Adaptive EWMA Research Articles

Adaptive EWMA and CUSUM charts with dynamic probability control limits

The utilization of dynamic probability control limits (DPCLs) can prove advantageous in the development of control charts, particularly in scenarios where sample sizes, areas of opportunity, or any other covariate values exhibit temporal fluctuations. In this study, we design the DPCLs-based two adaptive EWMA (AE) and adaptive CUSUM (AC) charts for monitoring the mean of a normally distributed process. We use Monte Carlo simulations to estimate the conditional false alarm rates, zero-state and steady-state (SS) average run-length profiles of the adaptive charts. It is found that the proposed AE and AC charts outperform the existing AE chart in terms of relative mean index. An example is given to demonstrate the implementation of the proposed charts.

Adaptive sample size strategies for process dispersion using EWMA control chart

AbstractMonitoring the stability of measured dispersion in a process quality parameter is one of the critical steps in statistical process control (SPC) and is a paramount activity carried out by specialists. For this purpose, the current research presents a promising and computationally effective tool where the exponentially weighted moving average (EWMA) statistic utilizes the quadratic sigmoid function by incorporating sample size leading to the Quadratic Sigmoid Exponential weighted Moving Average (QSEWMA) control chart. The adaptive sample size is a strategy that increases or decreases the sample size according to the conditions of the process and accordingly, increases the sensitivity and response of the control chart. The proposed strategy improves the detection of process dispersion changes, making it a more efficient and effective way of quality assurance. Our proposed control chart is superior to the EWMA‐S2 chart, HHW‐EWMA chart CUSUM‐S2chart, and parametric free adaptive EWMA (AEWMA) charts for dispersion through extensive Monte Carlo simulations. The proposed QSEWMA chart has better detection sensitivity and fewer false alarms, and is, in general, more effective comparatively. At last, a real data application test is done to measure the practicability and highest accuracy of the above chart.

A new adaptive EWMA chart for two‐parameter exponential distribution based on type‐II censored data

AbstractIn this article, we propose a new adaptive exponentially weighted moving average (AEWMA) chart for monitoring the joint shifts in the location and scale parameters of the two‐parameter exponential distribution, namely the AEWMA‐II chart. A key feature of the proposed chart is its straightforward post‐signal diagnostics. The Monte Carlo simulation method is used to compute the steady‐state run‐length profiles of the proposed chart. The run‐length properties include the average run‐length and standard deviation of the run‐length. Through a comprehensive run‐length comparison, it is found that the AEWMA‐II chart performs better than the existing AEWMA chart. Moreover, with post‐signal diagnostics, the proposed chart also surpasses the existing chart. Finally, a real dataset is applied to illustrate the excellent performance and practical application of the proposed chart.

A weighted dual cumulative sum chart for monitoring the process mean

AbstractThe cumulative sum (CUSUM) charts are well‐structured and widely used for detecting small‐to‐moderate changes in the process parameters. However, their performance can be limited when the shift size is unknown or varies over time. Various methods have been developed to address this issue, including dual CUSUM (DCUSUM), adaptive CUSUM, adaptive EWMA, and weighted CUSUM charts, all of which offer better sensitivity compared to traditional CUSUM charts. In this study, we propose a new weighted DCUSUM chart designed to effectively detect the mean shifts in a normally distributed process. Monte Carlo simulations are used to estimate the zero‐state and steady‐state average run‐length (ARL) profiles of the control charts. The ARL performances of the control charts are evaluated in terms of expected relative ARL (ERARL) and expected weighted run‐length (EWRL). Our results show that the proposed chart may outperform existing counterparts in terms of the ARL, ERARL, and EWRL measures, indicating superior performance in detecting a range of the mean shift sizes. Finally, we apply the existing and proposed charts to a real dataset, showcasing their practical utility in process monitoring.

Carbon emission warning method for machine tool manufacturing process based on dynamic adaptive EWMA control chart.

