Multivariate Exponentially Weighted Moving Average Control Chart Research Articles

Control charts for high-dimensional time series with estimated in-control parameters

In this article, we study the effect of misspecification caused by fitting the target process in the Phase I analysis of the monitoring procedure on the behavior of several types of multivariate exponentially weighted moving average (MEWMA) control charts in the high-dimensional setting. In particular, the classical MEWMA control charts, whose control statistics are based on the exact and asymptotic Mahalanobis distance, are considered together with the novel approaches where the Euclidean distance and the diagonalized Euclidean distance are employed in the construction of control statistics. The high-dimensional distributions of the control statistics are deduced at each time. These results are later used to assess the performance of the considered control charts under misspecification. Both theoretical and empirical findings lead to the conclusion that the control charts based on the Euclidean distance and the diagonalized Euclidean distance are robust to misspecification for moderate dimensions of the data-generating model, whereas they tend to overestimate the in-control average run lengths (ARLs) in the case of larger dimensions. On the other hand, the control schemes based on the Mahalanobis distance are considerably affected by the estimation of the parameters of the target process, and their application results in drastically smaller values of the ARLs, especially when the dimension of the data-generating model is large.

Economic design of residuals MEWMA control chart with variable sampling intervals and sample size

In order to improve the monitoring efficiency of the multivariable autocorrelation process and reduce the cost of process control, an economic design method of residual Multivariate Exponentially Weighted Moving Average (MEWMA) control charts with variable sample size and sampling intervals (VSSIs) was proposed. First, residual MEWMA control charts with VSSI were designed for monitoring multivariable autocorrelation processes. Second, the economic model of the VSSI residual MEWMA control chart was established, and a data example was given. The optimal design parameters of the control chart were obtained by using a genetic algorithm to minimize the expected cost per unit time. Third, using orthogonal experimental design and regression analysis, a sensitivity analysis of the economic model was carried out to get the relationship between the model parameters and the design parameters of the control chart. Finally, through the optimality analysis, it was verified that the proposed economic model was superior to the models established by the variable sampling intervals strategy and the variable sample size strategy and had less expected cost per unit time.

Penerapan Bagan Kendali MEWMA-MEWMV pada Pengendalian Kualitas Lulusan Prodi Statistika FMIPA Universitas Syiah Kuala

Statistical technique used to analyze quality problems and improve process performance is Statistical Process Control (SPC). In this study, multivariate control chart is used to control the quality of the graduates of Statistics Study Program, FMIPA USK, namely using Multivariate Exponentially Weighted Moving Average (MEWMA) control chart to control process average, Multivariate Exponentially Weighted Moving Variance (MEWMV) to control process variability, and analysis Process Capability to assess the entire process. Data used is secondary data, namely GPA data, duration of thesis preparation, and length of study for graduates of Statistics Study Program, FMIPA USK in 2016-2021 as many as 122 people. Results of the study, using MEWMA control chart, it was found that the average process for quality of graduates was statistically controlled in phase II. Selection of the most optimal weighting is λ=0.9. Meanwhile, for application of the MEWMV control chart, it was found that the process variability in the quality of graduates was also statistically controlled. The selection of the most optimal weights is λ =0.9 and ω=0.3. The results of the calculation of process capability, multivariately the GPA variable, length of the final project preparation, and length of the study show that all three are not capable.

Multivariate auto‐correlated process control by a residual‐based mixed CUSUM‐EWMA model

AbstractMultivariate auto‐correlated process control issues in industrial systems are a concern for statistical process monitoring (SPM). Traditional control charts produce large false alarms and/or miss timely detections of quality deterioration because they are unable to recognize the signals from multivariate auto‐correlated response variables. To track multivariate auto‐correlated processes, this paper presents a new residual‐based mixed multivariate control chart using cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) approaches. Using in‐control data, the multi‐output least square support vector regression model's optimal hyper‐parameters are determined, and a bootstrap method is used to estimate the upper control limit of the proposed control chart. The suggested control chart has strong detection performance for a small magnitude mean vector shift based on the average run length (ARL) performance for a particular range of shifts. Experimental result elaborates that the proposed control chart is more sensitive to detecting the mean vector shift compared with the existing commonly used models, such as multivariate CUSUM and multivariate EWMA control charts. The proposed control chart model and corresponding computational algorithm are successfully applied to SPM in an electronic conductor production line with multivariate auto‐correlated attributes.

