MEWMA Chart Research Articles

A control chart for bivariate discrete data monitoring

Control charts are sophisticated graphical tools used to detect and control aberrant variations. Different control schemes are designed to continuously monitor and improve the process stability and performance. This study proposes a bivariate exponentially weighted moving average chart for joint monitoring of the mean vector of Gumbel's bivariate geometric (GBG) data. The performance of the proposed chart is compared with Hotelling's T 2 chart. The results of the study indicated that the proposed control chart performs uniformly and substantially better than Hotelling's T 2 chart. In addition to two real-life examples, an example based on simulated data is also considered and compared to existing charts to verify the superiority of the proposed chart. Based on the comparisons, it turns out that the MEWMA (GBG) chart outperforms Hotelling's T 2 chart and individual EWMA control chart.

IMPLEMENTATION OF MEWMA CHART USING TIME SERIES MODEL FOR MONITORING THE WHITE CRISTAL SUGAR QUALITY

The basic assumption of implementing a control chart is that the observed process values should be normally distributed and independent. However, the production process at the factory is carried out repeatedly with the same machine, so there is a possibility that the observation data is not independent and the resulting control chart becomes inaccurate. Therefore, a time series model approach is needed to create an accurate control chart. This study aims to conduct statistical quality control of white crystal sugar (WCS) production at Madukismo Sugar Factory (MSF) Yogyakarta to maintain product stability and quality according to the standards. MSF performs quality control on WCS products with several quality characteristic variables, including drying shrinkage (%), grain size (mm), polarization, and color of sugar solution (ICUMSA). This study is only limited to the four quality characteristics with research data in the form of secondary data from the MSF QC Laboratory. The data used were WCS quality characteristics from May 9 - July 16, 2022. The four characteristics influence each other, so a MEWMA control chart is used. This study found autocorrelation between observations so that time series modeling was carried out and resulted in VARIMA (1,1,2) as the best time series model. While the implementation of the MEWMA chart shows uncontrollable results with an optimal weighting value λ of 0.8. For process capability, the results show that the process is capable.

Modified exponentially weighted moving average control chart for monitoring process dispersion

The exponentially weighted moving average ( EWMA ) charts are widely used memory-type charts for monitoring small to moderate shifts in process parameters. However, the performance of the EWMA chart has been improved over time due to various modifications and enhancements. This paper proposes two modified EWMA ( M ‐ EWMA ) charts to monitor process dispersion. The upper-sided modified EWMA chart is denoted by M ‐ EWMA U , while a lower-sided modified EWMA chart is symbolized as the M ‐ EWMA L chart. Monte Carlo simulations determine the proposed schemes’ run length (RL) properties in zero- and steady-state scenarios. The proposed upper- and lower-sided M ‐ EWMA charts are compared to the upper- and lower-sided CH ‐ EWMA and SJ-EWMA charts. The comparisons reveal that the proposed M-EWMA charts have better detection ability than the upper- and lower-sided CH-EWMA, and SJ-EWMA charts, respectively. Finally, a real-life application is provided to illustrate the implementation of the upper-sided M-EWMA and CH-EWMA charts practically in both zero-state and steady-state cases.

Sensitivity of the Modified Exponentially Weighted Moving Average Sign-Rank Control Chart to Process Changes in Counted Data

Control charts are generally used to detect mean process changes in continuous processes. However, counting procedures that characterize product quality are popular in production processes, such as the number of defects or the proportion of defective products. This research aims to investigate using the Modified Exponentially Weighted Moving Average combined with a nonparametric Sign Rank control chart, namely MEWMA-SR chart is a novel tool. Comparative analyses involving different run length measures are conducted to evaluate the proposed scheme against MEWMA, MEWMA-SR, and classical EWMA charts. The performance of the MEWMA-SR chart is assessed using Monte Carlo simulations based on its run-length profiles. It was found that the proposed combination control chart was effective in detecting changes better than other control charts along with presenting applications with real data. A study further validates the proposed chart’s practical utility through a case study analyzing COVID-19 mortality data.

An efficient MEWMA chart for Gumbel's bivariate Pareto distribution

Control charts play a vital role in process monitoring to ensure the product's desired standards. Due to rapid improvements in data collection methods, multivariate charts are preferred over univariate charts. This paper proposes a bivariate exponentially weighted moving average chart for the simultaneous monitoring of the mean vector of Gumbel's bivariate Pareto type II (also known as the Lomax distribution) time-between-events data. The performance of the proposed chart is assessed through average run length, median run length, and the standard deviation of the run length criteria. To show the implementation of the chart in the real world, illustrative examples are also presented.

