Exponentially Weighted Moving Average Statistic Research Articles

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.

Mean Estimation for Time-Based Surveys Using Memory-Type Logarithmic Estimators

This article examines the issue of population mean estimation utilizing past and present data in the form of an exponentially weighted moving average (EWMA) statistic under simple random sampling (SRS). We suggest memory-type logarithmic estimators and derive their properties, such as mean-square error (MSE) and bias up to a first-order approximation. Using the EWMA statistic, the conventional and novel memory-type estimators are compared. Real and artificial populations are used as examples to illustrate the theoretical findings. According to the empirical findings, memory-type logarithmic estimators are superior to the conventional mean estimator, ratio estimator, product estimator, logarithmic-type estimator, and memory-type ratio and product estimators.

Detection Sensitivity of a Modified EWMA Control Chart with a Time Series Model with Fractionality and Integration

Among the many statistical process control charts, the modified exponentially weighted moving average (EWMA) control chart has been designed to swiftly detect a small shift in a process parameter. Herein, we propose two explicit formulas for the average run length (ARL) for integrated moving average (IMA) and fractional integrated moving average (FIMA) models combined with the modified EWMA control chart for time series prediction. The application of the suggested control chart procedures depends on the residuals of the IMA and FIMA models. The performance of the control chart with both models is evaluated by using the ARL. Explicit formulas for the ARL for the two models with the modified EWMA statistic are derived and their precision is compared with the numerical integral equation method. The explicit formulas could accurately predict the true ARL while markedly decreasing the computational processing time compared to the numerical integration method. The capabilities of the IMA and FIMA models with the modified EWMA control chart were studied by varying g times the last term and exponential smoothing parameter λ, with the relative mean index being used to evaluate these situations. The results show that the modified EWMA control chart with either model performed better than the original EWMA control chart. Furthermore, the modified EWMA control chart with either model was highly efficient when g increased and λ was small. Two applications involving energy commodity prices are used to illustrate the efficacies of the proposed approaches, the results of which were in accordance with the experimental study. Doi: 10.28991/ESJ-2022-06-05-015 Full Text: PDF

Design of a new adaptive EWMA control chart

AbstractThe memory‐based control charts (CCs) such as exponentially weighted moving average (EWMA) and Cumulative sum (CUSUM) are good for quick detection of small or moderate shifts in the process mean. This study proposes a memory‐based CC to monitor the mean of a normally distributed process. The idea is to estimate the mean shift using an estimator based on an EWMA statistic and after that determine the smoothing constant of plotting EWMA statistics through the proposed continuous function. The performance of the proposed adaptive EWMA (AEWMA) chart is focused on utilizing extensive Monte Carlo simulations method with various shifts in the process mean. Taking into account the run‐length (RL) profiles, as an evaluation tool, the proposed chart is efficient as compared to the competitor charts. The demonstration of the proposed chart is presented by using a real dataset from the manufacturing process of substrates where the quality characteristic is the resistance of flow width.

An optimal construction of yield-based EWMA repetitive multivariate sampling plan

In this paper, a variable repetitive group sampling (VRGS) plan is proposed based on the exponentially weighted moving average (EWMA) statistic with yield index for inspection of mutually independent and multivariate normally distributed characteristics. Plan parameters are found optimally based on asymptotic distribution of using a non linear optimization. A simulation study indicates that the reported parameters can thoroughly warrant determined risks for finite sample sizes. This work also extends application of the proposed plan to the class of correlated characteristics. The obtained findings show that the proposed plan significantly reduces required average sample number compared to the existing modified VRGS plan, single, double, and multiple dependent state sampling plans with yield-based EWMA statistic. Two industrial examples are presented to illustrate the application of the proposed plan in real world.

A critique of a variety of “memory-based” process monitoring methods

Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based on alternative weighting of past data, usually to put greater emphasis on past data and less weight on current and recent data. In other cases, the output of one process monitoring method, such as the EWMA statistic, is used as the input to another method, such as the CUSUM chart. Often the recursive formula for a control chart statistic is itself used recursively to form a new control chart statistic. We find the use of these ad hoc methods to be unjustified. Statistical performance comparisons justifying the use of these methods have been either flawed by focusing only on zero-state run length metrics or by making comparisons to an unnecessarily weak competitor.

