Structural damage detection using autoregressive-model-incorporating multivariate exponentially weighted moving average control chart

The multivariate exponentially weighted moving average (MEWMA) control chart, in which the smoothing parameter is a principal diagonal matrix, is established based on the assumption that the samples follow the standard normal distribution to monitor the multivariate quality characteristics. However, monitoring quality characteristics always exists in the whole process. To make the MEWMA control chart more effective, a modified multivariate exponentially weighted moving average control chart, namely practical MEWMA (PEWMA) control chart, is proposed, in which the smoothing coefficient matrix is extended to a full-rank matrix which the smoothing parameter are all not zero. Analysis of both the in-control and out-of-control statistical performance of PEWMA control chart illustrate that the average run length of PEMWA control chart is more superior to the MEWMA. Finally combined with a factory example, a minimisation cost model is constructed based on the Lorenzen-Vance economic model to optimise the parameter combination.

ABSTRACTCompared to the grid search approach to optimal design of control charts, the gradient-based approach is more computationally efficient as the gradient information indicates the direction to search the optimal design parameters. However, the optimal parameters of multivariate exponentially weighted moving average (MEWMA) control charts are often obtained by using grid search in the existing literature. Note that the average run length (ARL) performance of the MEWMA chart can be calculated based on a Markov chain model, making it feasible to estimate the ARL gradient from it. Motivated by this, this paper develops an ARL gradient-based approach for the optimal design and sensitivity analysis of MEWMA control charts. It is shown that the proposed method is able to provide a fast, accurate, and easy-to-implement algorithm for the design and analysis of MEWMA charts, as compared to the conventional design approach based on grid search.

Water treatment is intended to change the original water quality that does not fulfill the health requirements become a water for human consumption and must comply with the levels of certain parameters. Quality control can be done by forming a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. In the Multivariate Exponentially Weighted Moving Average (MEWMA) control charts with λ = 0.25 and UCL = 13.92658 seen that process controlled statistically. Once the process is under control, it can be done analysis of the ability of the process to determine whether the process fulfill the specifications or not. In the calculation process capability univariate each characteristics and multivariate process capability index values obtained more than 1 means that the process is going well. Keywords : water quality, Multivariate Exponentially Weighted Moving Average (MEWMA), process capability.

Autocorrelation leads to a bias estimator of standard control charts. It is important to develop control chart that allows autocorrelation and to evaluate its performance. The objective of this paper is to evaluate the performance of multioutput least square support vector regression (MLS-SVR)-based multivariate exponentially weighted moving average (MEWMA) control chart for monitoring multivariate autocorrelated data. For first order of vector autoregressive (VAR) and first order of vector moving average data, the proposed control chart tends to yield stable in-control average run length at about 200. The proposed control chart becomes more insensitive due to the increase of MEWMA smoothing parameter. In the real application, the proposed method is successfully applied to monitor water turbidity and chlorine residual data in the drinking water manufacturing process.

Economic designs (with or without the addition of statistical constraints) provide reasonable approaches to the problem of choosing the parameters of a control chart. For the multivariate exponentially weighted moving average (MEWMA) control chart, the optimal choice of control limit, sample size, exponential weights for past observations and sampling interval according to economic and statistical considerations is a complex problem. This paper provides an algorithm for evaluating the ARL values for the MEWMA chart through simulation and then using these results to determine the optimal chart parameters given process cost and time information.

Quality control charts have proven to be very effective in detecting out of control signals. It is very important to practitioners to determine at what point in the past the signal was initiated. If a control chart signals a change in the process parameter, identifying the time of the change will substantially help the signal diagnostics procedure since it simplifies the search for special causes. In this paper the researchers propose the observations following multivariate normal distribution. They have used multivariate exponentially weighted moving average (MEWMA) control chart to detect signals. This research provides two ways to detect the change point, first MLE, and then neural network is used to identify the time of the change in the parameters (mean) in the past. The researchers intended to assess the performance of two approaches and compare them through computer simulation experiments. The results show that neural network performs effectively and equally well for the whole process dimensions. Thus, the neural network provides process engineers with an accurate and useful estimate of the actual time of the change in the process mean.

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.

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.