Machine tools constitute the backbone of the industrial sector, representing the largest global inventory of equipment. The carbon emissions resulting from the production of each machine tool merit attention. Effective management of carbon emissions in the machine tool manufacturing process is crucial. This paper introduces a novel method for early carbon emission warnings in the machine tool manufacturing process, utilizing an adaptive dynamic exponentially weighted moving average (EWMA) approach. This method addresses the challenges in identifying and monitoring abnormal carbon emissions, emerging from uncertainties and dynamic correlations. Utilizing dynamic sampling techniques and adaptive principles, this method constructs an adaptive dynamic EWMA control chart. The EWMA control chart incorporates a multi-objective optimization design model, concentrating on carbon emissions in the machine tool manufacturing process, and incorporates statistical, economic, and environmental objectives. To mitigate slow convergence rates and enhance optimization accuracy in complex control chart multi-objective optimization algorithms, this study proposes an enhanced Harris hawks optimization (HHO) algorithm as the solving algorithm. Finally, the application of this method is demonstrated through the monitoring of carbon emissions in the manufacturing process of a five-axis machine tool (EOC), as a case study. The results validate the method's rapid responsiveness to abnormal carbon emissions, providing alerts. This further confirms the efficacy and feasibility of the proposed approach. Ultimately, this approach offers a viable strategy for fostering environmentally conscious and high-quality growth in the machine tool industry.

An adaptive multivariate functional EWMA control chart

In many modern industrial scenarios, measurements of the quality characteristics of interest are often required to be represented as functional data or profiles. This motivates the growing interest in extending traditional univariate statistical process monitoring (SPM) schemes to the functional data setting. This article proposes a new SPM scheme, which is referred to as adaptive multivariate functional EWMA (AMFEWMA), to extend the well-known exponentially weighted moving average (EWMA) control chart from the univariate scalar to the multivariate functional setting. The proposed method distinguishes itself by adaptively selecting the weighting parameter in the calculation of the EWMA statistic to enhance the sensitivity of the AMFEWMA control chart across a spectrum of potential out-of-control scenarios. Such adaptability is essential in industrial processes, where multivariate functional quality characteristics are also subject to varying degrees of change. The favorable performance of the AMFEWMA control chart over existing methods is assessed via an extensive Monte Carlo simulation. Its practical applicability is demonstrated through a case study in monitoring the quality of a resistance spot welding (RSW) process in the automotive industry through online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and are recognized as highly representative of the RSW process quality. The proposed method is implemented in the R package funcharts, available online on CRAN.

Designing an efficient adaptive EWMA model for normal process with engineering applications

Stability in process parameters is required to ensure the quality of the finished item. Control charts, as one of the critical parts of statistical process monitoring (SPM), have seen widespread use across many disciplines for detecting and responding to shifts in process parameters. The adaptive EWMA (AEWMA) control chartis a well-known scheme that detects both small and large process shifts by integrating the features of the Shewhart and classical EWMA charts. In this study, we propose an enhanced AEWMA chart, termed the EAEWMA chart, that efficiently monitors small and large process mean shifts simultaneously. The proposed EAEWMA chart enhances the existing AEWMA chart using the shift estimator, based on the hybrid EWMA (HEWMA) statistic. The Monte Carlo simulation approach is employed as the computational method to obtain the numerical findings for the various performance metrics. The EAEWMA chart is compared with various existing charts, including AEWMA, HEWMA, EWMA, ACSUM, and IACCUSUM, in zero- and steady-state scenarios. Conclusively, two practical applications of the EAEWMA chart are presented, demonstrating its value for practitioners and engineers and illustrating its efficacy in real-world scenarios.

Adaptive EWMA control chart by using support vector regression

AbstractTraditional control charts depend on the process parameters that are used to monitor the shifts in the process. The adaptive control charts are used to adapt a process parameter during the online monitoring. This research introduces a support vector regression (SVR) based adaptive exponentially weighted moving average control chat to enhance the monitoring of the mean in industrial processes. The study systematically investigates the comparative efficiency of linear, radial basis function (RBF), and polynomial functions within the SVR framework. The proposed SVR‐based AEWMA control chart leverages the strengths of the RBF kernel, providing a robust mechanism for detecting shifts in the process mean by adapting the smoothing constant according to the size of the shift. To validate the efficacy of the proposed methodology, a practical application is presented by using real‐life data. The application showcases the adaptability and reliability of the SVR‐based adaptive EWMA control chart in effectively monitoring location shifts.