Modified One-Sided EWMA Charts without- and with Variable Sampling Intervals for Monitoring a Normal Process

Much research has been conducted on two-sided Exponentially Weighted Moving Average (EWMA) control charts, while less work has been devoted to the one-sided EWMA charts. Traditional one-sided EWMA charts involve resetting the EWMA statistic to the target whenever it falls below or above the target, or truncating the observations above or below the target and further applying the EWMA statistic to the truncated samples. In order to further improve the performance of traditional one-sided EWMA mean (X¯) charts, this paper studies the performance of the Modified One-sided EWMA (MOEWMA) X¯ charts to monitor a normally distributed process. The Monte-Carlo simulation method is used to obtain the zero- and steady-state Run Length (RL) properties of the proposed control charts. Through extensive simulations and comparisons with other charts, it is shown that the proposed MOEWMA X¯ charts compare favorably with some existing competing charts. Moreover, by attaching the variable sampling intervals (VSI) feature to the MOEWMA X¯ charts, it is shown that the VSI MOEWMA charts outperform the corresponding charts without the VSI feature. Finally, a real data example from manufacturing process shows the implementation of the proposed one-sided charts.

Product Acceptance Determination Based on EWMA Yield Index Using Repetitive and MDS Sampling Schemes

In this manuscript, we present a repetitive group sampling plan and a multiple dependent state sampling plan based on the EWMA (exponentially weighted moving average) yield index for product acceptance. The proposed plans utilize the current and the previous information through EWMA statistic to reach a decision of lot sentencing. A non-linear optimization model is developed to determine the plan parameters of the proposed plans for various specified conditions. The performance of the proposed plans over several existing sampling plans is analyzed, which shows that the proposed plans are efficient in reducing the sample size for lot sentencing. For industrial application, a real example is given to demonstrate the implementation of the proposed plans.

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

From the principles of statistical process control, the observations are assumed to be identically and independently normally distributed, although this assumption is frequently untrue in practice. Therefore, control charts have been developed for monitoring and detecting data which are autocorrelated. Recently, a modified exponentially weighted moving average (EWMA) control chart has been introduced that is a correction of the EWMA statistic and is very effective for detecting small and abrupt changes in independent normally distributed or autocorrelated observations. In this study, the performance of a modified EWMA chart is investigated by examining the 2 sides of the exact average run length based on an explicit formula when the observations are from a general-order moving average process with exponential white noise. A performance comparison of the EWMA and the modified EWMA control charts is also presented. In addition, the performance of the modified and EWMA control charts is contrasted using Dow Jones composite average from a real-life dataset. The findings suggest that the modified EWMA control chart is more sensitive than the EWMA control chart for almost every case of the studied smoothing parameter and constant values of the control chart.
 HIGHLIGHTS
 
 Autocorrelation data is frequency untrue of assumption practice in time series data
 Modified EWMA is a new control chart that is effective for detecting change in independent normal distribution and autocorrelated observations
 The efficiency of the control chart is measured by average run length
 Explicit formula is easy to derive and provides the exact value of the average run length

A trimmed EWMA control charts for non-normal processes

The traditional exponentially weighted moving average (EWMA) control chart is very popular in statistical process control (SPC) for detecting small shifts in process mean and variance. It performs well under the assumption of normality but when data violate this assumption, a modified approach is needed. In this paper, we proposed a variable control chart for monitoring the process mean by modifying the traditional EWMA control chart for non-normal processes based on the modified trimmed standard deviation (MTSD). The proposed EWMA control charts are based on three different heuristic methods, namely, the Trimmed Exponentially Weighted Moving Average (T-EWMA) control chart, the Trimmed Weighted Standard Deviation Exponentially Weighted Moving Average (TWSD-EWMA) control chart and the Trimmed Weighted Variance Exponentially Weighted Moving Average (TWV-EWMA) control chart. The performances of the control charts under study are evaluated via a Monte-Carlo simulation study by calculating expected out-of-control points and expected widths under non-normal distributions (i.e. Gamma and Exponential). Also, since the EWMA statistic $${Z}_{i}$$ is sensitive to detect mean shifts in the process, the out-of-control average run length ( $${ARL}_{1}$$ ) is considered in the simulation as a best tool to measure the sensitivity. The simulation studies are being carried out for the purpose and results showed that the proposed trimmed control charts performed well for non-normal processes in terms of their shorter expected widths, more number of expected out-of-control points and quick out-of-control signals as compared to non-trimmed versions of control charts. Moreover it is also observed that as weighing constant $$\lambda$$ increases, the sensitivity of the proposed trimmed control charts increases. For illustration purposes, a real-life data set from a public service industry is analyzed which confirming our conclusions from the simulation analysis. Consequently, for estimating of the process mean when the distribution of the data is non-normal, we recommend the trimmed versions of EWMA control charts for the practitioners to be used.

Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys

Exponentially weighted moving average (EWMA) statistic is a memory type statistic that used present and past information to estimate the population parameter. This study utilizes EWMA statistic to propose a ratio and product estimator for the surveys based on time scale. The usual ratio and product estimators consist of only current sample information, whereas the proposed estimators consist of current as well as past sample information. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. It is revealed from the results of simulation study that utilization of the past samples information excels the performance of estimator in terms of efficiency. Two real life examples are presented to demonstrate the use of proposed estimators.

