Exponentially Weighted Moving Average Chart Research Articles

Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process.

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results.

A critique on the use of the belief statistic for process monitoring

AbstractRecently, several control charts have been proposed in the statistical process monitoring literature based on a belief statistic. In this article we compare the zero‐state average run‐lengths and conditional expected delay profiles of the exponentially weighted moving average (EWMA) and belief statistic‐based (BSB) charts. We show that an ordinary EWMA chart is far better than the BSB chart when detecting delayed shifts in the mean of a normally distributed process.

Monitoring gamma type-I censored data using an exponentially weighted moving average control chart based on deep learning networks

In recent years, deep learning methods have been widely used in combination with control charts to improve the monitoring efficiency of complete data. However, due to time and cost constraints, data obtained from reliability life tests are often type-I right censored. Traditional control charts become inefficient for monitoring this type of data. Thus, researchers have proposed various control charts with conditional expected values (CEV) or conditional median (CM) to improve efficiency for right-censored data under normal and non-normal conditions. This study combines the exponentially weighted moving average (EWMA) CEV and CM chart with deep learning methods to increase efficiency for gamma type-I right-censored data. A statistical simulation and a real-world case are presented to assess the proposed method, which outperforms the traditional EWMA charts with CEV and CM in various skewness coefficient values and censoring rates for gamma type-I right-censored data.

Quasi-online failure times identification of mobile heat sources in 2D geometry

Identifying the failure instants in thermal systems subject to 2D parabolic partial differential equations presents a significant challenge, especially when the systems involve mobile heat sources. In the context of this study, mobile heat sources are examined, along with a set of stationary sensors, while assuming known and constant-velocity trajectories for the heat sources. This research introduces a quasi-online methodology that incorporates Exponentially Weighted Moving Average (EWMA) charts for immediate failure detection. When a failure is detected via the EWMA charts, the Conjugate Gradient Method, traditionally developed for offline applications, is activated. This method is adapted to a quasi-online framework, facilitating a more rapid and precise identification of malfunctioning heat sources, the exact time of their failures, and the possibility of restoring normal operations. To assess the performance and reliability of this approach, it is compared with a Bayesian filter-based method, particularly using the Kalman filter for this purpose. Monte Carlo simulations are employed to evaluate the resilience and effectiveness of the quasi-online method, focusing on the system’s sensitivity to the accuracy of sensor measurements.

On the performance and comparison of various memory-type control charts

Several versions of the exponentially weighted moving average (EWMA) control chart, such as the generally weighted moving average (GWMA), the double, triple, and quadruple EWMA (DEWMA, TEWMA, and QEWMA), and the homogeneously weighted moving average (HWMA) charts, have been developed to enhance its detection ability, especially for small and moderate shifts. These charts have been criticized as it is considered that an appropriately designed EWMA chart provides as good or better zero-state and steady-state average run-length (ARL) performance. In this article, we perform a careful comparison study of the above control charts under similar in-control (IC) run-length properties. We show that the “new” memory-type control charts have better out-of-control (OOC) run-length characteristics, especially for small to moderate shifts in the process mean for both the zero-state and steady-state cases, except for the HWMA chart where its steady-state OOC performance is very poor. We also present a comparison study based on the worst-case ARL measure. Finally, the extensions of the EWMA chart have better IC robustness ability than the EWMA and HWMA charts.

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.

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.

THE PERFORMANCES OF MIXED EWMA-CUSUM CONTROL CHARTS BASED ON MEDIAN-BASED ESTIMATORS UNDER NON-NORMALITY

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts have been regularly used to monitor small process mean shifts. More recently, a mixture of EWMA and CUSUM charts known as mixed EWMA-CUSUM (MEC) control chart has been introduced for better small shift detection. However, like its predecessor, the MEC chart requires the normality assumption to ensure optimal performances. In the presence of outliers, which is the cause of non-normality, the parameters of the chart may be overestimated, leading to an unreliable monitoring process. To mitigate this problem, this paper employed median-based estimators namely, the median and modified one-step M-estimator (MOM), to control the location parameter via the MEC control chart. In this study, the performance of robust MEC charts for Phase II monitoring of location was compared with the standard MEC chart that is based on the sample mean. The performance of the robust MEC charts in terms of the average run length (ARL) on various g-and-h distributions clearly shows that a robust MEC chart based on the MOM estimator performs well regardless of the distributional shapes.