Directionally sensitive adaptive MEWMA charts with fixed and variable sampling rates

AbstractA primary objective in detecting disease outbreaks is to precisely identify substantial increases in process means to control the spread of outbreaks. In this paper, we introduce a novel directionally sensitive adaptive multivariate exponentially weighted moving average chart for efficiently detecting either increases or decreases in the mean vector of a multivariate normally distributed process. In addition, the chart's sensitivity is enhanced through features such as variable sample size, variable sampling interval, and a combination of both. Monte Carlo simulation is employed to estimate zero‐state and steady‐state average time‐to‐signal (ATS) profiles. Performance measures, including expected weighted and relative ATS, are used for evaluating the performances of multivariate charts. Our results indicate that the proposed charts outperform existing charts in detecting various mean shift sizes. The application of these multivariate charts is demonstrated through illustrative examples.

Design of a new adaptive MEWMA chart to monitor the mean

The adaptive MEWMA (AMEWMA) charts have been broadly perceived as an effective process monitoring instrument due to the efficient detection of the mean shifts of diverse sizes. This study proposes an AMEWMA control chart to observe the irregular variations in the mean vector of the process which follows the multivariate normal distribution. The idea is to assess the mean shift by using an unbiased estimator and after that adapt the smoothing constant of plotting EWMA statistic through a continuous function. As an evaluation tool, the run-length profiles are computed by using the Monte Carlo simulation method. The proposed AMEWMA chart is proved to be efficient in shift detection as compared to the MEWMA and existing AMEWMA charts. The application of the proposed chart is shown by utilizing a real-life dataset from a case study of process capability for turning aluminum pins where six quality characteristics are to be observed.

A two-stage model for change point detection in large-scale weighted directed social networks using a MEWMA chart

A two-stage model for change point detection in large-scale weighted directed social networks using a MEWMA chart

Improved Control Charts for Phase II Monitoring of Simple Linear Profiles Using Auxiliary Information

In some manufacturing or non-manufacturing systems, the process outcome is better characterized by a relationship between a main variable and some associated supporting variables. The monitoring of this functional relationship over time is termed as profile monitoring. This study aims to improve Phase II monitoring of simple linear profiles by using auxiliary information which is correlated with the main variable. To accomplish that, using a mean estimator, two auxiliary information-based (AIB) control charts namely AIB-MEWMA and AIB-DMEWMA charts are proposed for detecting different shifts in model parameters. Using two numerical examples based on simulation studies, the sensitivity of the proposed control charts is evaluated and compared with the existing MEWMA and DMEWMA charts in terms of the average run length (ARL) metric. The results of simulations reveal that the proposed charts perform better than the existing MEWMA and DMEWMA charts. The applicability of the proposed control charting methods is demonstrated using a real-life data example from the cylinder production process.

Neutrosophic multivariate EWMA control chart

The MEWMA chart is one of the traditional multivariate charts which are widely employed in inspecting the quality of manufacturing and services. This chart is created through monitoring the small shifts of mean vectors of variable quality characteristics. Often in practice, the measurement of a quality characteristic produces uncertain, incomplete values, so that ambiguous numbers are obtained. In this condition, a neutrosophic-based control chart can overcome the problem resulting from the ambiguous data. The paper’s objective is to construct a new multivariate monitoring scheme based on a neutrosophic chart, namely the neutrosophic Multivariate EWMA (NMEWMA). Furthermore, the performance of the new multivariate monitoring scheme is evaluated in detecting process shifts employing the Average Run Length (ARL) and Standard Deviation Run Length (SDRL). This control chart is an innovation in the quality monitoring of uncertain data. The research result obtained indicates that the NMEWMA chart performs better than the MEWMA in finding the small mean shifts as well as in the real case application.

Phase II monitoring of logistic regression profiles with estimated parameters

In most profile monitoring applications, the regression parameters are unknown and must be estimated via Phase I reference samples. This study evaluates how parameter estimation affects the average run length (ARL) properties of two well-known charts in Phase II monitoring of logistic regression profiles. In this regard, the performance of T 2 and MEWMA charts established by estimated regression parameters is evaluated for both in-control and out-of-control situations. The results of simulation experiments confirm that estimation error affects the ARL properties of both T 2 and MEWMA charts. Two remedial procedures of increasing the Phase I samples and control limit modification are employed to compensate for the estimation error impact. Then, an illustrative example based on simulated data is given to indicate the impact of estimation error on detection ability of T 2 chart. Finally, a real-life example is provided to represent how estimation error increases the false alarm rate of T 2 chart.