Developing variables sampling plans based on EWMA yield index

Acceptance sampling plans are concerned with inspection and decision making regarding products one of the oldest facets of quality assurance. In this article, the procedures of various sampling plans based on the yield index with an exponentially weighted moving average (EWMA) statistic are probed for the submitted lot. The proposed sampling plans investigate the quality of the current lot and preceding lots. The double sampling plan and MDS sampling plan based on the EWMA yield index are executed for obtaining the required parameters based on the smoothing constant of the EWMA statistic and various combinations of two risks. Comparing miscellaneous sampling plans are carried out by minimizing ASN as the objective function and satisfying two constraints related to producer's and consumer's risks. In order to determine the proper sampling plan, a comparison study will be carried out. By comparing the results of sampling plans based on smaller values of ASN, we can deduce that the MDS sampling plan has better performance in comparison to existing sampling plans.

Exponentially Weighted Moving Average Control Chart Based on Normal Fuzzy Random Variables

Exponentially weighted moving average (EWMA) chart is an alternative to Shewhart control charts and can serve as an effective tool for detection of shifts in small persistent process. Notably, existing methods rely on induced imprecise observations of a normal distribution with fuzzy mean and variance. Such techniques did not investigate the statistical properties relevant to a fuzzy EWMA. To overcome this shortcoming, employing a common notion of normal fuzzy random variable with fuzzy mean and non-fuzzy variance could be helpful. This paper first developed a notion of fuzzy EWMA statistic as a natural extension to the classical counterpart. Then, the concept of fuzzy EWMA control limit was introduced and discussed in cases where fuzzy mean and/or non-fuzzy variance was unknown parameters. A degree of violence was also employed to monitor the proposed fuzzy EWMA control chart. Potential applications of the proposed fuzzy EWMA chart were also demonstrated based on a real-life example. The advantages of the proposed method were also discussed in comparison with other existing fuzzy EWMA methods.

Monitoring communication outbreaks among an unknown team of actors in dynamic networks

This article investigates the detection of communication outbreaks among a small team of actors in time-varying networks. We propose monitoring plans for known and unknown teams based on generalizations of the exponentially weighted moving average (EWMA) statistic. For unknown teams, we propose an efficient neighborhood-based search to estimate a collection of candidate teams. This procedure dramatically reduces the computational complexity of an exhaustive search. Our procedure consists of two steps: communication counts between actors are first smoothed using a multivariate EWMA strategy. Densely connected teams are identified as candidates using a neighborhood search approach. These candidate teams are then monitored using a surveillance plan derived from a generalized EWMA statistic. Monitoring plans are established for collaborative teams, teams with a dominant leader, as well as for global outbreaks. We consider weighted heterogeneous dynamic networks, where the expected communication count between each pair of actors is potentially different across pairs and time, as well as homogeneous networks, where the expected communication count is constant across time and actors. Our monitoring plans are evaluated on a test bed of simulated networks as well as on the U.S. Senate co-voting network, which models the Senate voting patterns from 1857 to 2015. Our analysis suggests that our surveillance strategies can efficiently detect relevant and significant changes in dynamic networks.

New GWMA‐CUSUM control chart for monitoring the process dispersion

AbstractThe cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely accepted because of their fantastic speed in identifying small‐to‐moderate unusual variations in the process parameter(s). Recently, a new CUSUM chart has been proposed that uses the EWMA statistic, called the CS‐EWMA chart, for monitoring the process variability. On similar lines, in order to further improve the detection ability of the CS‐EWMA chart, we propose a CUSUM chart using the generally weighted moving average (GWMA) statistic, named the GWMA‐CUSUM chart, for monitoring the process dispersion. Monte Carlo simulations are used to compute the run length profiles of the GWMA‐CUSUM chart. On the basis of the run length comparisons, it turns out that the GWMA‐CUSUM chart outperforms the CUSUM and CS‐EWMA charts when identifying small variations in the process variability. A simulated dataset is also used to explain the working and implementation of the CS‐EWMA and GWMA‐CUSUM charts.

Acceptance sampling plan based on an exponentially weighted moving average statistic with the yield index for autocorrelation between polynomial profiles

ABSTRACTAcceptance sampling plans based on process yield indices provide a proven resource for the lot-sentencing problem when the required fraction defective is very low. In this study, a new sampling plan based on the exponentially weighted moving average (EWMA) model with yield index for lot sentencing for autocorrelation between polynomial profiles is proposed. The advantage of the EWMA statistic is the accumulation of quality history from previous lots. In addition, the number of profiles required for lot sentencing is more economical than in the traditional single sampling plan. Considering the acceptable quality level (AQL) at the producer's risk and the lot tolerance percent defective (LTPD) at the consumer's risk, we proposed a new search algorithm to determine the optimal plan parameters. The plan parameters are tabulated for various combinations of the smoothing constant of the EWMA statistic, AQL, LTPD, and two risks. A comparison study and two numerical examples are provided to show the applicability of the proposed sampling plan.