A Weibull process monitoring with AEWMA control chart: an application to breaking strength of the fibrous composite

In recent times, there has been a growing focus among researchers on memory-based control charts. The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts and the adaptive control charting approaches got the attention. Control charts are commonly employed to oversee processes, assuming the monitored variable follows a normal distribution. However, it's worth noting that this assumption does not hold true in many real-world situations. The use of the algebraic expression for normalization, which can be used for all kinds of skewed distributions with a closed-form distribution function, using the proposed continuous function to adapt a smoothing constant, motivates this study. In the present manuscript, we design an EWMA statistic-based adaptive control chart to monitor the irregular variations in the mean of two parametric Weibull distribution and use Hasting approximation for normalization. The adaptive control charts are used to update the smoothing constant according to the estimated shift. Here we use the proposed continuous function to adapt the smoothing constant. The average run length and standard deviation of run length are calculated under different parameter settings. The effectiveness of the proposed chart is argued in terms of ARLs over the considered EWMA chart through Monte-Carlo (MC) simulation method. The proposed chart is examined, followed by a real data set to demonstrate the design and application procedures.

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.

Effect of estimation error on the conditional false alarm rate design of the EWMA chart

AbstractIn this article, we study the effect of estimation error on the conditional false alarm rate (CFAR) of the exponentially weighted moving average (EWMA) chart based on the estimated dynamic probability control limits (EDPCLs). It is found that the effect is large, but with an increase in the Phase‐I sample size, the effect of estimation error may be reduced. In addition, an alternative approach is suggested for determining the EDPCLs for the EWMA chart that may help reduce the effect of estimation error on the CFAR profiles.

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.

A new phase II change-point detection based EWMA chart for monitoring and diagnostics of linear profiles

ABSTRACT A new Phase II control chart, which is based on the change-point model and combined with the exponentially weighted moving average (EWMA) mechanism, is proposed to monitor general linear profiles. The new control chart can be used to monitor general linear profiles when the true in-control parameters are unknown, and only a few historical data are available. In addition, when the chart triggers an out-of-control signal, not only can it estimate the location of the change point, it can also identify which of the parameters have changed as well as the change directions. Using Monte-Carlo simulations, the proposed chart is shown to be effective and has good diagnostic performance. Furthermore, the simulation results show that the proposed chart has better performance than the existing charts in most of the out-of-control scenarios considered. An example is used to illustrate how the proposed chart can be implemented in practical applications.

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.

A phase II multivariate EWMA chart for monitoring multi-dimensional ratios of process means with individual observations

In recent years, there has been a resurgence in the development of control charts for monitoring the mean of the ratio of two correlated variables. However, most of the existing research has focused on the univariate mean of the ratio of two correlated variables under the assumption that the process follows a bivariate normal distribution. Furthermore, most of the existing research utilize biased estimators of the mean of the ratio of two correlated variables to develop control charts. More importantly, in certain applications, critical quality characteristics to be closely monitored are actually the ratios of the means of correlated variables, in that the process is considered to be stable as long as the ratios of the means of correlated variables remain constant at given levels, regardless of how each variable changes. We are thus motivated in this study to develop an exponentially weighted moving average (EWMA) based Phase II control chart for monitoring multi-dimensional ratios of the means of correlated variables.In this study, we provide a general framework for estimating parameters and control limits which is applicable without having to assume that the process follows a multivariate normal distribution. The performance of the proposed chart is evaluated under different multivariate distributions. Finally, a real data application of the proposed chart is presented to illustrate the practicality of the proposed chart.

