Exponentially Weighted Moving Average Control Research Articles

Risk adjusted EWMA control chart based on support vector machine with application to cardiac surgery data

In the current study, we demonstrate the use of a quality framework to review the process for improving the quality and safety of the patient in the health care department. The researchers paid attention to assessing the performance of the health care service, where the data is usually heterogeneous to patient’s health conditions. In our study, the support vector machine (SVM) regression model is used to handle the challenge of adjusting the risk factors attached to the patients. Further, the design of exponentially weighted moving average (EWMA) control charts is proposed based on the residuals obtained through SVM regression model. Analyzing real cardiac surgery patient data, we employed the SVM method to gauge patient condition. The resulting SVM-EWMA chart, fashioned via SVM modeling, revealed superior shift detection capabilities and demonstrated enhanced efficacy compared to the risk-adjusted EWMA control chart.

EWMA control charts based on robust estimators: A powerful tool for monitoring a process with a non-normal distribution

This paper presents a study on using memory-type control charts to detect small to moderate shifts in the process mean, particularly when the underlying distribution deviates from normal assumptions. To address this, robust estimators based on modified maximum likelihood estimation (MMLE) and Lloyd’s BLUE estimators using generalized least square estimation (GLSE) are proposed. The proposed estimators utilize auxiliary information to enhance sensitivity against abrupt changes in the mean. Additionally, they play a crucial role in refining the precision of the estimated mean, contributing to a more accurate and nuanced estimation of the true mean. The efficiency and robustness of these estimators are compared with conventional ones from the literature. The proposed robust estimators are integrated into the design of the exponentially weighted moving average (EWMA) control chart. Performance evaluation is based on average run lengths (ARLs), standard deviation, and percentiles of the run lengths. A real-life example illustrates the significance of the proposed estimators over conventional ones for non-normal distributions. The results demonstrate that the EWMA control chart with proposed estimators outperforms competitors in terms of ARLs, SDRLs, and percentiles. This study offers insights into using robust estimators to enhance memory-type control charts' performance for non-normal distributions.

Change-point design-based charting schemes for monitoring process variability

ABSTRACT Most of the recommended nonparametric control charts apply to monitor location parameter. In this paper, we propose a nonparametric exponentially weighted moving average (EWMA) control chart for monitoring scale parameter, which combines the Ansari–Bradley test and the framework of change point detection. As with most nonparametric control charts, a large number of historical observations are used to motivate the control chart, and we propose a nonparametric EWMA control chart that achieves the same purpose with a very small number of historical observations. Simulation results demonstrate that our control chart is effective and robust for monitoring scale parameter shifts. For illustration of our main results, an applied example demonstrates the practicality of this control chart for monitoring scale parameter.

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.

Statistical process control in pulsed drip irrigation systems

Pulse drip application is a management option to prevent clogging and improve water-use efficiency. The measurement of distribution uniformity is opportune for pulse irrigation projects to ensure efficiency since the shorter the pulse time, the more negative influence the transition periods have. The objective of the present work was to monitor the quality of a drip irrigation system with different emitter models and different pulse times. The experiment was conducted under laboratory bench conditions, and 25 tests were performed for each pulse application (2, 3, 6 and 12 minutes) and emitter model (non-compensated and auto-compensated). Uniformity was determined using Christiansen's uniformity coefficient (CUC) and distribution uniformity coefficient (DUC) and monitored by Shewhart control charts and exponentially weighted moving average (EWMA). The decrease in pulse time caused a decrease in flow rate and uniformity only in drip irrigation systems with non auto-compensated emitters. However, this decrease is subtle, to the point that uniformity presented an excellent performance for all pulses tested. The use of the Shewhart and EWMA control charts were effective in monitoring the uniformity of the pulsed drip irrigation system. The Shewhart control chart was more robust in identifying isolated non-compensated uniformities, while the EWMA control chart was more sensitive in identifying unstable propensity. In the treatments with the non-compensated emitter, the statistical process control was able to identify that shorter pulse times resulted in greater application instability. As for the auto-compensated emitters, the statistical process control highlighted the concern with application uniformity after maintenance interference.
 Keywords: anti-drain emitter, high-frequency irrigation, irrigation interval, statistical quality control.

