Multivariate Exponentially Weighted Moving Average Research Articles

A condition monitoring approach of multi-turbine based on VAR model at farm level

A multi-turbine condition monitoring method using supervisory control and data acquisition (SCADA) data for large-scale wind farm is proposed. The method takes the difference between the SCADA data of each turbine with the median of other remaining turbines, and establishes condition vector consisting of the differences. Considering the autocorrelation of turbine SCADA data, vector autoregression (VAR) model is used to remove the autocorrelation in the condition vector of wind farm. Hotelling and multivariate exponentially weighted moving average (MEWMA) control chart are applied to monitor the residual vector. An industrial wind farm example is given to illustrate the proposed method. Compared with the existing turbine condition monitoring charts, the false alarm of proposed method is reduced for considering the autocorrelation of operation data, and monitoring strategy using MEWMA improves detected rate and expedites alarm time compared with Hotelling. The proposed method realizes monitoring multiple turbines simultaneously in farm by a fault indicator, which has important theoretical and engineering significance to the practical operations and maintenance activities in large-scale wind farm.

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

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.

Effects of economic policy uncertainty shocks on the interdependence between Bitcoin and traditional financial markets

This paper analyses the effects of economic policy uncertainty (hereafter, EPU) on the relationship between Bitcoin and traditional financial markets during the period 27/04/2015 to 25/10/2018, represented by five stock market indices namely the NASDAQ100, S&P500, Euronext100, FTSE100 and NIKKEI225. EPU is measured in terms of economic policy, monetary policy, financial regulation, taxation policy, and the news-based policy uncertainty index for the U.S., U.K., Europe and Japan. By applying a variety of statistical techniques (multivariate EWMA models, Spearman’s rho, the Diebold and Yilmaz (2012) spill-over index, GAS models with conditional multivariate Student–t distribution and time–varying scales and correlations, BVAR models with the Litterman/ Minnesota priors and nonlinear impulse responses with local projections accounting for different regimes in uncertainty) we estimate interdependence between traditional financial and Bitcoin markets and their reaction to the selected policy shocks. Our findings indicate the investment attractiveness of bitcoin as a hedging tool against shocks in uncertainty in the USA economic policy.The results are significant and potentially useful to researchers, practitioners, and Bitcoin market participants to better understand the nature of Bitcoin and facilitate better portfolio and risk-management decisions.

An improved process monitoring by mixed multivariate memory control charts: An application in wind turbine field

Memory control chart such as multivariate CUSUM (MCUSUM) and multivariate EWMA (MEWMA) control charts are considered superior for the detection of small-to-moderate variation in the process mean vector. In this article, we have proposed two advanced forms of memory multivariate charts to identify the small amount of shifts in the process mean vector. The proposed control charts methodologies are based on the mixed features of the MCUSUM, MEWMA, classical EWMA chart, and chart based on principal component analysis. Monte Carlo simulation technique is used to simulate numerical results. To evaluate the performance of proposed control charts, we have used average run length for a single shift, extra quadratic loss function, relative average run length, and performance comparison index measures for certain range of shifts for overall performance. Results elaborate that proposed charts have outstanding performance for detection of small shifts in mean vector as compared to the various existing such as MCUSUM, MEWMA, etc. charts. For practical purpose, implementation of the proposed control charts with a real-life data in the field of wind turbine has included to make clear the advantages of proposed control chart(s) over other control charts for early detection of shifts.

누적결합방법을 적용한 다변량 정규공정을 위한 다변량 지수가중이동평균 관리도

누적결합방법을 적용한 다변량 정규공정을 위한 다변량 지수가중이동평균 관리도

Modern multivariate control chart using spatial signed rank for non-normal process

Modern multivariate control charts that use spatial signed rank are sensitive to the detection of small shifts under non-normal or gamma distributions. In this paper, Monte Carlo simulation is used to compare the performances of multivariate control charts based on the average run length. The results show that the spatial signed-rank multivariate exponentially weighted moving average (SSRM) control chart outperforms the multivariate exponentially weighted moving average (MEWMA) control chart, the double-MEWMA control chart, and the spatial signed-rank double multivariate exponentially weighted moving average control chart when detecting small shifts in the process mean. SSRM is appropriate for data from a non-normal distribution, which is valuable for the manufacturing industry when detecting waste. Moreover, SSRM is an excellent method suitable for most industrial processes, and therefore, is a very powerful tool.

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.