A nonparametric adaptive EWMA control chart for monitoring multivariate time-between-events-and-amplitude data

Multivariate time-between-events-and-amplitude (TBEA) data, which includes the time interval between two consecutive occurrences of the event as well as their amplitudes, is a common data type in manufacturing and service operations. Designing control charts to monitor TBEA data is of great significance to improve product quality. However, most TBEA control charts are typically constructed under the assumption that the data distribution is known. The monitoring performance of these parametric TBEA control charts may become less reliable when the assumed data distribution is unknown. To address this issue, we propose a nonparametric adaptive TBEA (NATBEA) control chart based on the antirank method and adaptive strategy. Firstly, a nonparametric monitoring statistic is constructed by using the antirank method. With using the adaptive strategy, a nonparametric adaptive EWMA control chart is designed to monitor TBEA data, and the monitoring performance of various shifts is improved. Then, we compare the monitoring performance of the NATBEA control chart and other eight control charts, and the numerical simulation results show that the NATBEA control chart has superior monitoring performance for various mean shifts with different data distributions. Finally, an example of a company’s production failure demonstrates that the developed NATBEA control chart outperforms various conventional control charts by providing rapid alarms when the process is out of control.

New adaptive EWMA CV control chart with application to the sintering process

This research presents a new adaptive exponentially weighted moving average control chart, known as the coefficient of variation (CV) EWMA statistic to study the relative process variability. The production process CV monitoring is a long-term process observation with an unstable mean. Therefore, a new modified adaptive exponentially weighted moving average (AAEWMA) CV monitoring chart using a novel function hereafter referred to as the "AAEWMA CV" monitoring control chart. the novelty of the suggested AAEWMA CV chart statistic is to identify the infrequent process CV changes. A continuous function is suggested to be used to adapt the plotting statistic smoothing constant value as per the process estimated shift size that arises in the CV parametric values. The Monte Carlo simulation method is used to compute the run-length values, which are used to analyze efficiency. The existing AEWMA CV chart is less effective than the proposed AAEWMA CV chart. An industrial data example is used to examine the strength of the proposed AAEWMA CV chart and to clarify the implementation specifics which is provided in the example section. The results strongly recommend the implementation of the proposed AAEWMA CV control chart.

Parameter free AEWMA control chart for dispersion in semiconductor manufacturing

The study presents a new parameter free adaptive exponentially weighted moving average (AEWMA) control chart tailored for monitoring process dispersion, utilizing an adaptive approach for determining the smoothing constant. This chart is crafted to adeptly detect shifts within anticipated ranges in process dispersion by dynamically computing the smoothing constant. To assess its effectiveness, the chart’s performance is measured through concise run-length profiles generated from Monte Carlo simulations. A notable aspect is the incorporation of an unbiased estimator in computing the smoothing constant through the suggested function, thereby improving the chart’s capability to identify different levels of increasing and decreasing shifts in process dispersion. The comparison with an established adaptive EWMA-S2 dispersion chart highlights the considerable efficiency of the proposed chart in addressing diverse magnitudes of process dispersion shifts. Additionally, the study includes an application to a real-life dataset, showcasing the practicality and user-friendly nature of the proposed chart in real-world situations.

Optimal design of adaptive EWMA monitoring schemes for the coefficient of variation and performance evaluation with measurement errors

The coefficient of variation (CV) usually describes the relative dispersion in production or service processes and has been widely applied in various fields. Monitoring the CV has received great attention in statistical process monitoring. This paper develops two one-sided adaptive EWMA (AEWMA) CV schemes to enhance the existing CV schemes’ monitoring efficiency. This scheme can effectively defect various shift sizes by dynamically adjusting the smoothing parameter of the EWMA based on the residuals. The optimization models of the AEWMA CV are designed based on the Markov chain method from two different perspectives, (i) a pair of changes; (ii) a range of changes. The numerical and graphical comparisons confirm the superiority of the proposed schemes. Moreover, in the data collection process, measurement errors from devices and human operations may arise. To assess the impact of such measurement errors on the monitoring performance, a linear covariate error model is adopted. For illustration and validation, the proposed schemes are implemented to a real industrial example from the sintering process.