This study proposes novel framework to enhance statistical process control (SPC) of water quality by addressing the pervasive issue of autocorrelation in time-series data. We investigate the characteristics of pH, turbidity, and KMnO₄ in Surabaya city's water, revealing significant autocorrelation that compromises statistical independence assumption crucial for reliable SPC. To overcome this, Generative Adversarial Network (GAN) model was developed to generate decorrelated residual time-series. The efficacy of GAN model in reducing autocorrelation was quantitatively validated, achieving Mean Squared Error (MSE) of 0.0054, Root Mean Squared Error (RMSE) of 0.0738, and Mean Absolute Error (MAE) of 0.0556. Subsequently, these GAN-derived residuals were integrated into Multivariate Exponentially Weighted Moving Average (MEWMA) control chart for process monitoring. Phase I analysis detected 33 out-of-control signals; after identifying and removing outliers, process was brought under statistical control with no further out-of-control signals detected. However, subsequent Phase II online monitoring detected eight statistically significant out-of-control signals, indicating a potential loss of process stability over time. Our findings underscore the significant utility of GAN-based residual analysis as a robust strategy for mitigating autocorrelation effects in environmental water quality data. This approach leads to improved process monitoring and enables early anomaly detection, crucial for proactive water quality management.

ABSTRACTProfile monitoring is one of the new research areas in statistical process control. Most of the control charts in this area are designed with fixed sampling rate which makes the control chart slow in detecting small to moderate shifts. In order to improve the performance of the conventional fixed control charts, adaptive features are proposed in which, one or more design parameters vary during the process. In this paper the variable sample size feature of EWMA3 and MEWMA schemes are proposed for monitoring simple linear profiles. The EWMA3 method is based on the combination of three exponentially weighted moving average (EWMA) charts for monitoring three parameters of a simple linear profile separately and the Multivariate EWMA (MEWMA) chart is based on the using a single chart to monitor the coefficients and variance of a general linear profile. Also a two-sided control chart is proposed for monitoring the standard deviation in the EWMA3 method. The performance of the proposed charts is compared in terms of the average time to signal. Numerical examples show that using adaptive features increase the power of control charts in detecting the parameter shifts. Finally, the performance of the proposed variable sample size schemes is illustrated through a real case in the leather industry.

The multivariate exponentially weighted moving average (MEWMA) control chart is a control charting scheme that uses weighted averages of previously observed random vectors to monitor the mean vector of a process. The in-control average run length (ARL) for the MEWMA control chart can be expressed as the solution of an integral equation. We give a FORTRAN program that uses the quadrature method to approximate the solution of this integral equation. The program can be used to obtain either the in-control ARL for a given value of the upper control limit or the appropriate upper control limit for a desired in-control ARL.

This article is concerned with the effect of the methods for handling missing values in multivariate control charts. We discuss the complete case, mean substitution, regression, stochastic regression, and the expectation–maximization algorithm methods for handling missing values. Estimates of mean vector and variance–covariance matrix from the treated data set are used to build the multivariate exponentially weighted moving average (MEWMA) control chart. Based on a Monte Carlo simulation study, the performance of each of the five methods is investigated in terms of its ability to obtain the nominal in-control and out-of-control average run length (ARL). We consider three sample sizes, five levels of the percentage of missing values, and three types of variable numbers. Our simulation results show that imputation methods produce better performance than case deletion methods. The regression-based imputation methods have the best overall performance among all the competing methods.

Anomaly Detection for Compositional Data using VSI MEWMA control chart

A control chart is one of the statistical process techniques that is used to monitor different processes. Some processes are characterized by functions or profiles, and a profile is a functional relationship between the dependent and independent variable(s) used to monitor the quality of the process. Several research studies were conducted on linear profiling where only fixed effects are considered. However, in this research, we focus on random effects as they represent the differences between profiles and thus are more proper for interpretation. Two approaches are proposed in this study for Phase II profile monitoring; the first approach is the nonparametric via residuals and the second is the semiparametric approach, where this technique combines the parametric estimates with a portion of the nonparametric estimates to the residuals. Usually, parametric estimations lead to biased estimates when the model is misspecified, whereas nonparametric estimates may give high variances, and thus semiparametric estimates are preferred. New nonparametric and semiparametric multivariate exponential weighted moving average (MEWMA) control charts are introduced and their performances compared to the parametric approach for different samples and shift sizes, and the correlation between and within profiles was considered. The average run length (ARL) and average time to signal (ATS) criteria are used for choosing the best approach. Simulation studies and real datasets were utilized for comparing the performance of the proposed MEWMA charts.

ABSTRACTIn this article, we assess the performance of the multivariate exponentially weighted moving average (MEWMA) control chart with estimated parameters while considering the practitioner-to-practitioner variability. We evaluate the chart performance in terms of the in-control average run length (ARL) distributional properties; mainly the average (AARL), the standard deviation (SDARL), and some percentiles. We show through simulations that using estimates in place of the in-control parameters may result in an in-control ARL distribution that almost completely lies below the desired value. We also show that even with the use of larger amounts of historical data, there is still a problem with the excessive false alarm rates. We recommend the use of a recently proposed bootstrap-based design technique for adjusting the control limits. The technique is quite effective in controlling the percentage of short in-control ARLs resulting from the estimation error.