate the implementation of the proposed chart. [ABSTRACT FROM AUTHOR]

In the present article, we propose a generally weighted moving average control chart based on a three-parameter logarithmic transformation for monitoring shifts in the process variability (regarded as S2-GWMA chart). Monte Carlo simulations are used to evaluate its performance in terms of the run-length distribution. A comparison study versus the S2-EMWA, S2-CUSUM, CS-EWMA, S2-HEWMA and GWMAV charts indicates that the proposed chart is more effective than its competitors in detecting small to moderate upward shifts while it performs similarly with the other charts for large shifts. Finally, a real example is presented to display the application of the S2-GWMA chart. [ABSTRACT FROM AUTHOR]

Nonparametric control charts are used in process monitoring when there is insufficient information about the form of the underlying distribution. In this article, we propose a triple exponentially weighted moving average (TEWMA) control chart based on the sign statistic for monitoring the location parameter of an unknown continuous distribution. The run‐length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. We also compare its statistical performance with existing nonparametric sign charts, such as the cumulative sum (CUSUM), exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double exponentially weighted moving average (DEWMA) sign charts as well as the parametric TEWMA‐X¯ chart. The results show that the TEWMA sign chart is superior to its competitors, especially for small shifts. Moreover, two examples are given to demonstrate the application of the new scheme. [ABSTRACT FROM AUTHOR]

Quality control charts are extensively used to monitor processes. The EWMA chart is a good alternative to the Shewhart chart to quickly detect small and moderate shifts in the process mean. The DEWMA charting procedure is an enhanced approach for the EWMA chart and performs much better, especially for small and moderate shifts. In this article, we propose the triple EWMA (TEWMA) chart in an effort to improve much more the detection ability of the classical EWMA chart. Monte Carlo simulations are used to evaluate the run-length characteristics of the proposed chart. A comparison study versus the DEWMA, EWMA and GWMA charts indicates that the TEWMA chart with time-varying control limits is more effective in detecting small shifts while it is comparable with the other charts in moderate and large shifts. Moreover, the proposed chart has better inertia properties than the competing charts and is also shown to be in-control robust for small values of the smoothing parameter. Finally, two examples are given to display the application of the TEWMA chart. [ABSTRACT FROM AUTHOR]

In various scenarios where products and services are accompanied by warranties to ensure their reliability over a specified time, the two-parameter (shifted) exponential distribution serves as a fundamental model for time-to-event data. In modern production process, the products often come with warranties, and their quality can be manifested by the changes in the scale and origin parameters of a shifted exponential (SE) distribution. This paper introduces the Max-EWMA chart, employing maximum likelihood estimators and exponentially weighted moving average (EWMA) statistics, to jointly monitor SE distribution parameters. Additionally, we extend two additional charts, namely the Max-DEWMA and Max-TEWMA charts to enhance early-stage shift detection. Performance evaluations under zero-state and steady-state conditions compare these charts with the existing Max-CUSUM chart in terms of expected value and standard deviation of the run length (RL) distribution. Our findings reveal that among the Max-EWMA schemes, the Max-EWMA SE chart outperforms the others in terms of steady-state performance, while the Max-TEWMA chart surpasses the Max-EWMA and Max-DEWMA SE charts in respect to zero-state performance. Moreover, the proposed Max-EWMA schemes demonstrate advantages over Max-CUSUM, especially for small to moderate smoothing constants. We also provide an illustrative example to demonstrate the implementation of the proposed schemes. [ABSTRACT FROM AUTHOR]

The moving average (MA) and double moving average (DMA) control charts are a good alternative to the Shewhart chart to detect small to moderate shifts of the process mean more quickly. In this article, we propose the triple moving average (TMA) control chart to improve the detection ability of the MA chart. It is shown that the proposed chart is more effective than the MA and DMA charts in detecting small to moderate shifts for a small value of span w. However, this range of shifts decreases as the value of w increases. The application of the proposed chart is demonstrated through two examples. [ABSTRACT FROM AUTHOR]