Modification of ARL for detecting changes on the double EWMA chart in time series data with the autoregressive model

This research aims to derive the average run length (ARL) evaluation of the double exponentially weighted moving average (double EWMA) control chart for observation data that follows exponential white noise in a time series model with an autoregressive model. Since most real-world data is automatically correlated, autoregressive models are available. Comparisons were made between the ARLs obtained using the explicit formula and the numerical integral equation (NIE) approach. The results showed that the explicit formula's use of the ARL outperformed the NIE approach in terms of computation time. After that, the efficacy of the exponentially weighted moving average (EWMA) and double EWMA charts is then compared using the suggested explicit ARL formula. The ARL of the double EWMA chart was found to perform better than the ARL of the EWMA chart in all situations. It also uses natural gas and diesel prices on stock exchanges around the world as cases studies. The results show that the double EWMA chart has better detection sensitivity than the EWMA chart, and the results are consistent with the experimental results. As a result, the sensitivity of the double EWMA chart in detecting changes makes it a good alternative for monitoring processes with real-world data.

Quality process control and resourcing in manufacturing firms

Statistical Process Control (SPC) is employed to support the effective quality performance of production and manufacturing processes. The control chart is a type of SPC utilized to reduce variability in key quality parameters, leading to the production of quality conforming products. Control charts, such as the Exponentially Weighted Moving Average (EWMA) are widely used to reduce variation, improve productivity, and ensure quality. However, small manufacturers face challenges that may prevent their effective use of quality control charts. One such challenge relates to resource constraints. These constraints tend to inhibit the conduct of quality inspections at high rates. With this in mind, the present study sets out to develop and present an improved EWMA control chart for effective quality control that takes into consideration significant resource constraints in a small aluminium manufacturing firm. The findings suggest that adopting the improved EWMA chart can enhance the detection of any increase in defectives without the need for additional resources. The improved EWMA control chart provides small manufacturers with an enhanced quality conforming tool developed based on practical realities. Implications for both practice and theory are also highlighted.

Memory‐type control charts for censored reliability data

AbstractControl charts are commonly used to monitor a process to detect undesirable changes. The main goal of this work is to propose exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts to track a process by utilizing type‐I censored generalized exponential (GE) distributed data. In particular, the censored data are replaced with the conditional expected value (CEV). A comparison between CUSUM and CUSUM ignoring unobserved covariates (CUSUM‐IUC) charts is also a part of this study. The GE distribution is considered due to its application in reliability analysis. The performance of the charts is evaluated by using the average run length along with the standard deviation of the run length. Furthermore, the study also examines the effect of smoothing parameters, censoring rate, and shifts on the proposed methodologies. The results indicate that the EWMA chart performs better than other schemes (CUSUM and CUSUM‐IUC) for shifts in the shape parameter of the GE distribution. Finally, the proposed schemes are also applied to a real‐life data set.

The Inertial properties of EWMA control charts

Since exponentially weighted moving average (EWMA) control charts combine information from the current and past samples, they are relatively more effective in detecting small process shifts than Shewhart control charts. A prevailing problem in control charts is the property of not responding quickly to process shifts, that is, showing statistical control of the process while a shift has occurred in the process parameter(s). This property of control charts, which is referred to as “inertia”, is an important issue in control charting and has been a major concern to engineers and statisticians. This study surveys the inertial properties of EWMA control charts in detail. First, the distribution of EWMA chart statistic and signal resistance probability (SRP) are studied for many different cases when there are undetected transient shifts. All measures are calculated and evaluated via a Markov chain approach. Then, an optimal scheme is proposed to minimize the out-of-control average run length (ARL) for a specified shift, subject to SRP constraints. The results reveal that the inertia can be sometimes a serious problem in EWMA control schemes that should not be overlooked. It is shown that an appropriate scheme based on both ARL and SRP measures could be useful for processes that may have sustained and/or transient out-of-control states.