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The coefficient of variation (CV) chart is widely used in the process where the standard deviation is proportional to the mean. In this work, two separate one-sided triple exponentially weighted moving average control charts are proposed to monitor the CV squared (denoted as TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 chart). By adding the variable sampling interval (VSI) feature to the proposed - $ {\mathrm{\gamma }^2} $ γ 2 charts, the VSI TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 charts are further proposed to improve the performance of the TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 charts. Through extensive Monte Carlo simulations, the zero-state and steady-state run length (RL) performances are presented. The comparisons with the existing CV charts, based on several run length metrics show the superiority of the proposed charts, especially for small shifts. Moreover, the overall measure, expected ARL (EARL), also shows the outperformance of the $ {\mathrm{\gamma }^2} $ γ 2 charts. In addition, based on the average time to signal (ATS) and adjusted ATS (AATS), it is shown that the VSI strategy makes the TEWMA- $ {\mathrm{\gamma }^2} $ γ 2 charts detect the shifts more quickly. An illustrative example from the sintering process is finally provided to display the application of the proposed charts. [ABSTRACT FROM AUTHOR]

Control charts based on Time Between Events (TBE) have been shown to be effective in high quality processes, where the defects or failures (events) occur at a very low probability. The occurrences of events are usually modeled as a homogeneous Poisson process. The TBE data is likely to follow a skewed distribution, such as the gamma distribution. In order to monitor high quality processes, this study focuses on the development of modified one-sided Exponentially Weighted Moving Average (EWMA) TBE charts. The Monte-Carlo simulation method is used to evaluate the Run Length (RL) properties of the proposed schemes. The results show that the proposed schemes are more sensitive to process shifts than some competitive procedures. Finally, a real data example is provided to illustrate the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

The classical cumulative SUM (CUSUM) chart is commonly used to monitor a particular size of the mean shift. In many real processes, it is assumed that the shift level varies within a range, and the exact level of the shift size is mostly unknown. For detecting a range of shift size, the dual-CUSUM (DC) and dual-Crosier CUSUM (DCC) charts are used to provide better detection ability as compared to the CUSUM and Crosier CUSUM (CC) charts, respectively. This paper introduces a new mixed exponentially weighted moving average (EWMA)-DCC (EDCC) chart to monitor process mean. In addition, AIB-based EWMA-DC (EDC) and EDCC charts (namely, AIB-EDC and AIB-EDCC charts) are suggested to detect shifts in the process mean level. Monte Carlo simulations are used to compute the run length (RL) characteristics of the proposed charts. A detailed comparison of the proposed schemes with other competing charts is also provided. It turns out that the proposed chart provides better performance than the counterparts when detecting a range of mean shift sizes. A real-life application is also presented to illustrate the implementation of the existing and proposed charts. [ABSTRACT FROM AUTHOR]

Several scholarly works intrinsically assume that the frequency and magnitude of events are two independent variables. However, in many practical situations, it is necessary to consider the dependence between these two characteristics of events. In this paper, two Smith–Adelfang–Tubbs (SAT) models, namely, the four‐ and the five‐parameter bivariate Gamma distributions (BGD) with a particular dependency parameter, are first reviewed. Then, a synthetic multivariate exponentially weighted moving average (synthetic MEWMA, or SMEWMA) type scheme is proposed to monitor the individual BGD observations (subgroups of size one) generated from those two specific SAT models. The Monte‐Carlo simulation method is developed to evaluate the run length (RL$\mathrm{RL}$) properties of the recommended SMEWMA BGD scheme in both the zero‐state and the steady‐state cases. Furthermore, we discuss the average run length (ARL) of the proposed SMEWMA BGD scheme with different design parameters, and then compare both the zero‐state and the steady‐state out‐of‐control ARL performances of the recommended SMEWMA BGD scheme with those of the classic MEWMA chart, the paired individual Gamma chart, and the MCUSUM chart. Simulation results suggest that the overall performance of the recommended SMEWMA BGD scheme is superior to the other comparative schemes. Finally, the implementation of the proposed SMEWMA BGD scheme is illustrated with a natural flood event dataset. [ABSTRACT FROM AUTHOR]

In statistical process control (SPC), t charts play a vital role in the monitoring of the process mean, especially when the process variance is unknown. In this paper, two separate upper-sided and lower-sided exponentially weighted moving average (EWMA) t charts are first proposed and the Monte Carlo simulation method is used to obtain their run length (RL) properties. Compared with the traditional one-sided EWMA t charts and several run rules t charts, the proposed charts are proven to have better performance than these competing charts. In addition, by adding the variable sampling interval (VSI) feature to the proposed charts, the new VSI one-sided EWMA t charts are shown to detect different shift sizes in the process more efficient than the chart without VSI feature. Finally, an example of a milk filling process illustrates the use of the charts. [ABSTRACT FROM AUTHOR]

A common assumption for most control charts is the fact that the process parameters are supposed to be known or accurately estimated from Phase I samples. But, in practice, this is not a realistic assumption and the process parameters are usually estimated from a very limited number of samples that, in addition, may contain some outliers. Recently, a median chart with estimated parameters has been proposed to overcome these issues and it has been investigated in terms of the unconditional Average Run Length (ARL). As this median chart with estimated parameters does not take the 'Phase I between-practitioners' variability into account, in this paper, we suggest to revisit it using the Standard Deviation of the ARL as a measure of performance. The results show that this Standard Deviation of the ARL-based median chart actually requires a much larger amount of Phase I data than previously recommended to sufficiently reduce the variation in the chart performance. Due to the practical limitation of the number of the Phase I data, the bootstrap method is recommended as a good alternative approach to define new dedicated control chart parameters. [ABSTRACT FROM AUTHOR]

Much research has been conducted on two-sided Exponentially Weighted Moving Average (EWMA) control charts, while less work has been devoted to the one-sided EWMA charts. Traditional one-sided EWMA charts involve resetting the EWMA statistic to the target whenever it falls below or above the target, or truncating the observations above or below the target and further applying the EWMA statistic to the truncated samples. In order to further improve the performance of traditional one-sided EWMA mean ( X ¯ ) charts, this paper studies the performance of the Modified One-sided EWMA (MOEWMA) X ¯ charts to monitor a normally distributed process. The Monte-Carlo simulation method is used to obtain the zero- and steady-state Run Length ( R L ) properties of the proposed control charts. Through extensive simulations and comparisons with other charts, it is shown that the proposed MOEWMA X ¯ charts compare favorably with some existing competing charts. Moreover, by attaching the variable sampling intervals (VSI) feature to the MOEWMA X ¯ charts, it is shown that the VSI MOEWMA charts outperform the corresponding charts without the VSI feature. Finally, a real data example from manufacturing process shows the implementation of the proposed one-sided charts. [ABSTRACT FROM AUTHOR]