Exponentially Weighted Moving Average Chart Research Articles

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.

Gear Crack Detection Based on Vibration Analysis Techniques and Statistical Process Control Charts (SPCC)

Vibration condition monitoring is a non-devastating technique that can be performed to detect tooth cracks propagating in gear systems. This paper proposes to apply a new methodology using time-domain analysis, frequency-domain analysis, and statistical process control charts (SPCC) for gear crack detection of a 10 DOF dynamic model of spiral bevel gear system (SBGS). The gear mesh stiffness effect used in the model has been studied analytically for different levels of crack faults. Adding Gaussian white noise is discussed as the first step to simulating the initial modeling signals of real-world conditions. Second, time-domain signal analysis was performed to identify periodic vibration pulses as failure components and calculate the statistical standard deviation (STD) feature as a fault-sensitive feature. Third, a fast Fourier transform (FFT) to time signals of the variable gear mesh stiffness was applied to determine the gear mesh frequency and sidebands to detect tooth cracks. Fourth, the SPCC was designed using the Shewhart X-bar chart and an exponentially weighted moving average (EWMA) chart based on the STD feature of the healthy gears. Finally, in the testing stage, the control charts are carried out with simulation signals under faulty conditions to detect the different levels of cracks. The results showed that the EWMA chart outperformed the time domain analysis, frequency domain analysis, and Shewhart X-bar chart in detecting all levels of cracks at an early stage.

A critique of the use of modified and moving average‐based EWMA control charts

AbstractWe show that the so‐called modified exponentially weighted moving average (EWMA) control chart is very closely related to a moving average‐based EWMA chart. These charts have ill‐advised weighting functions that assign more weight to some past data values than to the most recent data values. We show that these weighting functions adversely affect their run length properties and that one can obtain better overall performance with an ordinary EWMA chart.

Recurrence of depression can be foreseen by monitoring mental states with statistical process control.

Detecting early signs of recurrence of psychopathology is key for prevention and treatment. Personalized risk assessment is especially relevant for formerly depressed patients, for whom recurrence is common. We aimed to examine whether recurrence of depression can be accurately foreseen by applying Exponentially Weighted Moving Average (EWMA) statistical process control charts to Ecological Momentary Assessment (EMA) data. Participants were formerly depressed patients (n = 41) in remission who (gradually) discontinued antidepressants. Participants completed five smartphone-based EMA questionnaires a day for 4 months. EWMA control charts were used to prospectively detect structural mean shifts in high and low arousal negative affect (NA), high and low arousal positive affect (PA), and repetitive negative thinking in each individual. A significant increase in repetitive negative thinking (worry, negative thoughts about the self) was the most sensitive early sign of recurrence: this was detected in 18 out of 22 patients (82%) before recurrence and in 8 out of 19 patients (42%) who stayed in remission. A significant increase in NA high arousal (stress, irritation, restlessness) was the most specific early sign of recurrence: this was detected in 10 out of 22 patients (45%) before recurrence and in 2 out of 19 patients (11%) who stayed in remission. These mean changes were detected at least a month before recurrence in the majority of the participants. The outcomes were robust across EWMA parameter choices, but not when using fewer observations per day. The findings demonstrate the value of monitoring EMA data with EWMA charts for detecting prodromal symptoms of depression in real-time. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Transfer learning based deep learning model and control chart for bearing useful life prediction

AbstractThe remaining useful life (RUL) of the machine is one of the key information for predictive maintenance. If there is a lack of predictive maintenance strategy, it will increase the maintenance and breakdown costs of the machine. We apply transfer learning techniques to develop a new method that predicts the RUL of target data using degradation trends learned from complete bearing test data called source data. The training length of the model plays a crucial role in RUL prediction. First, the exponentially weighted moving average (EWMA) chart is used to identify the abnormal points of the bearing to determine the starting point of the model's training. Secondly, we propose transfer learning based on a bidirectional long and short‐term memory with attention mechanism (BiLSTMAM) model to estimate the RUL of the ball bearing. At the same time, the public data set is used to compare the estimation effect of the BiLSTMAM model with some published models. The BiLSTMAM model with the EWMA chart can achieve a score of 0.6702 for 11 target bearings. The accuracy of the RUL estimation ensures a reliable maintenance strategy to reduce unpredictable failures.

Memory-Type Control Charts Through the Lens of Cost Parameters

A memory-type control chart utilizes previous information for chart construction. An example of a memory-type chart is an exponentially-weighted moving average (EWMA) control chart. The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts. Meanwhile, the EWMA median chart is robust against outliers. In light of this, the economic model of the EWMA and EWMA median control charts are commonly considered. This study aims to investigate the effect of cost parameters on the out-of-control average run length in implementing EWMA and EWMA median control charts. The economic model was used to compute the parameter. The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis. When the input parameters change based on a predetermined percentage, the is affected. According to the results of the EWMA chart, nine input parameters had an effect and five input parameters had no effect on the parameter. Further, only seven of the 14 input parameters had an effect on the ARL1 of the EWMA median chart. However, the effect of each input parameter on the was different. Moreover, the for the EWMA median chart was smaller than the EWMA chart. This analysis is crucial to observe and determine the input parameters that have a significant impact on the of the EMWA and EWMA median control charts. Hence, practitioners can obtain an overview of the influence of the input parameters on the when implementing the EWMA and EWMA median control charts.