Self-starting monitoring of the progressive type II censoring data based on goodness-of-fit test

ABSTRACT Censoring is a common occurrence in life testing and reliability analysis, primarily due to constraints such as time and cost. In this paper, we construct control charts using goodness-of-fit test statistics to monitor novel and effective progressive Type II censoring data. In practice, scenarios where the number of samples in Phase I is insufficient often arise, prompting the proposal of self-starting exponentially weighted moving average (EWMA) control charts based on goodness-of-fit test statistics to monitor such processes. Numerous Monte Carlo simulation experiments demonstrate the excellent performance of the control charts proposed in this paper under different settings. A breakdown time of an insulating fluid example is utilized to illustrate the proposed EWMA and self-starting EWMA control charts.

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.

Reassessment of performance evaluation of EWMA control chart for exponential process

AbstractMemory control charts or charts, such as cumulative sums and exponentially weighted moving average (EWMA), are widely used for tracking minor to moderate changes in process parameters. The literature presented an EWMA chart for monitoring exponential processes, assuming probability limits to determine both in‐ and out‐of‐control average run length (ARL). The use of probability limits for memory charts is an incorrect method. So, we are aiming to correct the EWMA chart by Aslam et al. and the proposed EWMA chart (represented by ) for the exponential process using the run‐length (RL) method based on the simulation method instead of the probability‐based method. The ARL, standard deviation of RL, and median of RL are used to evaluate the proposed chart's performance. For practical consideration of the proposed chart, a real‐world example of a urinary tract infection is also presented.

Early neurological deterioration detection with a transformer convolutional auto-encoder model

This paper proposes an improved transformer convolutional auto-encoder model combined with the exponentially weighted moving average (EWMA) control chart to detect early neurological deterioration (END) of ischemic stroke patients after endovascular therapy in advance. In the proposed method, the transformer convolutional auto-encoder is used to extract crucial features of multivariate clinical monitoring time series data and obtain the reconfiguration loss while EWMA control chart is utilized to monitor the derived reconfiguration loss and identify anomalies. To verify the feasibility and effectiveness of the proposed END detection approach, multivariate clinical monitoring time series data of ischemic stroke patients in the neurocritical care unit from Beijing Tiantan hospital are collected. Meanwhile, the proposed approach is benchmarked with seven state-of-the-art models. The computation results show that the proposed approach achieves the best performance with the lowest false alarm rate and the highest detection rate. Therefore, the proposed END detection model is practical to guide doctors in conducting clinical interventions in advance to prevent deterioration in patients with ischemic stroke.

Designing a Log-Logistic-Based EWMA Control Chart Using MOPSO and VIKOR Approaches for Monitoring Cardiac Surgery Performance

This study aims to develop a risk-adjusted Exponentially Weighted Moving Average (EWMA) control chart for computer-based performance monitoring in cardiac surgery. Patients have distinct risk factors that impact the surgical process before it even begins. As a result, risk adjustment is carried out utilizing the Accelerated Failure Time (AFT) model to consider these factors. Before using the risk-adjusted EWMA chart, the optimal parameter design should be established, considering the required statistical and economic factors. A model for Multi-Objective Decision Making (MODM) with multiple assignable causes has been proposed to accomplish this. The model is solved using a two-stage methodology based on the Multi-Objective Particle Swarm Optimization (MOPSO) method and the VIekriterijumsko KOmpromisno Rangiranje (VIKOR) method. An actual case study for cardiovascular patients has been undertaken to demonstrate the performance and effectiveness of the suggested model. The multi-objective and pure economic models have been thoroughly compared. The economic model with statistical constraints and the multi-objective model have also been compared again. The findings suggest that the multi-objective design of the risk-adjusted EWMA chart exhibits higher statistical performance in both cases against a small augment in cost.