A Comparative Analysis of Bootstrap Multivariate Exponentially-Weighted Moving Average (BMEWMA) Control Limits

In the manufacturing and service industries, multivariate statistical quality control charts are mostly used to determine whether a process is performing as intended or if there are some special causes resulting in the variation of an overall statistics. Normally, control charts are obtained under the assumption that the variable under study follows some form of parametric distribution. When this assumption is violated, the performance of such control chart often gives false alarm signals. To address this problem, the Multivariate Exponential Weighted Moving Average (MEWMA) control limits have been proposed in existing literature. This article focuses on reviewing this existing method with a view to developing a novel approach based on the use of bootstrap. Results from a performance study shows that the proposed method enables the setting of control limits that can enhance the easy detection of out of control signals.

Multivariate syndromic surveillance for cattle diseases: Epidemic simulation and algorithm performance evaluation

Multivariate Syndromic Surveillance (SyS) systems that simultaneously assess and combine information from different data sources are especially useful for strengthening surveillance systems for early detection of infectious disease epidemics. Despite the strong motivation for implementing multivariate SyS and there being numerous methods reported, the number of operational multivariate SyS systems in veterinary medicine is still very small. One possible reason is that assessing the performance of such surveillance systems remains challenging because field epidemic data are often unavailable. The objective of this study is to demonstrate a practical multivariate event detection method (directionally sensitive multivariate control charts) that can be easily applied in livestock disease SyS, using syndrome time series data from the Swiss cattle population as an example. We present a standardized method for simulating multivariate epidemics of different diseases using four diseases as examples: Bovine Virus Diarrhea (BVD), Infectious Bovine Rhinotracheitis (IBR), Bluetongue virus (BTV) and Schmallenberg virus (SV). Two directional multivariate control chart algorithms, Multivariate Exponentially Weighted Moving Average (MEWMA) and Multivariate Cumulative Sum (MCUSUM) were compared. The two algorithms were evaluated using 12 syndrome time series extracted from two Swiss national databases. The two algorithms were able to detect all simulated epidemics around 4.5 months after the start of the epidemic, with a specificity of 95%. However, the results varied depending on the algorithm and the disease. The MEWMA algorithm always detected epidemics earlier than the MCUSUM, and epidemics of IBR and SV were detected earlier than epidemics of BVD and BTV. Our results show that the two directional multivariate control charts are promising methods for combining information from multiple time series for early detection of subtle changes in time series from a population without producing an unreasonable amount of false alarms. The approach that we used for simulating multivariate epidemics is relatively easy to implement and could be used in other situations where real epidemic data are unavailable. We believe that our study results can support the implementation and assessment of multivariate SyS systems in animal health.

Control charts for monitoring two-dimensional spatial count data with spatial correlations

The quality characteristic of some manufacturing processes is represented by two-dimensional (2D) spatial count data in which spatial correlations are commonly observed. Statistical process control (SPC) is important and challenging for monitoring such kind of data. However, there is a scarcity of methods for monitoring spatial count data in SPC. In this paper, we integrate an intrinsic Gaussian Markov random field (IGMRF) with the hierarchical Bayesian model for modelling 2D spatial count data. Then, we adopt the Markov chain Monte Carlo (MCMC) method to tackle the issue of hierarchical model parameter estimation. Moreover, based on the estimates, we develop corresponding monitoring schemes utilizing the multivariate exponentially weighted moving average (MEWMA) procedure to detect shifts in the general trend and the spatial correlation. Extensive numerical results are presented with regard to the performance of the proposed schemes for detecting changes in the coefficient and the random spatial error. Finally, a real example from the wafer manufacturing process is used to illustrate the implementation and effectiveness of the proposed approach.

Memory‐type multivariate charts with fixed and variable sampling intervals for process mean when covariance matrix is unknown

AbstractMemory‐type multivariate charts have been widely recognized as a potentially powerful process monitoring tool because of their excellent speed in detecting small‐to‐moderate shifts in the mean vector of a multivariate normally distributed process, namely, the multivariate EWMA (MEWMA), double MEWMA, Crosier multivariate CUSUM (MCUSUM), and Pignatiello and Runger MCUSUM charts. These multivariate charts are based on the assumption that the covariance matrix is known in advance; but, it may not be known in practice. It is thus not possible to use these multivariate charts unless a large Phase I dataset is available from an in‐control process. In this paper, we propose multivariate charts with fixed and variable sampling intervals for the process mean vector when the covariance matrix is estimated from sample. Using the Monte Carlo simulation method, the run length characteristics of the multivariate charts are computed. It is shown that the in‐control and out‐of‐control run length performances of the proposed multivariate charts are robust to the changes in the process covariance matrix, while the existing multivariate charts are not. A real dataset is taken to explain the implementation of the proposed multivariate charts.