A Comparison Between the MEWMA and Mahalanobis Distance Control Chart

Statistical Process Control (SPC) is approaching that uses statistical techniques to monitor the process. The methods of quality control are widely used in controlling any strategy—the widely used control charts. A traditional variable control chart includes three lines: the Centre Line (CL), the Upper Control Limit (UCL), and the Lower Control Limit (LCL), all of which are represented by numeric values—represented by numeric values. A control chart illustrates the centerline of the average value of the quality feature under investigation.
 Depending on numeric observation values, a process is either "in control" or "out of control."
 Considering the current, there are no questions regarding the observations and their values during the production process. However, when these observations include human judgments, assessments, and choices, a continuous random variable (xi) of a manufacturing process should be made up of the variable.
 The MEWMA and Mahalanobis distance control chart techniques are used when more than one variable is involved.
 This paper aims to compare the MEWMA and Mahalanobis distance chart for three compounds for water drinking production in the ALA -Factory in the Sulaimani-Iraq region.
 So, linguistic terms can be used instead of the exact value of the continuous random variable. Today, quality control has become one of the most essential techniques for studying all variables to control production or consumption decision factors. Quality control's primary aim is to guarantee that the goods, services, or processes delivered satisfy particular standards and are reliable and satisfactory. The factor's direct approach is based on the product's quality.

A multivariate triple exponentially weighted moving average control chart

AbstractStatistical process monitoring (SPM) is mostly populated with univariate control charts used to monitor a single variable (or quality characteristic). Nowadays, industries and online environments are filled with processes in which two or more quality characteristics are related. In such situations, univariate control charts are replaced with multivariate control charts for the sake of monitoring several characteristics simultaneously. This paper develops a new multivariate triple exponentially weighted moving average (MTEWMA) chart to serve this purpose. Moreover, the design of the multivariate simple and double exponentially weighted moving average (denoted as MEWMA and MDEWMA) charts are revisited using extensive simulations. It is observed that the MTEWMA chart has very interesting time‐varying properties as compared to the asymptotic properties. The newly proposed MTEWMA chart is superior over the MEWMA and MDEWMA charts in many situations of the asymptotic control limits. An illustrative example is provided to demonstrate the sensitivity of the proposed charts.

A synthetic multivariate exponentially weighted moving average scheme for monitoring of bivariate Gamma distributed processes

AbstractSeveral scholarly works intrinsically assume that the frequency and magnitude of events are two independent variables . However, in many practical situations, it is necessary to consider the dependence between these two characteristics of events. In this paper, two Smith–Adelfang–Tubbs (SAT) models, namely, the four‐ and the five‐parameter bivariate Gamma distributions (BGD) with a particular dependency parameter, are first reviewed. Then, a synthetic multivariate exponentially weighted moving average (synthetic MEWMA, or SMEWMA) type scheme is proposed to monitor the individual BGD observations (subgroups of size one) generated from those two specific SAT models. The Monte‐Carlo simulation method is developed to evaluate the run length () properties of the recommended SMEWMA BGD scheme in both the zero‐state and the steady‐state cases. Furthermore, we discuss the average run length (ARL) of the proposed SMEWMA BGD scheme with different design parameters, and then compare both the zero‐state and the steady‐state out‐of‐control ARL performances of the recommended SMEWMA BGD scheme with those of the classic MEWMA chart, the paired individual Gamma chart, and the MCUSUM chart. Simulation results suggest that the overall performance of the recommended SMEWMA BGD scheme is superior to the other comparative schemes. Finally, the implementation of the proposed SMEWMA BGD scheme is illustrated with a natural flood event dataset .

Enhanced directionally sensitive and directionally invariant MCUSUM and MEWMA charts for process mean

Control charts with an appropriate use of auxiliary information based (AIB) strategies have shown improved run length performances compared with control charts without this feature. In this article, by adopting an AIB estimator, enhanced directionally sensitive and directionally invariant MCUSUM and MEWMA charts for monitoring the mean vector of a process that follows a multivariate normal distribution are proposed. The proposed AIB directionally sensitive and directionally invariant MCUSUM and MEWMA charts surpass their existing basic counterparts, in terms of the average run length (ARL), median run length (MRL) and standard deviation of the run length (SDRL) performances obtained via the Monte Carlo simulation approach. In general, it is found that the directionally sensitive charts outperform their directionally invariant counterparts in detecting shifts in the process mean vector, in terms of the ARL, MRL and SDRL criteria. A real dataset is considered to demonstrate the implementation of the existing and proposed charts.