Exact Average Run Length Evaluation on One-Sided and Two-Sided Extended EWMA Control Chart with Correlated Data

The Extended Exponentially Weighted Moving Average (Extended EWMA) control chart is one of the control charts that can rapidly detect a minor shift. Using the average run length (ARL), the control charts' effectiveness can be evaluated. This research aims to derive the explicit formulations for the ARL on one-sided and two-sided Extend EWMA control charts for the MA(1) model with exponential white noise, as they have not been previously presented. The analytical solution accuracy was determined and compared to the numerical integral equation (NIE) method. The results indicate that the ARL calculated using the explicit formula and the NIE method are nearly identical, demonstrating the validity of the explicit formula. In addition, this study is extended to compare the performance with the Exponentially Weighted Moving Average (EWMA) control chart. The results show that the Extended EWMA control chart has superior efficacy to the EWMA control chart. To demonstrate the efficacy of the proposed method, the analytical solution of ARL is finally applied to real-world data on Thailand's monthly fuel price.

ON EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART FOR TIME TRUNCATED LIFE TEST USING INVERSE WEIBULL DISTRIBUTION

Statistical control charts are widely used in industry for process and measurement control to monitor production processes in order to discover any problem or issues that may arise during the production process and to help in finding solutions for these issues. This research proposes the exponentially weighted moving average (EWMA) control chart, comparing it’s performance to NP and MA control chart for monitoring the number of nonconforming with the truncated lifetime of a product when the lifetimes of products follows inverse Weibull (IW) distribution. The number of failures during the life test is used as an indicator of the quality of the product. EWMA control chart was proposed for this specific situation, thus extending the applicability of control charts methodology to situations involving truncated life tests. The performance of these control charts was measured with the average run length (ARL). The simulation shows that the results obtained from the EWMA chart using IW distribution is more sensitive in detecting small shift and performs much better to monitoring shifts as when compared to other control charts considered in the study.

An Expected Average Run Length (EARL) Performance Comparison of the SSGR and EWMA Control Charts

The acceleration use of control charts in industrial processes has led to the effectiveness in their evaluation by quality practitioners. This is crucial, as it influences their decisions on the choice of which control charts to employ. This study aims to explore and compare the performance of the side sensitive group runs (SSGR) and exponentially weighted moving average (EWMA) control charts. In general, the average run length (ARL) characteristics were used to evaluate the performance of these control charts. The ARL, which considers the exact shift size in the process, is restricted in the case when the practitioner cannot identify the process shift size (unknown shift size). In this situation, the expected average run length (EARL) is an alternative performance criterion. Upon comparison of the findings obtained, the EWMA chart has superior performance when (δmin, δmax) = (0.1, 0.4). In contrast, the SSGR chart overtakes the EWMA chart when (δmin, δmax) = (0.5, 0.8) and (δmin, δmax) = (0.9, 1.2), except when the sample size n = 3 for (δmin, δmax) = (0.5, 0.8). For this particular combination, the EWMA chart performs slightly better than the SSGR chart. The outcome of this study is expected to contribute to practitioners in identifying suitable control charts in process monitoring and implementation.

Error detection through modified phase II process monitoring under different classical estimators

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.