PENERAPAN DIAGRAM KONTROL MEWMA DALAM PENGENDALIAN KUALITAS PRODUKSI KERIPIK SINGKONG PADA UMKM DI KOTA SEMARANG

Quality is the main thing that needs to be considered by every company. Ceriping Bintang Putra Bu Slamet is an UMKM (Usaha Mikro, Kecil dan Menengah) that produces cassava chips. During production, there are three quality characteristics, namely large crumbs defects, small crumbs, and chips sticking together. It is important to control these defects to produce quality products according to customer needs. This research was conducted from July to August 2021. The purpose of this study was to control the production quality of cassava chips using the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart and multivariate process capability analysis. The MEWMA control chart is used to detect the shift in the process average which is more sensitive using weights (λ), while the process capability analysis is used to determine the process performance. The implementation of the MEWMA control chart is carried out in two stages, namely phase I control to obtain the optimal weighting and control limits so that it can be used in phase II control to monitor the average process for the next period. Based on the results of the analysis, the optimal weighting is λ =0,4 with BKA=201,7434, GT=113,538, and BKB=0 in phase I control. Then, the results of phase II control show a shift in the average process in a better direction. In addition, the results of the process capability analysis show an improvement in the performance of the production process from July 2021 to August 2021 with MCpm values of 0,535 and 1,147

A Monitoring Kualitas Kaca Panasab dengan Diagram Kontrol MEWMA

Panasab glass is one type of glass that can absorb some of the heart's heat so that the temperature in the room is more comfortable. One of the national glass companies that produce hot glass monitors the silvering coating process. The silvering method is considered less effective because it is expensive. Therefore, in this paper, the process of controlling the quality of hot glass is carried out on the quality characteristics of the left and right CD edge distortion, which is the length of the roll marks on the right and left sides of the net glass that affect the presence or absence of distortion in the visual check results. The two quality characteristics correlate with each other. Therefore, quality control is carried out using a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart to monitor process variability and averages. MEWMA control chart statistics are affected by the weighting value . The quality characteristic data of panasab glass is divided into phase 1 and phase 2. Phase 1 is used to obtain an in-control parameter estimate (IC) which is then used for monitoring phase 2. Quality monitoring in phase 1, the process has been statistically controlled after iterations have been carried out. By using =0.4. Meanwhile, phase 2, based on the MEWMA control chart, shows that the producton procrss of panasab glass production has not been controlled statistically. Based on process capability analysis, the results obtained that the level of precision and accuracy of the quality of panasab glass products is still low. So it can be concluded that the production process of panasav glass is not yet capable.

Sequential monitoring of high‐dimensional time series

AbstractIn the paper we derive new types of multivariate exponentially weighted moving average (EWMA) control charts which are based on the Euclidean distance and on the distance defined by using the inverse of the diagonal matrix consisting of the variances. The design of the proposed control schemes does not involve the computation of the inverse covariance matrix and, thus, it can be used in the high‐dimensional setting. The distributional properties of the control statistics are obtained and are used in the determination of the new control procedures. Within an extensive simulation study, the new approaches are compared with the multivariate EWMA control charts which are based on the Mahalanobis distance.

The impact of a random vector with variables from normal and non‐normal distributions on multivariate control charts

AbstractMultivariate control charts are widely used to simultaneously monitor several quality characteristics for detecting the mean changes in manufacturing industry processes. A multivariate Shewhart, multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) are types of multivariate control charts which have been discussed extensively. For those control charts, a multivariate normal distribution is an important assumption that is used to describe a behavior of a set of quality characteristics. However, sometimes the normal assumption is violated. This research explores the sensitivity of an average run length (ARL), the standard deviation of run length (SDRL) and the shape of distribution of run length for multivariate Shewhart, MEWMA, and MCUSUM control charts when the distribution of some quality characteristics (or variables) in a random vector are not normal. The results show how robust or sensitive multivariate control charts are to violations of the multivariate normal assumption.

