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This study introduces a novel Adaptive EWMA (AEWMA) control chart designed to monitor the mean of a normally distributed process with enhanced responsiveness. The proposed methodology dynamically adjusts the smoothing constant based on a proposed continuous function of the estimated mean shift derived from the EWMA statistic. The Monte Carlo simulations are conducted to assess the performance of the AEWMA chart across various magnitudes of process mean shifts, using run-length profiles as the primary evaluation metric. The results indicate that the AEWMA chart outperforms traditional methods in terms of detection efficiency. To demonstrate its practical applicability, the AEWMA chart is applied to a real-world manufacturing dataset, specifically analyzing the flow width resistance of substrates. The findings highlight the efficiency of the proposed chart, making it a valuable tool for improving process monitoring and quality control in industrial environments.

Statistical Process Control is essential for ensuring process stability and detecting variations in a production environment. This study introduces a control chart based on the Exponentially Weighted Moving Average (EWMA) that uses an adaptive sample size. The proposed approach enhances shift detection by dynamically adjusting the sample size in response to changes in process variation. Extensive Monte Carlo simulations were performed to assess the performance of the proposed control chart, focusing on metrics such as the Average Run Length (ARL) and the Standard Deviation of Run Length (SDRL). The findings show that the new chart surpasses both the Fixed Sample Size EWMA (FEWMA) and the Variable Sample Size EWMA charts, particularly in detecting small to moderate shifts in the process. This approach strikes a balance between detection sensitivity and computational efficiency, enabling prompt identification of process changes while maintaining robustness during in-control conditions. To illustrate its practical applicability, a real-world dataset was analyzed, demonstrating the effectiveness of the proposed method in actual process monitoring scenarios.

Variable parameters (VP) schemes are the most effective adaptive schemes in increasing control charts' sensitivity to detect small to moderate shift sizes. In this paper, we develop four VP adaptive memory-type control charts to monitor multivariate multiple linear regression profiles. All the proposed control charts are single-chart (single-statistic) control charts, two use a Max operator and two use an SS (squared sum) operator to create the final statistic. Moreover, two of the charts monitor the regression parameters, and the other two monitor the residuals. After developing the VP control charts, we developed a computer algorithm with which the charts' time-to-signal and run-length-based performances can be measured. Then, we perform extensive numerical analysis and simulation studies to evaluate the charts’ performance and the result shows significant improvements by using  the VP schemes. Finally, we use real data from the national quality register for stroke care in Sweden, Riksstroke, to illustrate how the proposed control charts can be implemented in practice.

We provide an overview and perspective on the Phase I collection and analysis of data for use in process improvement and control charting. In Phase I, the focus is on understanding the process variability, assessing the stability of the process, investigating process-improvement ideas, selecting an appropriate in-control model, and providing estimates of the in-control model parameters. In our article, we review and synthesize many of the important developments that pertain to the analysis of process data in Phase I. We give our view of the major issues and developments in Phase I analysis. We identify the current best practices and some opportunities for future research in this area.

Process monitoring plays a vital role in ensuring quality stability, and, operational efficiency across fields such as manufacturing, finance, biomedical science, and environmental monitoring. Among statistical tools, control charts are widely adopted for detecting variability and abnormal patterns. Since the introduction of the basic X-bar control chart by Shewhart in the 1920s, various improved methods have emerged to address the challenge of identifying small and latent process shifts, including CUSUM, MA, EWMA, and Exp-EWMA control charts. This study introduces a novel control chart—the Moving Average–Exponentiated Exponentially Weighted Moving Average (MA-Exp-EWMA) control chart—combining the smoothing effect of MA and the adaptive weighting of Exp-EWMA. Its goal is to improve the detection of small shifts and gradual changes. Performance is evaluated using average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL). Monte Carlo simulations under different distributions (normal, exponential, gamma, and Student’s t) and parameter settings assess the control chart’s sensitivity under various shift scenarios. Comparisons with existing control charts and an application to real data demonstrate the practical effectiveness of the proposed method in detecting small shifts.

A nonparametric control chart is a type of control chart that does not rely on assumptions regarding the underlying distribution of the data. This characteristic provides greater flexibility and robustness, particularly when handling non-normal data, skewed distributions, or datasets containing outliers. The primary objective of this study is to propose a nonparametric TEWMA–MA control chart based on the sign statistic, designed to operate under both symmetric and asymmetric distributions for effective process monitoring. This chart aims to enhance the ability to quickly detect shifts in the production process. The run-length characteristics obtained through Monte Carlo simulation (MC) were employed as performance measures. In addition, overall efficiency was assessed using AEQL, RMI, and PCI. The proposed control chart was compared against MA, TEWMA, MA–TEWMA, TEWMA–MA, and MA–TEWMA sign charts. The findings indicate that the proposed chart is effective for process control and demonstrates superior detection capability compared to competing charts, particularly in identifying small to moderate shifts. Furthermore, to validate its practical utility, the proposed control chart was applied to real-world data.

The purpose of this paper is to provide an overview and our perspective of recent research and applications of statistical process monitoring. The focus is on work done over the past decade or so. We review briefly a number of important areas, including health-related monitoring, spatiotemporal surveillance, profile monitoring, use of autocorrelated data, the effect of estimation error, and high-dimensional monitoring, among others. We briefly discuss the choice of performance metrics. We provide references and offer some directions for further research.

The Max-Mixed EWMA Exponentially Weighted Moving Average (MM EWMA) control chart is a statistical process control technique used for joint monitoring of the mean and variance of a process. This control chart is designed to detect small and moderate shifts in the mean and variance of a process by comparing the maximum of two statistics, one based on the mean and the other on the variance. In this paper, we propose a new MM EWMA control chart. The proposed chart is compared with existing control charts using simulation studies, and the results show that the chart performs better in detecting small and moderate shifts in both the mean and variance. The proposed chart can be helpful in quality control applications, where joint monitoring of mean and variance is necessary to ensure a product’s or process’s quality. The real-life application of the proposed control chart on yogurt packing in a cup data set shows the outperformance of the MM EWMA control chart. Both simulations & real-life application results demonstrate the better performance of the proposed chart in detecting smaller shifts during the production process.

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (ARL1). Tables of ARL1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of ARL1 detecting small and moderate shifts in the process nonconforming rate in-control (p0) compared with MDSRS and DS-np.

In this paper, we investigate the effect of the measurement error on the performance of the cumulative sum (CUSUM) control charts monitoring the coefficient of variation. The measurement errors are supposed to follow a linear covariate error model. The obtained results show that the precision error ratio and the accuracy error have negative impact on the chart performance. Moreover, in order to overcome the difficulty in predetermining a specific value for the process shift size, we suggest to optimize the parameters of the charts according to the random shift size in a given interval. The robustness of the proposed method is studied. An example is given to illustrate the use of the CUSUM charts on a real quality control problem from sintering process.