A novel approach based on multiple correspondence analysis for monitoring social networks with categorical attributed data

ABSTRACTIn in most cases, the distribution of communications is unknown and one may summarize social network communications with categorical attributes in a contingency table. Due to the categorical nature of the data and a large number of features, there are many parameters to be considered and estimated in the model. Hence, the accuracy of estimators decreases. To overcome the problem of high dimensionality and unknown communications distribution, multiple correspondence analysis is used to reduce the number of parameters. Then the rescaled data are studied in a Dirichlet model in which the parameters should be estimated. Moreover, two control charts, Hotelling’s T2 and multivariate exponentially weighted moving average (MEWMA), are developed to monitor the parameters of the Dirichlet distribution. The performance of the proposed method is evaluated through simulation studies in terms of average run length criterion. Finally, the proposed method is applied to a real case.

New Robust MEWMA Control Chart for Monitoring Contaminated Data

Multivariate Exponential Weighted Moving Average (MEWMA), E2 control chart is a popular multivariate control chart for monitoring the stability of time series data (non-random pattern). However, in this paper, we have shown that the existing MEWMA, E2 control chart is sensitive in contaminated data or in the presence of outliers. To address this problem, this paper proposed an alternative MEWMA E2 control chart using robust mean vector and covariance matrix instead of the classical mean vector and covariance matrix respectively. The classical mean vector in MEWMA E2 control chart is replaced by Winsorized Modified One-step M-estimator (WM) while the classical covariance matrix is replaced by the Winsorized covariance matrix. The proposed MEWMA E2 control chart known as robust MEWMA control chart, denoted as RE2 control chart. The control limit for the RE2 control chart was calculated based on simulated data. The performance of RE2 and existing MEWMA E2 control charts are based on the false alarm rate. The result revealed that the RE2 control chart is more effective in controlling false alarm rates as compared to the existing MEWMA, E2 control chart. The zinc-lead flotation data show that the RE2 performs better in application

Change point detection in social networks using a multivariate exponentially weighted moving average chart

Although the significant role of social networks in communications between individuals has attracted researchers’ attention to the social networks, only few authors investigated social network monitoring in their studies. Most of the existing studies in this context suffer from the following three main drawbacks: (1) using the case-based network attributes such as person experiences and departments instead of the main attributes such as network density and centrality attributes, (2) monitoring the social attributes separately with the assumption that they are independent of each other and (3) ignoring detection of real time of change in the network. To overcome the above-mentioned disadvantages, this research develops a statistical method for monitoring the connections among actors in the social networks with the four most important network attributes consisting of (1) network density, (2) degree centrality, (3) betweenness centrality and (4) closeness centrality. To this end, a multivariate exponentially weighted moving average (MEWMA) control chart is used for simultaneous monitoring of these four correlated attributes. Furthermore, since the control chart usually does not alert a signal in the exact time of change due to type II error, this study presents a change point detection method to reduce cost and time required for diagnosing the control chart signal. Eventually, the efficiency of the proposed approach in comparison with the existing methods is evaluated through a simulation procedure. The results indicate that the suggested method has better performance than the univariate approach in detecting change point.

Automatic extraction and integration of behavioural indicators of malware for protection of cyber–physical networks

Abstract Conventional isolated cyber–physical systems (CPS) based industrial networks are increasingly being integrated with modern corporate information technology (IT) network. Therefore, cyber-attacks on CPS are increasing enormously and this could result in a massive damage to the machines themselves or the humans who interact with them. Malware has been one of the major source of attacks and threats to the CPS networks and computer systems. The high growth and the variety of malware variants such as Internet worms, Trojan horses and computer viruses requires periodic update of the database. Traditional malware system fulfil this requirement by manual effort from the experts though signature generation. However manual update could result into potential drawback for integrity and availability of services provided by CPS systems and protection in real-time. Machine learning technique is a natural choice to address the malware challenge for CPSs, since it can easily model and discover the underlying patterns from large-scale data sets. This paper introduces intelligent models and algorithms that can extract behavioural features and inherent attack patterns from the existing malware data, then integrates the behavioural indicators into the detection system. The main contribution of the paper is that the proposed models do not require periodic manual effort to update the database of the detection engine. We have introduced semi-supervised models using unsupervised learning including independent component analysis (ICA), global K-means clustering and multivariate exponentially weighted moving average (MEWMA) for extracting behavioural indicators which clusters the malware. Then the extracted geometric information of the clusters and hoteling T 2 of the behavioural indicators from MEWMA are incorporated into the database of existing detection system which are used with support vector machine (SVM) based supervised system. This enables the detection system to update the dynamic behavioural patterns of new malware automatically. The performances of developed semi-supervised models have been verified using malware data for both static and dynamic characteristics of malware. The summary of our experimental results demonstrate that the combination of unsupervised and supervised learning can successfully extracts behavioural indicators automatically from new malware. Performance comparison from experimental results summarize that the semi-supervised models can detect more accurately than the existing supervised models where accuracies are increased up to 100% for SVM and random forest based semi-supervised models.