Controlling the conditional false alarm rate for the MEWMA control chart

An integral part of the design of control charts, including the multivariate exponentially weighted moving average (MEWMA) control chart, is the determination of the appropriate control limits for prospective monitoring. Methods using Markov chain analyses, integral equations, and simulation have been proposed to determine the MEWMA chart limits when the limits are based on a specified in-control average run length (ARL) value. A drawback of the usual approach is that the conditional false alarm rate (CFAR) for these charts varies over time in what might be in an unexpected and undesirable way. We define the CFAR as the probability of a false alarm given no previous false alarm. We do not condition on the results of a Phase I sample, as done by others, in studies of the effect of estimation error on control chart performance. We propose the use of dynamic probability control limits (DPCLs) to keep the CFAR constant over time at a specified value. The CFAR at any time, however, could be controlled to be any specified value using our approach. Using simulation, we determine the DPCLs for the MEWMA control chart being used to monitor the mean vector with an assumed known variance-covariance matrix. We consider cases where the sample size is both fixed and time-varying. For varying sample sizes, the DPCLs adapt automatically to any change in the sample size distribution. In all cases, the CFAR is held closely to a fixed value and the resulting in-control run length performance follows closely to that of the geometric distribution.

An MEWMA control chart based on multivariate Poisson distribution data

Count data appears widely in finance, biomedical science, psychology, actuarial insurance, road safety and many other areas of life, and it is often multivariate. In this paper, we consider using the multivariate exponentially weighted moving average (MEWMA) control chart method to monitor count data under the assumption of multivariate Poisson distribution, which is derived by He [1] from another form of multivariate gamma distribution. We illustrate the proposed scheme by numerical simulation. In this paper, we provide two tables of average run length (ARL) values of the MEWMA control chart with different parameter shifts. The performance of the proposed control chart is evaluated by the ARL, given a parameter shift occurred, which is able to deliver satisfactory control efficiency.

A generalized exponentially weighted moving average control chart for monitoring autocorrelated vectors

With recent advancement in automation and data acquisition technologies, a number of quality variables are often measured at high frequency and thus are likely to be autocorrelated. The multivariate exponentially weighted moving average (MEWMA) control chart with a scalar smoothing parameter has been widely suggested for monitoring autocorrelated vectors, owing to its simplicity. However, the use of a scalar smoothing parameter cannot take the correlation structure of variables into account, which in turn could deteriorate the detection performance of MEWMA control charts. Motivated by this, we generalize the MEWMA chart for monitoring autocorrelated vectors by using a weight matrix instead of a scalar smoothing parameter. The weight matrix is expected to have non-zero off-diagonal elements in order to make use of the correlation structure of the variables. The comparison results show that the generalized MEWMA chart can outperform the traditional MEWMA chart under a majority of shift directions, although it complicates the chart design to some extent.

Quality Control of Water Production Process Using Multivariate Control Charts

Water is very important for life, no life in the world can exist without the availability of water. Turbidity, organic substance, and chlorine residual are the main characteristics of water quality. To monitor the quality of a water production process, Multivariate Exponentially Weighted Moving Covariance Matrix (MEWMC) control chart is used for monitoring the stability of the covariance matrix of a process, and Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is used for monitoring the stability of the mean vector of a process. In this study, the optimum λ for the MEWMC and MEWMA control chart for the water production process during the dry season and the rainy season is λ = 0.1. The variability of water production process during both dry and rainy seasons is in control, while the mean of water production process during both dry and rainy seasons is not in control. Based on the analysis of process capability, it is known that the water production process during the dry season and rainy season is capable of producing water with turbidity level that meets the specification limit, but is not capable to produce water with organic substance and chlorine residual that matches the specification limit.

PENERAPAN METODE PENGENDALIAN KUALITAS MEWMA BERDASARKAN ARL DENGAN PENDEKATAN RANTAI MARKOV (Studi Kasus: Batik Semarang 16, Meteseh)

An industrial company requires quality control to maintain quality consistency from the production results so that it is able to compete with other companies in the world market. In the industrial sector, most processes are influenced by more than one quality characteristic. One tool that can be used to control more than one quality characteristic is the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. The graph is used to determine whether the process has been controlled or not, if the process is not yet controlled, the next analysis that can be used is to use the Average Run Length (ARL) with the Markov Chain approach. The markov chain is the chance of today's event is only influenced by yesterday's incident, in this case the chance of the incident in question is the incident in getting a sampel of data on the production process of batik cloth to get a product that is in accordance with the company standards. ARL is the average number of sample points drawn before a point indicates an uncontrollable state. In this study, 60 sample data were used which consisted of three quality characteristics, namely the length of the cloth, the width of the cloth, and the time of the fabric for the production of written batik in Batik Semarang 16 Meteseh. Based on the results and discussion that has been done, the MEWMA controller chart uses the λ weighting which is determined using trial and error. MEWMA control chart can not be said to be stable and controlled with λ = 0.6, after calculating, the value is obtained Upper Control Limit (BKA) of 11.3864 and Lower Control Limit (BKB) of 0. It is known that from 60 data samples there is a Tj2 value that comes out from the upper control limit (BKA) where the amount of 15.70871, which indicates the production process is not controlled statistically. Improvements to the MEWMA controller chart can be done based on the ARL with the Markov Chain approach. In this final project, the ARL value used is 200, the magnitude of the process shift is 1.7 and the r value is 0.28, where the value of r is a constant obtained on the r parameter graph. The optimal MEWMA control chart based on ARL with the Markov Chain approach can be said to be stable and controlled if there is no Tj2 value that is outside the upper control limit (BKA). The results of the MEWMA control chart based on the ARL with the Markov Chain approach show that the process is not statistically capable because the MCpm value is 0.516797 and the MCpmk value is 0.437807, the value indicates a process capability index value of less than 1. Keywords: Handmade batik, Multivariate Exponentially Weighted Moving Average (MEWMA), Average Run Length (ARL), Capability process.

