Exponentially Weighted Moving Average Control Chart Research Articles

A new risk‐adjusted EWMA control chart based on survival time for monitoring surgical outcome quality

AbstractMonitoring surgical outcome quality by risk‐adjusted control charts has attracted wide attention. The hidden medical errors may cause increasing of adverse events such as infection, rehospitalization, and even death. Quickly and timely detecting abnormal changes of surgical performance helps reduce the probability of adverse events and improve health care quality. Most existing monitoring schemes focus on the binary surgical outcomes. However, continuous survival times of patients should be considered for more accurate monitoring. In this paper, a new exponentially weighted moving average (EWMA) control chart is proposed for monitoring continuous surgical outcomes. To describe surgical performance, a patient's actual survival time and predicted mortality are combined in an illustrative and interpretable way. Performance of the proposed chart is evaluated with different chart parameters under different shifts by a simulation study. We compare our chart with the risk‐adjusted survival time cumulative sum chart, and the simulation results demonstrate that the proposed monitoring scheme has better efficiency. The implementation of the proposed chart is illustrated by a real example. Besides an analysis of the entire dataset, the surgical performance of each surgeon is monitored, because each of them has patients with different risk levels.

Episode detection based on personalized intensity of care thresholds: a schizophrenia case study.

Schizophrenia Spectrum Disorder (SSD) is characterized by its chronic, episodic nature. The clear definition of such episodes is essential for various clinical and research purposes. Most current definitions of episodes in SSD are based on either hospitalizations or on symptom scales. Both have drawbacks; symptom scales are measured infrequently, while hospitalization rates are often affected by policy. This study presents an approach for defining episodes in healthcare data that does not suffer such drawbacks. Healthcare use of 13,155 SSD patients in the Northern Netherlands with up to 12 years of follow-up was available. Patient-level structural changes in the trend of healthcare use costs were determined using Exponentially Weighted Moving Average (EWMA) control charts. Control charts restart with updated parameters after a detected structural change. Episodes were defined using these structural changes. The resulting episodes were validated by investigating their association with the Global Assessment of Functioning (GAF) scale. The mean number of episodes was 0.61 (sd: 0.60) per patient per year. For the sub-group without hospitalizations this was 0.51 (sd: 0.71). Average episode duration of the sub-group (147 days, sd: 309.4) was similar to that of the full sample (150 days, sd: 305.5). A significant inverse association was identified between GAF scores and the episode-state indicator. The repeated application of EWMA control charts based on healthcare-intensity is a feasible and promising tool for quantifying patient-level healthcare episodes. The validation using GAF scores indicates that our episode indicator is associated with lower levels of global functioning. Results for individuals without hospitalizations indicate that the method is robust with regard to changes in healthcare policy.

Proposed α-cut CUSUM and EWMA Control Charts for Fuzzy Response Observations

This research proposesalpha ([Formula: see text]-cut Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts with fuzzy response observations in a manufacturing process under the existence of mean shift utilizing the fuzzy logic. In this research, the replicate’s observation is a fuzzy number represented by a triangular membership function, with the lower, average, and upper observation values. The fuzzy numbers are then normalized and assigned as input to the fuzzy logic, while a common output measure (COM) value is the output. Finally, the original values of the COM values are employed in developing the EWMA and CUSUM control charts with different [Formula: see text]-cut values. Three real case studies are adopted to illustrate the proposed EWMA and CUSUM control charts; including piston inside diameter, cap’s angel, and tablet weight. Results showed that the proposed EWMA and CUSUM control charts efficiently monitor fuzzy observations and detect the shift in process means. Moreover, the amount mean shift and [Formula: see text]-cut values affect the decision on process condition. In conclusion, the proposed approach is found effective in monitoring quality characteristic of fuzzy observations under mean shift which can be applied in a wide range of business applications.

An adaptive EWMA control chart for monitoring the process mean in Bayesian theory under different loss functions

AbstractThe Shewhart control chart is used for detecting the large shift and an exponentially weighted moving average (EWMA) control chart is used for detecting the small/moderate shift in the process mean. A scheme that combines both the Shewhart control chart and the EWMA control chart in a smooth way is called the adaptive EWMA (AEWMA) control chart. In this paper, we proposed a new AEWMA control chart for monitoring the process mean in Bayesian theory under different loss functions (LFs). We used informative (conjugate prior) under two different LFs: (1) squared error loss function and (2) linex loss function for posterior and posterior predictive distributions. We used the average run length and standard deviation of run length to measure the performance of the AEWMA control chart in the Bayesian theory. A comparative study is conducted for comparing the proposed AEWMA control chart in Bayesian theory with the existing Bayesian EWMA control chart. We conducted a Monte Carlo simulation study to evaluate the proposed AEWMA control chart. For the implementation purposes, we presented a real‐data example.

