Impact of measurement error on maximum hybrid exponentially weighted moving average control chart

Hybrid control charts have become part of statistical process control (SPC) but still, need more emphasis. Researchers are developing charts for joint monitoring of process mean and variance shifts just like Max‐EWMA and their hybrid version using auxiliary information but are ignoring the effect of measurement error on the efficiency of charts. We propose maximum hybrid exponentially weighted moving average with measurement error using auxiliary information and name it Max‐HEWMAMEAI control chart. The efficiency of this chart is proved through calculations of average run lengths () and standard deviations of run lengths (SDRLs) using the Monte Carlo simulations method whereas, and are shown in tabular form. The effect of measurement error on the efficiency of the chart has been analyzed and the impact of multiple measurements to reduce the error effect has been studied using the covariate model. Real‐life application is also part of this article to support the simulation results.

ABSTRACTControl charts have been popularly used as a user-friendly yet technically sophisticated tool to monitor whether a process is in statistical control or not. These charts are basically constructed under the normality assumption. But in many practical situations in real life this normality assumption may be violated. One such non-normal situation is to monitor the process variability from a skewed parent distribution where we propose the use of a Maxwell control chart. We introduce a pivotal quantity for the scale parameter of the Maxwell distribution which follows a gamma distribution. Probability limits and L-sigma limits are studied along with performance measure based on average run length and power curve. To avoid the complexity of future calculations for practitioners, factors for constructing control chart for monitoring the Maxwell parameter are given for different sample sizes and for different false alarm rate. We also provide simulated data to illustrate the Maxwell control chart. Finally, a real life example has been given to show the importance of such a control chart.

Monitoring peak flow using control charts: Comments from experience

In real life, the distribution of the errors during any life testing of products or process does not meet the assumption of normality. Statistical process control (SPC) is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help to monitor process behavior, discover problems in internal systems, and find solutions for production issues. To identify and remove the variation in different reliability processes and to monitor the reliability of machines where the number of errors follows skewed distributions, we develop control charts to keep the process in control. For such situations, we have modified the existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA), hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA) control charts. The current study introduced classical estimator based modified control charts for phase-II monitoring by assuming that the errors occur during the process follow skewed distribution called Beta Lehmann 2 Power function distribution (BL2PFD). The proposal for these control charts is based on the percentile estimator. We have compared all these control charts using Monte Carlo simulation studies and real-life applications to compare the proposed control charts. This study shows that an EEWMA control chart based on PE performs better than Shewhart, EWMA and HEWMA control charts, when the underlying distribution of the errors in process monitoring follows BL2PFD. These findings can be useful for researchers and practitioners in dealing with production errors and optimizing the output.

Control charts are an important tool for statistical process control (SPC). SPC has the characteristics of fluctuation and asymmetry in the symmetrical coordinate system. It is a graph with control limits used to analyze and judge whether the process is in a stable state. Its fast and accurate identification is of great significance to the actual production. The existing control chart pattern recognition (CCPR) method can only recognize a control chart with fixed window size, but cannot adjust with different window sizes according to the actual production needs. In order to solve these problems and improve the quality management effect in the manufacturing process, a new CCPR method is proposed based on convolutional neural network (CNN) and information fusion. After undergoing feature learning, CNN is used to extract the best feature set from the control chart, while at the same time, expert features (including one shape features and four statistical features) are fused to complete the CCPR. In this paper, the control charts of 10 different window sizes are generated by the Monte Carlo simulation method, and various data patterns are drawn into images, then the CCPR model is set up. Finally, simulation experiments and a real example are addressed to validate its feasibility and effectiveness. The results of simulation experiments demonstrate that the recognition method based on CNN can be used for pattern recognition for different window size control charts, and its recognition accuracy is higher than the traditional ones. In addition, the recognition method based on information fusion performs much better. The result of a real example shows that the method has potential application in solving the pattern recognition problem of control charts with different window sizes.