Monitoring Blockchain Cryptocurrency Transactions to Improve the Trustworthiness of the Fourth Industrial Revolution (Industry 4.0)

A completely new economic system is required for the era of Industry 4.0. Blockchain technology and blockchain cryptocurrencies are the best means to confront this new trustless economy. Millions of smart devices are able to complete transparent financial transactions via blockchain technology and its related cryptocurrencies. However, via blockchain technology, internet-connected devices may be hacked to mine cryptocurrencies. In this regard, monitoring the network of these blockchain-based transactions can be very useful to detect the abnormal behavior of users of these cryptocurrencies. Therefore, the trustworthiness of the transactions can be assured. In this paper, a novel procedure is proposed to monitor the network of blockchain cryptocurrency transactions. To do so, a hidden Markov multi-linear tensor model (HMTM) is utilized to model the transactions among nodes of the blockchain network. Then, a multivariate exponentially weighted moving average (MEWMA) control chart is applied to the monitoring of the latent effects. Average run length (ARL) is used to evaluate the performance of the MEWMA control chart in detecting blockchain network anomalies. The proposed procedure is applied to a real dataset of Bitcoin transactions.

Construction of Bivariate Copulas on a Multivariate Exponentially Weighted Moving Average Control Chart

The control chart is an important tool in multivariate statistical process control (MSPC), which for monitoring, control, and improvement of the process control. In this paper, we propose six types of copula combinations for use on a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. Observations from an exponential distribution with dependence measured with Kendall's tau for moderate and strong positive and negative dependence (where ) among the observations were generated by using Monte Carlo simulations to measure the Average Run Length (ARL) as the performance metric and should be sufficiently large when the process is in-control on a MEWMA control chart. In this study, we develop an approach performance on the MEWMA control chart based on copula combinations by using the Monte Carlo simulations.The results show that the out-of-control (ARL1) values for were less than for in almost all cases. The performances of the Farlie-Gumbel-Morgenstern×Ali-Mikhail-Haq copula combination was superior to the others for all shifts with strong positive dependence among the observations and . Moreover, when the magnitudes of the shift were very large, the performance metric values for observations with moderate and strong positive and negative dependence followed the same pattern.

KOMPUTASI METODE MULTIVARIATE EXPONENTIALLY WEIGHTED MOVING AVERAGE (MEWMA) UNTUK PENGENDALIAN KUALITAS PROSES PRODUKSI MENGGUNAKAN GUI MATLAB (STUDI KASUS: PT. Pismatex Textile Industry Pekalongan)

Control chart is one of the effective statistical tools to overcome the problem of process quality in a production. Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is an effective quality control tool in processes with more than one variable and correlated (multivariate). The MEWMA control chart has a weight value (λ) which makes this chart more sensitive in detecting small shifts process mean. The weight (λ) has values ranging from 0 to 1 ( ), where this weight will be given to each data. The MEWMA control chart in this study was used to form a control chart by the product defects percentage of grade B and grade B at PT. Pismatex Textile Industry Pekalongan. In this study, GUI Matlab was formed to assist the computational process in forming MEWMA control charts to control the quality of production at PT. Pismatex Textile Industry Pekalongan. Based on the result, the optimal weight is obtained at the weight value λ = 0.9. Keywords: Multivariate Exponentially Weighted Moving Average (MEWMA), Weight (λ), GUI Matlab, Percentage of product defects.