Dynamic probability control limits for the adaptive multivariate EWMA chart

AbstractEffective monitoring of the control charts requires the establishment of appropriate control limits. Various methods have been proposed to determine the fixed control limits (FCLs) based on a specified in‐control average run‐length value, such as Markov chains, integral equations, and Monte Carlo simulations.With the FCLs, the conditional false alarm rate (CFAR) of a control chart varies over time in an unexpected and undesirable way, where the CFAR refers to the probability of a false alarm at a particular time given no previous false alarm. To address this issue, dynamic probability control limits (DPCLs) can be employed to keep the CFAR constant over time. In this study, we determine the DPCLs using fixed and time‐varying sample sizes for the adaptive multivariate EWMA chart when the underlying process is assumed to follow a multivariate normal distribution. The DPCLs are designed to automatically adjust to changes in the probability distribution of the sample size, while maintaining a consistent CFAR. This results in a closely matched run‐length performance for an in‐control process compared to that of the geometric distribution.

An adaptive EWMA chart for Poisson process

ABSTRACT This paper introduces an adaptive EWMA (AEWMA) chart designed for monitoring Poisson processes. This chart offers a streamlined implementation process, eliminating the need for additional parameters. Notably, it demonstrates the ability to effectively detect a range of the mean shift sizes. Using Monte Carlo simulations, this study provides estimates for various performance metrics, including the zero-state and steady-state average run-length (ARL), expected weighted run-length, and expected relative ARL profiles for existing and proposed charts. The results indicate that the AEWMA chart surpasses the performances of existing EWMA, CUSUM, and two other AEWMA charts in detecting multiple shifts in the process mean. Additionally, an illustrative example is presented to showcase the practical implementation of the considered charts.

Process dispersion monitoring: Innovative AEWMA control chart in semiconductor manufacturing

This study introduces a novel adaptive exponentially weighted moving average (AEWMA) control chart for monitoring process dispersion, employing adaptation to determine the smoothing constant. It is designed to effectively track shifts within expected ranges in process dispersion by computing the smoothing constant through a suggested adaptive approach. To determine its efficacy, the chart’s performance is evaluated by using smaller run-length profiles derived from Monte Carlo simulations. A key feature is the utilization of an unbiased estimator to calculate the smoothing constant via the proposed function, enhancing the chart’s ability to detect various magnitudes of decreasing and increasing process dispersion shifts. A comparison with an existing adaptive EWMA dispersion chart underscores the significant efficiency of the proposed chart across various types of process dispersion shift magnitudes. Moreover, the study encompasses a real-life dataset application, demonstrating the practical implementation and ease of use in real-world scenarios.

A nonparametric adaptive EWMA control chart for monitoring mixed continuous and categorical data using self-starting strategy

In the context of big data-driven smart manufacturing, data is often characterized by high dimensionality, numerous variables, and complex associations. As a result, mixed continuous and categorical data are increasingly common. In the case of data that consist of a combination of continuous and categorical variables with unknown distributions, the application of traditional parametric control charts for monitoring purposes becomes challenging. Therefore, a novel nonparametric adaptive exponentially weighted moving average (EWMA) control chart using a self-starting strategy is proposed in this paper. First, the process of converting continuous data into categorical data is conducted using the data categorization method. The log-linear modeling is subsequently employed to investigate the relationships between various variables. Next, a nonparametric adaptive EWMA statistic is constructed to monitor mixed continuous and categorical data, and the self-starting strategy is employed to gradually expand the size of the in-control (IC) dataset and to update the parameters in real time. Then, a numerical simulation is conducted to compare the IC and out-of-control (OC) performance of the proposed chart with other control charts. According to the simulation result, it can be concluded that the proposed chart offers a more effective means of detecting shifts in the production process. Finally, a concrete illustration of an authentic dataset regarding red wine quality is provided to further clarify the effectiveness of the proposed control chart in monitoring mixed continuous and categorical data.