Proposed variable sampling interval maximum EWMA and distance EWMA charts with unknown process parameters

The variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart which varies the chart's sampling interval according to the value of the current plotting statistic increases the speed of the standard EWMA chart in detecting shifts. Joint monitoring schemes use a single combined statistic for the mean and variance in process monitoring. To simultaneously monitor the mean and variance of a process from the normal distribution, two VSI EWMA schemes with unknown process parameters, based on (i) Maximum (Max) and (ii) Distance (Dis) type combining functions, are proposed in this paper. Each of these schemes uses a single plotting statistic. The effects of parameter estimation on the performance of the proposed VSI Max EWMA and VSI Dis EWMA schemes, in terms of the average time to signal, standard deviation of the time to signal, expected average time to signal and median time to signal criteria, are studied using Monte Carlo simulation. The results show that the proposed schemes can identify process shifts quicker than the existing Max/Dis Shewhart (SH), Max/Dis cumulative sum (CUSUM) and Max/Dis EWMA schemes. The implementation of the proposed schemes is demonstrated using a commercial dataset.

A Markov Chain Model for Approximating the Run Length Distributions of Poisson EWMA Charts under Linear Drifts

In addition to monitoring the Poisson mean rate with step shifts, increasing attention has been given to monitoring Poisson processes subject to linear trends. The exponentially weighted moving average (EWMA) control chart has been widely implemented to monitor normal processes, but it lacks investigation for detecting the Poisson mean change under a linear trend. In this paper, we analyze the performance of the EWMA chart by extending the Markov chain model from monitoring Poisson processes under a step shift to a Poisson process with linear drift. The results demonstrate that the proposed method is able to provide accurate average run length approximation, compared with the Monte Carlo simulation. Optimal design tables and sensitivity analysis are presented to facilitate the use of the EWMA chart in practice.

Recalibration of prediction model was needed for monitoring health care quality in subgroups: a retrospective cohort study

ObjectivesTo evaluate the predictive ability of a mortality prediction model in subgroups of intensive care unit (ICU) patients and test the validity for monitoring the outcome. Study Design and SettingA Japanese ICU database was used for the analyses. Adults admitted to an ICU between April 1, 2019, and March 31, 2020, were included. Nine clinically relevant subgroups were selected, and we evaluated the discrimination and calibration of the Japan Risk of Death model, a recalibrated Acute Physiology and Chronic Health Evaluation III-j model. Funnel plots and exponentially weighted moving average (EWMA) charts were used to check its validity for monitoring in-hospital mortality. If the predictive performance was poor, the model was recalibrated and model performance was reassessed. ResultsThe study population comprised 14,513 patients across nine subgroups. The in-hospital mortality rate ranged from 11.3% to 30.9%. The calibration was poor in most subgroups, and the funnel plots and EWMA charts frequently revealed “out-of-control” signals crossing the control limit of three standard deviations (SDs). The calibration improved after recalibration, and the number of “out-of-control” signals decreased. ConclusionWhen monitoring the quality of care among subgroups of patients, testing the predictive ability and recalibration of the risk model are needed.

EWMA control charts using generalized centrality measures for social network monitoring

The monitoring and detection of network anomalies have become an interesting topic in social network analysis. One approach for detecting such anomalies is to apply conventional centrality measures, such as degree centrality, closeness centrality, and betweenness centrality, to control charts. Another approach involves the use of hybrid centrality measures, such as degree-degree, degree-closeness, and degree-betweenness, which are generated by combining traditional centrality measures and emphasize the importance of actors in the network. From another perspective, most studies on weighted networks have used centrality measures based on tie weights alone and have not accounted for the number of ties. In this paper, we propose exponentially weighted moving average (EWMA) charting procedures that use several types of centrality measures based on the number and weights of ties in undirected weighted networks. We then evaluate the anomaly-detection performance of these measures on weighted networks using EWMA charts. Simulation results indicate that degree and degree-degree centralities perform well for small changes, while betweenness and degree centralities perform well for large changes. In addition, centrality measures that consider both the number and weights of ties, with more importance given to the weights were determined to be better at detecting anomalies.

Generalization of time‐varying fast initial response for exponentially weighted moving average control charts

AbstractFor monitoring processes, exponentially weighted moving average (EWMA) control charts have been found to be very powerful and reliable tools. Meanwhile, some processes require great attention at the startup to ascertain that the processes are free from any disturbances. In this article, we propose a generalized time‐varying fast initial response for EWMA control charts. This chart is a special case of the previously proposed time‐varying EWMA control chart. The proposed scheme is highly sensitive in detecting small shifts in a given process, particularly at the process startup. The proposed chart is compared with its counterparts using the zero state average run length. We also show an application of the proposed EWMA chart to a real‐life situation.

A phase II EWMA chart for the balanced one‐way random effects model

AbstractStatistical process control (SPC) techniques are used in applications where more than one sources of variation are present, for example, in a one‐way random effects (variance components) model. The Shewhart control charts for this situation have been studied by several researchers. However, exponentially weighted moving average (EWMA) charts are generally recommended in Phase II, as they are more sensitive to detecting smaller process mean shifts. We consider EWMA charts for the one‐way random effects model in the balanced case, properly accounting for the effects of parameter estimation while designing and implementing the control charts. In the sequel we derive and calculate the corrected (adjusted) control limits for Phase II applications. Following the recent literature, the limits are formulated under two perspectives, the unconditional and the conditional. Tabulations of the charting constants are provided under both perspectives along with an illustration with some actual data. A simulation study examining in‐control (IC) robustness performance is conducted under both perspectives. Finally, some conclusions are given. An R package is provided to support deployment of the proposed control chart in practice.