Statistical Design for Monitoring Process Mean on Modified EWMA Control Chart based on Autocorrelated Data

This research endeavor is focused on establishing explicit formulas for the computation of the average run length (ARL) within the context of a moving average process characterized by exogenous variables, denoted as MAX(q,r), and subjected to exponential white noise. Additionally, we aim to conduct a comparative analysis of their performance against the exponentially weighted moving average (EWMA) and the modified exponentially weighted moving average (modified EWMA) methodologies. The evaluation of their performance will be based on metrics such as the absolute percentage relative error (APRE) and the relative mean index (RMI). Furthermore, we undertake a rigorous assessment of the accuracy of these explicit formulas in relation to ARL by considering CPU time, utilizing the numerical integral equation (NIE) method derived through the application of the Gauss-Legendre quadrature rule. This comparative evaluation is carried out for both control chart methodologies. To ascertain the efficacy of our explicit formulas approach, we apply it to two distinct datasets. The first dataset pertains to the closing price of natural gas, with the crude oil WTI price serving as the exogenous variable. The second dataset encompasses the closing stock price of KTB Public Company Limited, with daily foreign exchange rates for USD/JPY and EUR/USD as the exogenous variables. The results of applying the ARL based on the explicit formulas to these two datasets demonstrate that, under these conditions, the modified EWMA control chart outperforms the EWMA control chart.

Symmetry of gamma distribution data about the mean after processing with EWMA function

Statistical Process Control (SPC) plays a vital role in maintaining quality and reducing variability in manufacturing processes. Among SPC techniques, the Exponentially Weighted Moving Average (EWMA) stands out for its ability to detect small process shifts quickly, making it a valuable tool in ensuring product consistency and preventing quality issues. EWMA constructs control charts to monitor process mean shifts, tracks product/service quality by identifying variations, and monitors manufacturing process parameters for early detection of deviations and necessary adjustments. EWMA control chart has been proposed as an alternative to the Shewhart control chart. Sequential measurements are processed using the EWMA function before being placed on the control chart. One of the crucial concerns about the EWMA control chart is the asymmetry of the data around the mean. Although processing with the EWMA function reduces data skewness, the problem of asymmetric data may not be solved. The control chart is designed to leave in front of the upper control limit (UCL) α/2 of the data and behind the lower control limit (LCL) another α/2 of the data, and this does not occur in the case of symmetric data. α/2 represents the significance level for each tail in a two-tailed hypothesis test, indicating the probability of incorrectly rejecting the null hypothesis for each side of the distribution. Since many of the distributions in real life can be approximated by the Gamma distribution, the Gamma distribution was adopted in this study. The Monte Carlo simulation methodology was implemented to generate Gamma distributed data, process it with EWMA function and assess the skewness and kurtosis. The purpose of this paper is to evaluate the effect of EWMA parameters on the performance of the EWMA control chart. Moreover, it focuses on skewness and kurtosis reduction after data processing using the EWMA function. The findings help researchers and practitioners to select the best parameters. Further, the research investigates the effect of EWMA parameter on the shape of distribution.

Triple exponentially weighted moving average control chart with measurement error

Measurement error (M.E) can have a substantial impact on quality control applications, diminishing the sensitivity to detect changes in the mean or variance of quality characteristics. To monitor shifts in process mean and dispersion, Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts are commonly employed. In our research, we investigated the influence of M.E on the Triple Exponentially Weighted Moving Average (TEWMA) control chart. We assessed the performance of the control chart using Average Run Length (ARL) as the evaluation metric. To compute the ARL properties, we adopted the Monte-Carlo simulation method. A comparison section has been made to check the performance efficiency of the control chart with the existing EWMA control chart. The implementation of a control chart on a real data set is also presented.

Performance of Bayesian EWMA control chart with measurement error under ranked set sampling schemes with application in industrial engineering

The objective of this study is to investigate the behavior of the Bayesian exponentially weighted moving average (EWMA) control chart in the presence of measurement error (ME). It explores the impact of different ranked set sampling designs and loss functions on the performance of the control chart when ME is present. The analysis incorporates a covariate model, multiple measurement methods, and a conjugate prior to account for ME. The performance evaluation of the proposed Bayesian EWMA control chart with ME includes metrics such as average run length and standard deviation of run lengths. The findings, obtained through Monte Carlo simulation and real data application, indicated that ME significantly affects the performance of the Bayesian EWMA control chart when RSS schemes are employed. Particularly noteworthy is the superior performance of the median RSS scheme compared to the other two schemes in the presence of ME.