Detection of Forest Disturbances with Different Intensities Using Landsat Time Series Based on Adaptive Exponentially Weighted Moving Average Charts

Forest disturbance detection is important for revealing ecological changes. Long-time series remote sensing analysis methods have emerged as the primary approach for detecting large-scale forest disturbances. Many of the existing change detection algorithms focus primarily on identifying high-intensity forest disturbances, such as harvesting and fires, with only a limited capacity to detect both high-intensity and low-intensity forest disturbances. This study proposes an online continuous change detection algorithm for the detection of multi-intensity forest disturbances such as forest harvest, fire, selective harvest, and insects. To initiate the proposed algorithm, the time series of the Normalized Difference Vegetation Index (NDVI) is fitted into a harmonic regression model, which is then followed by the computation of residuals. Next, the residual time series is entered into the adaptive exponentially weighted moving average (AEWMA) chart. This chart adaptively adjusts the smoothing coefficients to identify both high-intensity and low-intensity disturbances. When the chart value consistently deviates from the control limit, the forest pixel is classified as disturbed. With an overall spatial accuracy of 85.2%, including 86.1% producer’s accuracy and 84% user’s accuracy, along with a temporal accuracy of 96.7%, the algorithm enables precise and timely detection of forest disturbances with multiple intensities. This method provides a robust solution for detecting multi-intensity disturbances in forested regions.

Monitoring of semiconductor manufacturing process on Bayesian AEWMA control chart under paired ranked set sampling schemes

Quality control often employs memory-type control charts, including the exponentially weighted moving average (EWMA) and Shewhart control charts, to identify shifts in the location parameter of a process. This article pioneers a new Bayesian Adaptive EWMA (AEWMA) control chart, built on diverse loss functions (LFs) such as the square error loss function (SELF) and the Linex loss function (LLF). The proposed chart aims to enhance the process of identifying small to moderate as well as significant shifts in the mean, signifying a notable advancement in the field of quality control. These are implemented utilizing an informative prior for both posterior and posterior predictive distributions, employing various paired ranked set sampling (PRSS) schemes. The effectiveness of the suggested chart is appraised using average run length (ARL) and the standard deviation of run length (SDRL). Monte Carlo simulations are employed to contrast the recommended approach against other control charts. The outcomes demonstrate the dignitary performance of the recommended chart in identifying out-of-control signals, especially applying PRSS designs, in comparison to simple random sampling (SRS). Finally, a practical application was conducted in the semiconductor manufacturing context to appraise the efficacy of the offered chart using various paired ranked set sampling strategies. The results reveal that the suggested control chart performed well in capturing the out-of-control signals far better than the already in use control charts. Overall, this study interposes a new technique with diverse LFs and PRSS designs, improving the precision and effectiveness in detecting process mean shifts, thereby contributing to advancements in quality control and process monitoring.

Monitoring the process mean under the Bayesian approach with application to hard bake process

This study introduces the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart within the framework of measurement error, examining two separate loss functions: the squared error loss function and the linex loss function. We conduct an analysis of the posterior and posterior predictive distributions utilizing a conjugate prior. In the presence of measurement error (ME), we employ a linear covariate model to assess the control chart's effectiveness. Additionally, we explore the impacts of measurement error by investigating multiple measurements and a method involving linearly increasing variance. We conduct a Monte Carlo simulation study to assess the control chart's performance under ME, examining its run length profile. Subsequently, we offer a specific numerical instance related to the hard-bake process in semiconductor manufacturing, serving to verify the functionality and practical application of the suggested Bayesian AEWMA control chart when confronted with ME.

Adaptive EWMA control chart for monitoring two-parameter exponential distribution with type-II right censored data

Two-parameter exponential distributions have a widespread application in insurance, medical and industrial production. However, incomplete samples are often obtained due to experimental conditions. In this paper, a new adaptive exponentially weighted moving average control chart, called AEWMA-LR control chart, is proposed for monitoring the quality characteristics of two-parameter exponential distributions based on type-II censored data. The proposed monitoring scheme aims to achieve an adaptive effect by combining exponentially weighted moving averages and adjusting the weight factors according to the relative magnitude of the estimated location and scale parameter shifts. We explored the effects of smooth parameters, sample size, and censored parameters on the performance of AEWMA-LR control charts through a Monte Carlo simulation study. Then, a comparative analysis was conducted with existing EWMA-LR and EWMA-Max-MLE control charts based on the two-parameter exponential model. The simulation results of zero-state average run length (ARL) and conditional expected delay (CED) show that the proposed monitoring scheme outperforms the existing control charts. Finally, to demonstrate the usefulness of the AEWMA-LR control chart in real-world applications, we give three instances of two-parameter exponential distributions based on type-II right censored data.