An improved exponentially weighted moving average chart for monitoring proportions using maxima nomination sampling

We develop a new proportion control chart using the exponentially weighted moving average (EWMA) for the maxima nomination sampling (MNS) method. By using average run length (ARL), we compare it with conventional Shewhart and EWMA control charts based on the simple random sampling (SRS) method. We study the effect of the sample size, the set size, the in-control and out-of-control non-conforming proportion, the smoothing parameter, and the refinement factor on the performance of MNS-EWMA charts using ARL curves. We show that the MNS-EWMA control chart is an excellent indicator of changes in the quality of processes relative to SRS-Shewhart and SRS-EWMA charts. We present optimal ranges for the smoothing parameter of MNS-EWMA charts. An illustrative example with simulated data is enclosed. The results show that MNS-EWMA control charts produce significant enhancement over the traditional charts based on SRS.

Control charts for monitoring drip irrigation with different hydraulic heads

This study monitored a drip irrigation system with different hydraulic heads, using control charts. The study included 25 tests, and was conducted at the Experimental Nucleus of Agricultural Engineering of the State University of Western Paraná, located in the municipality of Cascavel, Paraná. The drip irrigation system was operated by gravity, and had four hydraulic heads (10, 11, 12 and 15 kPa). The uniformity of the system was determined based on uniformity distribution. Uniformity monitoring was performed using Shewhart and exponentially weighted moving-average (EWMA) control charts. An increase in the hydraulic head increased uniformity. The use of 12 and 15 kPa hydraulic heads yielded good performance, whereas 10 and 11 kPa yielded regular performance. The use of control charts proved to be efficient; the Shewhart control chart was more robust, whereas the EWMA control chart, which indicated trends and deviations not shown by Shewhart control charts, was more sensitive.

Auxiliary information based joint monitoring control chart using generalized likelihood ratio test statistic

The use of auxiliary variable has given considerable attention to improving the sensitivity of control charts to observe the changes in process parameters. Exponentially weighted moving average (EWMA) control chart is effective to identify the small or moderate changes in the process parameters. This study is designed to develop EWMA control chart by using auxiliary information for joint monitoring of process mean and variance using the generalized likelihood ratio test statistic named as MdELRt-EWMA control chart. Performance measures average run length (ARL) and the standard deviation of the run length (SDRL) are used to assess the efficiency of the proposed chart. An extensive Monte Carlo simulations are performed to evaluate the sensitivity of the MdELRt-EWMA control chart. A comparative study is conducted and observed the superiority of the proposed control chart over the competitors.

Performance of robust EWMA control chart for variability process using non-normal data

The main purpose of quality control is to quickly detect the presence of assignable causes and shifts in the process so that an investigation of the process can be carry out as early as possible. The Shewhart control chart provides good performance when the observation data is normally distributed, whereas when the normality assumption is not met, a Robust control chart is needed. The performance of the control chart depends on the stability of the estimator used to estimate the process parameters and establish control limits in phase I. In this study, a Robust Exponentially Weighted Moving Average (EWMA) control chart will be present to monitor process variability using one of estimator Robust scale to estimate standard deviation. This estimator is used to develop robust control limits. Then evaluate the control chart performance using Average Run Length (ARL) and Standard Deviation Run Length (SDRL) with Monte Carlo simulation. Furthermore, the robust chart was applied to monitor the quality characteristics of the number of bacterial colonies in each aquaculture medicine product. The results obtained in this study are formed a control chart that is resistant to the existence of outliers and sensitive to shifts in the process of variability.

A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data

ABSTRACT Many control charts have been developed for the simultaneous monitoring of the time interval T between successive occurrences of an event E and its magnitude X. All these TBEA (Time Between Events and Amplitude) control charts assume a known distribution for the random variables T and X. But, in practice, as it is rather difficult to know their actual distributions, proposing a distribution free approach could be a way to overcome this ‘distribution choice’ dilemma. For this reason, we propose in this paper a distribution free upper-sided EWMA (Exponentially Weighted Moving Average) type control chart, for simultaneously monitoring the time interval T and the magnitude X of an event. In order to investigate the performance of this control chart and obtain its run length properties, we also develop a specific method called ‘continuousify’ which, coupled with a classical Markov chain technique, allows to obtain reliable and replicable results. A numerical comparison shows that our distribution-free EWMA TBEA chart performs as the parametric Shewhart TBEA chart, but without the need to pre-specify any distribution. An illustrative example obtained from a French forest fire database is also provided to show the implementation of the proposed EWMA TBEA control chart.

Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables

The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters—which are the reference value ( a ) and control limit ( h )—for designing a CUSUM chart with a minimum out-of-control ARL is presented. In addition, the explicit formulas for the CUSUM control chart were applied with the practical data of a stock price from the stock exchange of Thailand, and the resulting performance efficiency is compared with an exponentially weighted moving average (EWMA) control chart. This comparison showed that the CUSUM control chart efficiently detected a small shift size in the process, whereas the EWMA control chart was more efficient for moderate to large shift sizes.

A novel procedure to improve traditional EWMA control chart performance in detecting both small and large shifts

Different control charts are proposed by many researchers for the aim of detecting process shifts in the mean and assuring quality of the product. Exponentially weighted moving average (EWMA) control charts is one of the famous charts which performs well in detecting small shifts in the process mean. In this paper, a new statistic based on different smoothing parameters is proposed to improve the performance of the exponentially weighted moving average (EWMA) control chart in detecting large shifts as well as small and medium shifts. The performance of the developed scheme based on the proposed smoothing parameter is evaluated in terms of average run length criterion in comparison with the traditional EWMA control chart. The results show the better performance of the proposed scheme rather than the traditional EWMA control charts in most cases.

Modeling and predicting reservoir landslide displacement with deep belief network and EWMA control charts: a case study in Three Gorges Reservoir

The accurate modeling and predicting of landslide deformation is crucial to the prevention of landslide hazard. This paper presents a pioneering study of modeling and predicting the reservoir landslide displacement with deep learning algorithm. A data-driven framework using deep belief network and control chart has been introduced to explore the temporal patterns of displacement and potential of identifying seasonal faster displacement. First, the continuous wavelet analysis has been applied to decompose the time-series precipitation, reservoir water level, and displacement into seasonal and residual components. Second, the deep belief network has been constructed to predict the future displacement. Third, it utilizes the exponentially weighted moving average (EWMA) control chart to derive the boundaries as alarm conditions of seasonal faster displacement. A group of tests are conducted to compare the performance of the deep belief network with other state-of-the-art machine learning algorithms. Computational results demonstrated the effectiveness of the deep belief network in extracting highly non-linear data features. In addition, the advantage of utilizing control charts has been further validated by the accuracy of examining the seasonal faster displacement based on the case study in Baishuihe landslide in Three Gorges Reservoir, China.

A simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations

AbstractIt is common in modern manufacturing to simultaneously monitor more than one process quality characteristic. In such a multivariate scenario, the monitoring of the covariance matrix, along with the mean vector, plays an important role in assessing whether a process stays in control or not. However, monitoring the covariance matrix is technically more difficult, especially when there is only one observation available in each subgroup, disabling the usual sample covariance matrix as an effective estimator. To monitor the covariance matrix with individual observations in Phase II stage, several exponentially weighted moving average (EWMA) control charts have been constructed based on the distance between the estimated process covariance matrix and its target value. In this paper, two new control charts are devised using the sum of the square roots of the absolute deviations and its combination with the sum of squared deviations. These distance‐based control charts are compared via the simulation experiments on different simulated out‐of‐control covariance matrices with respect to the number of quality characteristics being monitored, the shift pattern, and the shift magnitude. The simulation results identify the control charts that perform relatively robust and show that these various control charts may have their respective merits on different out‐of‐control scenarios.

Control charts for monitoring the ratio of two Poisson rates

AbstractIn this paper, we are concerning in monitoring the ratio ρ of two Poisson rates by control charts. Let X and Y be two independent Poisson random variables with means λ1 and λ2=λ1/ρ, respectively. The study considers that only individual observations Xi and Yi are available at each sampling time i. The performance in detecting shifts on the ratio ρ using several statistics, some based on normalized transformations, is evaluated by an extensive simulation study. Two types of control charts, Shewhart and exponentially weighted moving average (EWMA), are considered. The one‐sided control chart with upper control limit (UCL) is applied so that we are focusing on detecting when the ratio ρ shifted to higher rate in this paper. The results pointed out that EWMA control chart is a better alternative. Some guidelines indicating which statistics yield best performance are proposed for the practitioners.

Estimation Mean by the Bayesian Approach on the Exponentially Weighted Moving Average Control Chart

A control chart is one of the primary techniques of statistical quality control. Exponentially Weighted Moving Average (EWMA) control chart is one of the control charts used to detect a small shift in the mean process. In the quality control process, the control chart is often constructed by ignoring parameter uncertainty. This can affect the long-term performance of the control chart in a controlled or out-of-control state, so parameter estimation is necessary. The parameter estimation method used in this paper is the Bayesian approach. The Bayesian approach is used to develop an EWMA control chart in monitoring a process. The performance of the EWMA control chart with the Bayesian approach has been evaluated using Average Run Length (ARL). Based on the comparison of the ARL value from the EWMA control chart with the Bayesian approach and the Classical EWMA control chart, it shows that the EWMA control chart with the Bayesian approach is more sensitive in detecting the shift in the mean process.

