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Single control charts are widely used to control assignable causes that shift the process due to variations in the mean and the dispersion. In the present article, the exponentially weighted moving average maximum (EWMA-Max) control chart is extended to the new single generally weighted moving average maximum (referred as GWMA-Max) control chart for joint monitoring of the process mean and variability. The proposed chart is compared with the EWMA-Max and DEWMA-Max charts in terms of the run-length performance measures. The results reveal that the GWMA-Max chart is very efficient in detecting small shifts in the process mean and variability concurrently. Finally, a practical implementation of the GWMA-Max chart is displayed using real and simulated datasets. [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 are very popular 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 maximum triple exponentially weighted moving average chart (referred as Max-TEWMA chart), that simultaneously detects both upward and downward shifts in the process mean and/or process dispersion. The run length performance and the diagnostic ability of the Max-TEWMA control chart are compared with that of the Max-EWMA, Max-DEWMA and Max-GWMA charts, through Monte-Carlo simulations. The comparisons reveal that the proposed chart is more efficient, than the competing ones, in detecting shifts in the process mean and variability simultaneously. Furthermore, the Max-TEWMA chart provides a satisfactory overall performance for identifying a wide range of shifts in the process mean and variability. Finally, two illustrative examples are presented to explain the application of the Max-TEWMA control chart. [ABSTRACT FROM AUTHOR]

In this article, we develop a new Triple EWMA-Max (TEWMA-Max) control chart for joint monitoring of the process mean and variance. The run-length characteristics of the proposed chart are computed through Monte-Carlo simulations. A detailed comparative study is conducted to compare the performance of the proposed chart with that of the EWMA-Max and DEWMA-Max charts. The comparison results reveal that the TEWMA-Max chart is more sensitive than the EWMA-Max chart in detecting small to moderate shifts in the mean and variability. Furthermore, it is more efficient than the DEWMA-Max chart for small to moderate shifts in the mean and small to large downward and large upward shifts in the dispersion, while it is quite comparable for small upward shifts in the variability with an increase of the smoothing parameter λ. Additionally, the TEWMA-Max chart shows a satisfactory overall performance for detecting a wide range of shift combinations in the process mean and dispersion. Finally, real and simulated datasets are considered to present the implementation of the new chart. [ABSTRACT FROM AUTHOR]

In the present article, a double generally weighted moving average (DGWMA) control chart based on a three-parameter logarithmic transformation is proposed for monitoring the process variability, namely the S 2 -DGWMA chart. Monte-Carlo simulations are utilized in order to evaluate the run-length performance of the S 2 -DGWMA chart. In addition, a detailed comparative study is conducted to compare the performance of the S 2 -DGWMA chart with several well-known memory-type control charts in the literature. The comparisons indicate that the proposed one is more efficient in detecting small shifts, while it is more sensitive in identifying upward shifts in the process variability. A real data example is given to present the implementation of the new S 2 -DGWMA chart. [ABSTRACT FROM AUTHOR]

This paper considers the design construction and model selection for mixture-process variable experiments where the number of variables is large. For such experiments the generalized least squares estimates cannot be obtained and hence it will be difficult to identify the important model terms. To overcome these problems, here we employ the generalized Bayesian-D criterion to choose the optimal design and apply the Bayesian analysis method to select the best model. Two algorithms are developed to implement the proposed methods. A fish-patty experiment demonstrates how the Bayesian approach can be applied to a real experiment. Simulation studies show that the proposed method has a high power to identify important terms and well controls the type I error. [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 moving average (MA) control chart is a memory-type scheme and effective for monitoring small and moderate shifts in the process mean. Several modifications of the MA chart, such as the double MA (DMA) and the triple MA (TMA) charts, have been introduced to improve the detection ability of the MA chart. In the present article, we propose the quadruple MA (QMA) chart for normally distributed data to improve much more the performance of the MA chart for small shifts. Comparing with the existing MA, DMA, TMA, EWMA and DEWMA charts, it is shown that the proposed chart is more effective for small shifts. Furthermore, it is found that the QMA chart is more in-control (IC) robust to non normality than its competitors. Finally, an illustrative example is provided to demonstrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

The repetitive sampling scheme is utilized in control charts to enhance their detection ability in process shifts. Their performance is usually evaluated under the assumption that the process parameters are known. In this article, we investigate the performance of the X ¯ and S2 charts under repetitive sampling when the process parameters are estimated from a preliminary in-control (Phase I) sample. We also present the exact expressions of the average run-length (ARL), standard deviation of run-length (SDRL) and average sample number (ASN) measures. A numerical analysis demonstrates that the effect of parameters estimation is significant when the Phase I sample and the sample size are small. [ABSTRACT FROM AUTHOR]