Integration of hybrid score functions to design new adaptive EWMA control chart to monitor the process mean shift

Small-to-moderate shifts in the process parameters can be detected using the traditional Exponentially Weighted Moving Average (EWMA) control chart. The classical EWMA control chart's parameter helps only to identify the specific size of the shift. However, various shifts occur in real-world processes, so the conventional EWMA control chart performs inefficiently for off-target shifts. This problem has been confronted by applying an adaptive EWMA (AEWMA) control chart, an advanced version of the classical EWMA control chart. The score functions are utilized to design the AEWMA control chart. Generally, the Huber and Bi-square (score) functions have unique characteristics, such as monotone and redescended, respectively.There has not been any investigation into the simultaneous and/or joint deployment of score functions. So, by taking this point as motivation, this study aims to propose a new score function by blending the Huber and Bi-square characteristics into one hybrid formulation and then utilize it to design a new AEWMA control chart to monitor different sizes of the shift in the process location parameter. To evaluate the proposed control chart performance against other control charts, Monte Carlo simulation is applied to obtain the run length properties under zero-state and steady-state environments. Performance measures, such as average run length, standard deviation of run length, and median of run length, are considered to evaluate the performance at a single shift. In contrast, extra quadratic loss, relative average run length, and performance comparison index are utilized to evaluate effectiveness for a specific range of shifts. The comparison based on performance measures and visual presentation reveals the superiority of the proposed control chart. Besides, the proposed control chart is employed in the real-world chemical engineering process industry problem, demonstrating excellent detection ability of anomalies in air pollutant data. The comparison based on performance measures and visual presentation reveals the good performance of the proposed control chart.

The Optimal Control Chart Selection for Monitoring COVID-19 Phases: A Case Study of Daily Deaths in the USA.

Epidemiologists frequently adopt statistical process control tools, like control charts, to detect changes in the incidence or prevalence of a specific disease in real time, thereby protecting against outbreaks and emergent health concerns. Control charts have proven essential in instantly identifying fluctuations in infection rates, spotting emerging patterns, and enabling timely reaction measures in the context of COVID-19 monitoring. This study aims to review and select an optimal control chart in epidemiology to monitor variations in COVID-19 deaths and understand pandemic mortality patterns. An essential aspect of the present study is selecting an appropriate monitoring technique for distinct deaths in the USA in 7 phases, including pre-growth, growth, and post-growth phases. Stage-1 evaluated control chart applications in epidemiology departments of 12 countries between 2000 and 2022. The study assessed various control charts and identified the optimal one based on maximum shift detection using sample data. This study considered at Shewhart (Javid Shabbir2, ) control charts and exponentially weighted moving average (EWMA) control chart with smoothing parameters were all investigated in this study. In Stage-2, we applied the EWMA control chart for monitoring because of its outstanding shift detection capabilities and compatibility with the present data. Daily deaths have been monitored from March 2020 to February 2023. Control charts in epidemiology show growing use, with the United States leading at 42% applications among top countries. During the application on COVID-19 deaths, the EWMA chart accurately depicted mortality dynamics from March 2020 to February 2022, indicating six distinct stages of death. The third and fifth waves were extremely catastrophic, resulting in a considerable loss of life. Significantly, a persistent sixth wave appeared from March 2022 to February 2023. The EWMA map effectively determined the peaks associated with each wave by thoroughly examining the time and amount of deaths, providing vital insights into the pandemic's progression. The severity of each wave was measured by the average number of deaths. The United States entered a seventh phase (6th wave) from March 2022 to February 2023, marked by fewer deaths. While reassuring, it remains crucial to maintain vaccinations and pandemic control measures. Control charts enable early detection of daily COVID-19 deaths, providing a systematic strategy for government and medical staff. Incorporating the EWMA chart for monitoring immunizations, cases, and deaths is recommended.