Quality of Water Production Process Using Mixed Multivariate EWMA-CUSUM (MEC) Control Chart

Human life is highly dependent on clean and freshwater. Therefore, the quality of water used by humans must be properly monitored and controlled. Based on the regulations of the Ministry of Health, the quality of clean water can be monitored from the parameters of physics, chemistry, and microbiology. The main characteristics of water quality are turbidity level, organic substance, and chlorine residual which are correlated with each other. This research proposes the combination of MEWMA and MCUSUM charts called MEC control chart for monitoring the process mean of water quality with the variables used are turbidity level, organic substance, and chlorine residual. This charting method is divided into two-part, namely MEC1 and MEC2. Further, the water production process is characterized by dry and rainy seasons. Based on the analysis results, it is found that the optimum λ in the production process during the dry and rainy season for the MEC1 control chart is 0.3. Meanwhile, the optimum λ in the production process during the dry and rainy season for the MEC2 control chart is 0.1. In this condition, the MEC1 control chart is more sensitive than the MEC2 control chart because of the higher number of out of control observations. Moreover, the organic substance is the main issue causing the out of control observations during the dry and rainy season. In the capability process analysis, the process of water production during the dry and rainy season is said to be capable because the capability index of the turbidity level is larger than the specification limit. On the other hand, the water production process with organic substance and chlorine residual are not capable due to the lower capability index compared to the specification limit.

One-sided and two one-sided MEWMA charts for monitoring process mean

ABSTRACTThis study focuses on the development of new one-sided and two one-sided MEWMA charts for monitoring the mean of a multivariate normal process. The one-sided MEWMA chart detects either increases or decreases while the two one-sided MEWMA chart detects both increases and decreases, in the process mean vector. The idea is to first truncate either positive or negative normalized observations to zero, and then apply the one-sided MEWMA charts to transformed data. This helps increase the sensitivities of one-sided and two one-sided MEWMA charts. The Monte Carlo simulation method is used to compute the run length characteristics of the proposed multivariate charts. A detailed run length comparison reveals that the proposed one-sided and two one-sided MEWMA charts are uniformly more sensitive than the existing counterparts when detecting moderate-to-large shifts in the process mean. In addition, with reasonable assumptions, the proposed two one-sided MEWMA chart outperforms the conventional MEWMA chart. Real datasets are considered to explain the implementation of the proposed multivariate charts.

Monitoring of an aquatic environment in aquaculture using a MEWMA chart

Monitoring an aquatic environment in aquaculture is usually carried out by controlling its physicochemical and biological parameters. The global state of the process is evaluated though the individual conditions shown in each parameter. However, the correlation structure in the data, caused by interdependence between these parameters, provides relevant information which must be controlled. Thus, the complex structure of the data requires a multivariate control method to explore both the individual and interactive effects of the environmental parameters. To achieve this goal, this paper presents a statistical method based on a Multivariate Exponentially Moving Average (MEWMA) chart to monitor the multivariate structure of an aquatic environment in aquaculture, especially in a crop of tilapia in Mozambique. The results show that the adjusted MEWMA chart is more consistent when controlling the conformity and stability of environmental parameters. Therefore, it can be considered an efficient statistical method to monitor an aquatic environment in aquaculture.

An adaptive multivariate EWMA chart

Abstract The adaptive multivariate EWMA (AMEWMA) and adaptive multivariate CUSUM (AMCUSUM) charts are recently proposed as they provide an overall good detection over a range of mean shift sizes than their non-adaptive conventional counterparts. In this paper, we propose an adaptive MEWMA (AMEWMA) chart for monitoring the infrequent changes in the mean of a multivariate normally distributed process. The idea is to consider an unbiased estimator of the mean shift using an MEWMA statistic, and then use it to adaptively update the smoothing constant of the MEWMA chart. By using Monte Carlo simulations, the run length characteristics of the AMEWMA chart are computed. The AMEWMA chart is comprehensively compared with the existing AMEWMA and AMCUSUM charts in terms of the average run length when detecting mean shifts in different ranges. It is found that the proposed chart is able to perform uniformly and substantially better than the existing charts. Both real and simulated datasets are considered to support the theory.

Mixed multivariate EWMA-CUSUM control charts for an improved process monitoring

ABSTRACTMultivariate exponential weighted moving average and cumulative sum charts are the most common memory type multivariate control charts. They make use of the present and past information to detect small shifts in the process parameter(s). In this article, we propose two new multivariate control charts using a mixed version of their design setups. The plotting statistics of the proposed charts are based on the cumulative sum of the multivariate exponentially weighted moving averages. The performances of these schemes are evaluated in terms of average run length. The proposals are compared with their existing counterparts, including HotellingT2, MCUSUM, MEWMA, and MC1 charts. An application example is also presented for practical considerations using a real dataset.