A EWMA control chart based on an auxiliary variable and repetitive sampling for monitoring process location

ABSTRACTThis article develops an exponentially weighted moving average (EWMA) control chart using an auxiliary variable and repetitive sampling for efficient detection of small to moderate shifts in location. A EWMA statistic of a product estimator of the average (which utilities the information of auxiliary variables as well as repetitive sampling) is plotted on the proposed chart. The control chart coefficients of the proposed EWMA chart are determined for two strategic limits known as outer and inner control limits for the target in-control average run length. The performance of the proposed EWMA chart is studied using average run length when a shift occurs in the process average. The efficiency of the developed chart is compared with the competitive existing control charts. The results of the study revealed that proposed EWMA chart is more efficient than others to detect small changes in process mean.

An efficient adaptive EWMA control chart for monitoring the process mean

AbstractIn recent years, the memory‐type control charts—exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)—along with the adaptive and dual control‐charting structures have received considerable attention because of their excellent ability in providing an overall good detection over a range of mean‐shift sizes. These adaptive memory‐type control charts include the adaptive exponentially weighted moving average (AEWMA), dual CUSUM, and adaptive CUSUM charts. In this paper, we propose a new AEWMA chart for efficiently monitoring the process mean. The idea is to first design an unbiased estimator of the mean shift using the EWMA statistic and then adaptively update the smoothing constant of the EWMA chart. The run length profiles of the proposed AEWMA chart are computed using extensive Monte Carlo simulations. Based on a comprehensive comparative study, it turns out that the proposed AEWMA chart performs better than the existing AEWMA, adaptive CUSUM, dual CUSUM, and Shewhart‐CUSUM charts, in terms of offering more balanced protection against mean shifts of different sizes. An example is also used to explain the working of the existing and proposed control charts.

Midpoint-radii principal component analysis -based EWMA and application to air quality monitoring network

Monitoring air quality is crucial for the safety of humans and the environment. Moreover, real world data collected from air quality network is often affected by different types of errors as measurement noise and variability of pollutant concentrations. The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering interval-valued data analysis. In practical cases of measured data, the true value cannot be measured and the collected data on a process are only approximations given by sensors, and are thus imprecise. This is due mainly to the uncertainties induced by measurement errors or determined by specific experimental conditions. Thus, the main aim of this paper is to develop an enhanced monitoring of air quality network by taking into account the uncertainties on the data. To do that, we develop a new monitoring technique that merges the advantages of Midpoint-radii PCA (MRPCA) method with exponentially weighted moving average (EWMA) chart, in order to enhance sensor fault detection technique of air quality monitoring process. MRPCA is the most popular interval multivariate statistical method, able to tackle the issue of uncertainties on the models and one way to improve the fault detection abilities. On the other hand, the EWMA statistic allows an exponential weighted average to successive observations and able to detect small and moderate faults. The developed MRPCA-based EWMA method relies on using MRPCA as a modeling framework for fault detection and EWMA as a detection chart. The proposed MRPCA-based EWMA scheme is illustrated using a simulation example and applied for sensor fault detection of an air quality monitoring network. The monitoring performances of the developed technique are compared to the classical monitoring techniques. MRPCA model performances are compared with the interval PCA models: complete-information principal component analysis (CIPCA) and Centers PCA (CPCA). The MRPCA-based EWMA monitoring performances are compared to MRPCA-based Shewhart, generalized likelihood ratio test (GLRT) and squared prediction error (SPE) techniques.

A HEWMA-CUSUM control chart for the Weibull distribution

ABSTRACTThe Weibull distribution is one of the most popular distributions for lifetime modeling. However, there has not been much research on control charts for a Weibull distribution. Shewhart control is known to be inefficient to detect a small shift in the process, while exponentially weighted moving average (EWMA) and cumulative sum control chart (CUSUM) charts have the ability to detect small changes in the process. To enhance the performance of a control chart for a Weibull distribution, we introduce a new control chart based on hybrid EWMA and CUSUM statistic, called the HEWMA-CUSUM chart. The performance of the proposed chart is compared with the existing chart in terms of the average run length (ARL). The proposed chart is found to be more sensitive than the existing chart in ARL. A simulation study is provided for illustration purposes. A real data is also applied to the proposed chart for practical use.