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart‐type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts are intended to spot small and moderate disturbances. In this article, we proposed a mixed EWMA–CUSUM control chart for detecting a shift in the process mean and evaluated its average run lengths. Comparisons of the proposed control chart were made with some representative control charts including the classical CUSUM, classical EWMA, fast initial response CUSUM, fast initial response EWMA, adaptive CUSUM with EWMA‐based shift estimator, weighted CUSUM and runs rules–based CUSUM and EWMA. The comparisons revealed that mixing the two charts makes the proposed scheme even more sensitive to the small shifts in the process mean than the other schemes designed for detecting small shifts. Copyright © 2012 John Wiley & Sons, Ltd.

Controlling over-adjusted process means and variances using VSI cause selecting control charts

The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included.

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

The present study advocates the application of statistical process control (SPC) as a performance monitoring tool for a PACS. The objective of statistical process control (SPC) differs significantly from the traditional QC/QA process. In the traditional process, the QC/QA tests are used to generate a datum point and this datum point is compared to a standard. If the point is out of specification, then action is taken on the product and action may be taken on the process. To move from the traditional QC/QA process to SPC, a process control plan should be developed, implemented, and followed. Implementing SPC in the PACS environment need not be a complex process. However, if the maximum effect is to be achieved and sustained, PACSSPC must be implemented in a systematic manner with the active involvement of all employees from line associates to executive management. SPC involves the use of mathematics, graphics, and statistical techniques, such as control charts, to analyze the PACS process and its output, so as to take appropriate actions to achieve and maintain a state of statistical control. While SPC is extensively used in the healthcare industry, especially in patient monitoring, it is rarely applied in the PACS environment. One may refer to a recent SPC application that Mercy Hospital (Alegent Health System) initiated after it implemented a PACS in November 2003 (Stockman & Krishnan, 2006). The anticipated benefits characteristic to PACS through the use of SPC include: • Reduced image retake and diagnostic expenditure associated with better process control. • Reduced operating costs by optimizing the maintenance and replacement of PACS equipment components. • Increased productivity by identification and elimination of variation and outof- control conditions in the imaging and retrieval processes. • Enhanced level of quality by controlled applications. SPC involves using statistical techniques to measure and analyze the variation in processes. Most often used for manufacturing processes, the intent of SPC is to monitor product quality and maintain processes to fixed targets. Hence besides the HSSH techniques, the proposed TQM approach would include the use of SPC. Although SPC will not improve the reliability of a poorly designed PACS, it can be used to maintain the consistency of how the individual process is provided and, therefore, of the entire PACS process. A primary tool used for SPC is the control chart, a graphical representation of certain descriptive statistics for specific quantitative measurements of the PACS process. These descriptive statistics are displayed in the control chart in comparison to their “in-control” sampling distributions. The comparison detects any unusual variation in the PACS delivery process, which could indicate a problem with the process. Several different descriptive statistics can be used in control charts and there are several different types of control charts that can test for different causes, such as how quickly major vs. minor shifts in process means are detected. These control charts are also used with service level measurements to analyze process capability and for continuous process improvement efforts.

Statistical process control (SPC) charts are important tools for detecting process shifts. The control chart is an important statistical technique that is used to monitor the quality of a process. Shewhart control charts help to detect larger shifts in the process parameters, but Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts are expected for smaller and moderate changes. The CUSUM control chart is normally used in industry for the result of small and moderate shifts in process spot and disparity. It can be shown that if there are sharp, irregular changes to a process, these types of charts are highly effective. On the other hand, if one involved in a small, persistent shift in a process, other types of control charts may be chosen, for instance the CUSUM control chart, originally developed by Page (1954). In this article, we used CUSUM control chart for monitoring the moisture level of the paper sheet.