Control chart based on residues: Is a good methodology to detect outliers?

The purpose of this article is to evaluate the application of forecasting models along with the use of residual control charts to assess production processes whose samples have autocorrelation characteristics. The main objective is to determine the efficiency of control charts for individual observations (CCIO) and exponentially weighted moving average (EWMA) charts when they are applied to residuals of models of AR(1) or MA(1) to detect outlier in autocorrelated processes. Considering autocorrelation strength and sign in the data series and the outlier range, the series were simulated accomplishing 640,000 sets. The series were contaminated by anomalous observations at 100th position, an AR(1) or MA(1) model were fitted, and the residuals were evaluated by CCIO and EWMA control charts; the points correctly detected as an autocorrelation were recorded. For the parameters investigated (autocorrelation and outlier range), a detection rate was generated in each chart, and nonparametric comparison tests were applied. The result of the tests showed the superiority (p < 0.05) of the CCIO chart for both models. The study of the influence of the sign and magnitude of the autocorrelation parameter showed no significant (p > 0.05) for either AR(1) or MA(1) charts and models. In this context, control charts for individual observations (CCIO) were confirmed to effectively detect outliers through residuals in industrial autocorrelated processes originated in first-order AR and MA models.

An economic statistical design of the Poisson EWMA control charts for monitoring nonconformities

ABSTRACTAn economic statistical model of the exponentially weighted moving average (EWMA) control chart for the average number of nonconformities in the sample is proposed. The statistical and economic performance of proposed design are evaluated using the average run length (ARL) and the hourly expected cost, respectively. A Markov chain approach is applied to derive expressions for ARL. The cost model is established based on the general cost function given in Lorenzen and Vance [The economic design of control charts: a unified approach. Technometrics. 1986;28:3–11]. An example is provided to illustrate the application of the proposed model. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments (DOE) technique.

Generally weighted moving average control charts using repetitive sampling

Generally weighted moving average (GWMA) control charts have been validated for effective detection of small process shifts, and perform better than exponentially weighted moving average (EWMA) control charts. These charts are available based on single sampling; however, repetitive sampling charts have received less attention. Here, a GWMA control chart based on repetitive sampling (namely an RS-GWMA chart) is proposed for enhancing detectability of small process shifts. Simulations show that the proposed RS-GWMA chart with large design and small adjustment parameters outperforms existing hybrid EWMA (HEWMA) control charts based on repetitive sampling. An in-silico example is considered for demonstrating the applicability of the proposed RS-GWMA chart.

An EWMA control chart for categorical processes with applications to social network monitoring

Statistical process monitoring (SPM) has traditionally been applied to manufacturing processes; however, more recent developments highlight its application to social networks. We propose a network monitoring strategy using the exponentially weighted moving average (EWMA) control chart, with the goal of detecting shifts in the hierarchical tendency of directed graphs over time. Such a strategy might prove useful to an organization’s stakeholders when interest lies in monitoring for shifts in the general health of the organization. Although development of the proposed control chart was motivated by a network monitoring problem, our method is generally applicable to multinomial categorical processes. We study the detection performance of our proposed control chart, relative to that of the multinomial cumulative sum (CUSUM) alternative. Results suggest that if the out-of-control shift in the multinomial probabilities cannot be specified a priori, the proposed EWMA control chart should be considered as an alternative to the CUSUM strategy. Application of the proposed method is demonstrated on a real data set, namely, the open-source Enron e-mail corpus.

An EWMA control chart for the multivariate coefficient of variation

AbstractMonitoring the multivariate coefficient of variation over time is a natural choice when the focus is on stabilising the relative variability of a multivariate process, as is the case in a significant number of real situations in engineering, health sciences, and finance, to name but a few areas. However, not many tools are available to practitioners with this aim. This paper introduces a new control chart to monitor the multivariate coefficient of variation through an exponentially weighted moving average (EWMA) scheme. Concrete methodologies to calculate the limits and evaluate the performance of the chart proposed and determine the optimal values of the chart's parameters are derived based on a theoretical study of the statistic being monitored. Computational experiments reveal that our proposal clearly outperforms existing alternatives, in terms of the average run length to detect an out‐of‐control state. A numerical example is included to show the efficiency of our chart when operating in practice.