MEWMA charts when parameters are estimated with applications in gene expression and bimetal thermostat monitoring

Multivariate exponentially weighted moving average (MEWMA) control charts for individual monitoring require a priori knowledge of the in-control parameters. In practice, this assumption is not always tenable, and estimated parameters are generally obtained from an in-control reference sample of m preliminary observations (Phase I sample). Here, we compared the Phase II performance of MEWMA control charts using different methods for estimating the covariance matrix when the in-control covariance structure is unknown, and only a small Phase I sample is available. The performance of the MEWMA control charts varied among the methods. For simulated data with small m, the performance of MEWMA control charts using a shrinkage estimate of the covariance matrix was superior (in terms of run-length properties) to the alternative methods considered in this study. The improved performance of MEWMA control charts using the shrinkage estimate was also demonstrated via illustrative case studies of bimetal thermostat and gene expression applications; changes were detected earlier by the shrinkage-based MEWMA method

GRAFIK PENGENDALI MULTIVARIATE EXPONENTIALLY WEIGHTED MOVING COVARIANCE MATRIX (MEWMC) PADA DATA SAMPEL ZAT KANDUNGAN BATU BARA (Studi Kasus : PT Bukit Asam (Persero) Tbk. Tahun 2016)

The progress of industrial business in the midst of global competition increased rapidly. A businessman should have special treatment for their products to compete of market quality. The quality of product is an important factor in choosing a product or service, particularly for the costumers. In technological development, the factors of failure in the product can be minimized by Statistical Quality Control. Besides to reducing diversity in product characteristics, statistical quality control can increase business income. The data source of this research is sekunder sample data of coal products of PT Bukit Asam (Persero) Tbk. with seven variables, the variables is Total Moisture (TM), Inherent Moisture (IM), Ash Content (ASH), Volatile Matter (VM), Fixed Carbon (FC), Total Sulfur (TS), and Calorific Value (CV). The analytical method is the controlling chart of Multivariate Exponentially Weighted Moving Covariance Matrix (MEWMC) which is one of the multivariate charts that serves to detect small shift in covariance matrix and the development of Multivariate Exponentially Weighted Moving Average (MEWMA) charts. Based on the results of the analysis, the MEWMA control chart is statistically controlled with a weighting value λ=0,2 while the MEWMC chart with λ=0,2 is not controlled statistically and detected small shift in covariance matrix . In a controlled process, the capability value of multivariate process is 0,83222 < 1 which means the process is not capable.Keywords: MEWMA control chart, MEWMC control chart, Process capability analysis.

PENGENDAIAN MULTIVARIATE DENGAN DIGRAM KONTROL MEWMA ENGGUNAKAN METODE SIX SIGMA (STUDI KASUS PT FUMIRA SEMARANG TAHUN 2019)

As one of the biggest corrugation producing industries, PT Fumira Semarang is always required to fulfill customer needs by continuously improving their quality. Galvanized Steel is the raw material for the production of corrugation at PT Fumira Semarang. There are three important quality characteristics to be controlled in order that the results of galvanized steel production fit the standards to be manufactured as corrugation are waves, rust, and scratches. Six Sigma is a method for controlling quality. Six Sigma has focus on reducing defects, by standard 3,4 defects per one million opportunties. This research aims to identify the galvanized steel production process using Six Sigma method with MEWMA control chart and the capability of the process to fit the standards. Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is a tool used to control multivariate process averages. The result of this research are MEWMA control chart with lambda 0.7 shows that the process is controlled statistically and The Sigma value for waves is 2,33, for rust 2,05, and for scratches 2,64. And the research reveals the galvanized steel production process has not fit to the standard because the process capabilty index is 0,2805. Keywords: Galvanized Steel, Quality Control, Six Sigma, Multivariate Exponentially Weighted Moving Average, Process Capability Analysis

The efficiency of constructed bivariate copulas for MEWMA and Hotelling’s T2 control charts

A multivariate exponentially weighted moving average (MEWMA) and Hotelling’s T2 control charts are types of multivariate control charts for monitoring the mean vector. In this paper, we propose an efficient construction of bivariate copulas on MEWMA and Hotelling’s T2 control charts. Observations are classified with Kendall’s tau values as weak, moderate, and strong positive dependence by using a Monte Carlo simulation to measure the average run length as a performance metric. The numerical results obtained from the simulation show that the performances of the MEWMA and Hotelling’s T2 control charts were similar for small shifts () but the MEWMA control chart showed higher performance for moderate to large shifts.