Statistical process control (SPC) techniques are applied to monitor a process. The control chart is a valuable tool in SPC. the shewhart control chart was the first chart proposed in the literature of SPC and it is still used in process monitoring in today's manufacturing and service industries. both the exponentially weighted moving average (EWMA) and synthetic charts outperform the shewhart control chart for detecting shifts in the process mean. Since both the EWMA and synthetic charts provide better process mean shifts detection performance, a study on which chart to use in process monitoring under different situations is the aim of this work. this paper compares the average run length (ARL) and standard deviation of the run length (SDRL) profiles of the EWMA and synthetic charts. comparisons are made based on the normality assumption. The mathematica programs are used to compute the ARLs and SDRLs of the EWMA and synthetic charts. the ARL results indicate that the EWMA chart is superior to the synthetic chart for detecting small mean shifts, but the latter prevails for detecting moderate and large shifts. however, in terms of the SDRL, the EWMA chart surpasses the synthetic chart for small and moderate shifts. Index Terms—Average run length (ARL), exponentially weighted moving average (EWMA) chart, synthetic chart, standard deviation of the run length (SDRL).

An adaptive cumulative sum (ACUSUM) control chart is an advance form of the classical CUSUM control chart to identify different sizes of shift in the process parameters (location and/or dispersion). In the continuation of the ACUSUM control chart, this study also proposed ACUSUM control charts to enhance the performance of the process dispersion for a broad range of shift. The proposed ACUSUM control charts methodologies are based on the dispersion CUSUM statistic, score (Huber and Bi‐square) functions, generalized likelihood ratio test, and nonlinear optimization technique. The use of dispersion CUSUM statistic helps to distinguish a specific shift as the classical CUSUM statistic does, the score functions, the nonlinear optimization technique and generalized likelihood ratio test enhance the ability of the proposed ACUSUM control charts to distinguish a shift of different size. For the assessment of control charts, run length (RL) measure is used, and it is generated by developing an algorithm in MATLAB through Monte Carlo simulation method. Further, average of RL is utilized to carry out comparative analysis of control charts for a single shift, while for a certain range of shift (comprehensive analysis), extra quadratic loss (EQL), relative average run length (ARL), and performance comparison index (PCI) measures are used. Findings based on numerical results and visual presentations reveal the superiority of the proposed control charts against some existing control charts. Moreover, for real‐world point of assessment, the proposed control chart is implemented with numerical data to show the worth over other control charts.

In statistical process control, measurement error plays an important role which is usually ignored. Measurement error can lead to incorrect conclusions about the performance of the process. In this paper, we examined the effect of measurement error on the shift detection ability of the mixed exponentially weighted moving average-cummulative sum (EWMA-CUSUM) control chart. We investigate the performance of mixed EWMA-CUSUM chart in case of mean shift by using (i) covariate method (ii) multiple measurement method (iii) linearly increasing variance method. The performance measuring tools such as average run length (ARL) and standard deviation of run length (SDRL) are estimated by using the Monte-Carlo simulation method. It is concluded that the performance of the mixed EWMA-CUSUM control chart is adversely effected by considering the measurement error. It is revealed from the comparative study that the mixed EWMA-CUSUM control chart is performing better than EWMA and CUSUM control charts in the presence of measurement error. An illustrative example is presented to demonstrate the performance of control charts in case of measurement error.

Statistical Process Control (SPC) improves product quality by monitoring process performance, with control charts being the primary tool to detect and manage variability. The effectiveness of a control chart can be enhanced by incorporating additional pertinent information regarding the study variable. This study revisits the DEWMA chart, which is designed to monitor variations in the process mean under the assumption that the underlying process follows a normal distribution. We propose a Regression-based DEWMA (MRDEWMA) control chart that utilizes an auxiliary variable through a regression estimation method to determine the process mean. The control limits for the proposed chart are established based on both time-varying and asymptotic conditions. The features of run length (RL), including Average Run Length (ARL), Standard Deviation of Run Length (SDRL), and Median Run Length (MRL), are evaluated using Monte Carlo simulations. A comparative analysis reveals that the proposed MRDEWMA chart outperforms the traditional DEWMA chart in detecting small to moderate shifts in the process mean. The efficacy of the proposed approach is demonstrated using both Monte Carlo simulated data and a real-life industrial case study.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-27540-6.