Linear profiles monitoring in the presence of nonnormal random errors

AbstractProfile monitoring is a technique to test the stability of the relationship between a response variable and explanatory variables over time. The most relevant linear profile monitoring methods have been constructed using the normality assumption. However, the normality assumption could be violated in many quality control applications. In this study, we consider a situation in which the random errors in a linear profile model follow a skew‐normal distribution. The skew‐normal distribution is a generalized version of the normal distribution. A new Shewhart‐type chart and exponentially weighted moving average (EWMA) chart, named the ShewhartR and EWMAR charts, respectively, are constructed based on residuals to monitor the parameters of linear profile model. The simulation results show that the multivariate EWMA chart is sensitive to the normality assumption and that the proposed ShewhartR and EWMAR charts have good ability to detect big and small‐to‐moderate process shifts, respectively. An example using photo mask techniques in semiconductor manufacturing is provided to illustrate the applications of the ShewhartR and EWMAR charts.

Phase II Monitoring of Generalized Linear Profiles Under Different Types of Changes

Various control charts have been proposed to monitor generalized linear profiles in Phase II. However, robustness of the proposed methods in detecting different types and especially different directions of changes is not well-studied in the literature. In real-world applications different kinds of changes such as drift and multiple change are likely to happen which can be isotonic (increasing) or antitonic (decreasing). This paper studies the robustness of Rao Score Test (RST) method, T2, and multivariate exponential weighted moving average (MEWMA) in different types, drift and multiple, and directions of changes. Rao Score Test method also benefits from a change-point detection approach whose performance is studied as well. According to the results, generally RST method shows a better performance in detecting different types of changes. Moreover, the performance of the RST method is robust to direction of the change, while T2 and MEWMA are not ARL-unbiased and show different performances under isotonic and antitonic changes. Therefore, to address this issue, we proposed a bias-reduced estimator to be used in T2. Our results demonstrate that the proposed control chart outperforms T2 and is less biased than T2. Finally, a real-world problem is presented in which aforementioned methods are applied to real data.

A spatial rank–based multivariate EWMA chart for monitoring process shape matrices

AbstractIn this article, we propose a nonparametric EWMA control chart for monitoring the shape matrix of a multivariate process based on a spatial rank test and the exponentially weighted moving average scheme. The proposed control chart is essentially developed using an estimated spatial rank covariance matrix to test the shape matrix of the covariance matrix of multivariate distributions with heavy tails. Based on our simulation studies, the proposed control chart outperforms the only existing nonparametric control chart in many practical out‐of‐control scenarios for monitoring the shape matrix of the covariance matrix of many multivariate processes. Further, we point out the weaknesses of both the nonparametric EWMA control charts for monitoring the shape matrix of multivariate processes in real applications and propose one possible method to overcome these weaknesses. We also use an example from a white wine production process to demonstrate the applicability and implementation of the proposed control chart.

PENERAPAN PENGENDALIAN KUALITAS DENGAN MEWMA DAN FUNGSI DENSITAS KERNEL MULTIVARIAT (Studi Kasus: PT Sukorejo Indah Textile Kab. Batang)

In an era of industrial revolution 4.0, technology is increasingly sophisticated, requiring companies to be more creative. Product quality control is an effort to minimize the defective products produced by the company. The production of weaving sarongs at PT SUKORINTEX pays attention to the accuracy of the length and width of the sarong to conform to the standards set by the company. To find out the quality of woven sarong products at PT SUKORINTEX, analysis was performed using Multivariate Exponentially Weighted Moving Average (MEWMA) control charts and multivariate kernel control charts. The research variable was the characteristics of the X sarongs which is reflected in 2 variates, namely the average length and average width. Based on the results and discussion that has been done, the MEWMA control chart used a weighting λ which is determined using trial and error. MEWMA control charts can be said to be stable and controlled by λ = 0.1, Upper Control Limit (UCL) of 14.62943, and Lower Control Limit (LCL) of 0. Multivariate kernel control chart were declared uncontrolled with α = 0.1 and level = 0.06130611 because there were data that was outside the contour. Chart improvement was done by trial and error and obtained a controlled chart results at α = 0.01 and a level value of 0.03125701. Based on this case study, the quality control of the average length and width of WADIMOR woven sarong types 30 STR with MEWMA is better than the multivariate kernel density, because MEWMA is controlled and stable in controlling product quality. The results of the MEWMA control chart show a capable process because more than 1 process capability index value is obtained. Keywords: Multivariate Exponentially Weighted Moving Average (MEWMA) control chart, multivariate kernel control chart, process capability.