Multioutput least square SVR-based multivariate EWMA control chart: The performance evaluation and application

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.

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.

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.

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.

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.

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.

Since multi-attribute control charts have received little attention compared with multivariate variable control charts, this research is concerned with developing a new methodology to employ the multivariate exponentially weighted moving average (MEWMA) charts for m-attribute binomial processes; the attributes being the number of nonconforming items. Moreover, since the variable sample size and sampling interval (VSSI) MEWMA charts detect small process mean shifts faster than the traditional MEWMA, an economic design of the VSSI MEWMA chart is proposed to obtain the optimum design parameters of the chart. The sample size, the sampling interval, and the warning/action limit coefficients are obtained using a genetic algorithm such that the expected total cost per hour is minimized. At the end, a sensitivity analysis has been carried out to investigate the effects of the cost and the model parameters on the solution of the economic design of the VSSI MEWMA chart.

Anomaly Detection for Compositional Data using VSI MEWMA control chart

In this paper, we review multivariate control charts designed for monitoring changes in a covariance matrix that have been developed in the last 15 years. The focus is on control charts developed for multivariate normal processes, assuming that independent subgroups of observations or independent individual observations are sampled as process monitoring proceeds. Control charts developed between 1990 and 2005 are reviewed according to the types of the control chart: multivariate Shewhart chart, multivariate CUSUM chart and multivariate EWMA chart. In addition to these developments, a new multivariate EWMA control chart is proposed. We also discuss comparisons of chart performance that have been carried out in the literature, as well as the issue of diagnostics. Some potential future research ideas are also given.

Traditional multivariate control charts such as Hotelling’s χ2 and T2 control charts are designed to monitor vectors of variable quality characteristics. However, in certain situations, data are expressed in linguistic terms and, under these circumstances, variable or attribute multivariate control charts are not suitable choices for monitoring purposes. Fuzzy multivariate control charts such as fuzzy Hotelling’s T2 could be considered as efficient tools to overcome the problems of linguistic observations. The purpose of this paper is to develop a fuzzy multivariate exponentially weighted moving average (F-MEWMA) control chart. In this paper, multivariate statistical quality control and fuzzy set theory are combined to develop the proposed method. Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling uncertain systems in industry, nature, and humanity. Through a numerical example, the performance of the proposed control chart was compared to the fuzzy Hotelling’s T2 control chart. Results indicate uniformly superior performance of the F-MEWMA control chart over Hotelling’s T2 control chart.

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.

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

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.

In many statistical process control (SPC) applications, the quality of a process or product is represented by a relationship or the so-called quality profile, between a quality characteristic and one or more explanatory variables. The process quality characteristics are sometimes measured with a reasonable degree of approximation. Often, especially when qualitative assessments arise, evaluation of quality characteristics is carried out ambiguously or using linguistic qualifiers. The fuzzy sets theory has proved to be a well-established approach for dealing with uncertainty due to the approximate measurement, ambiguity in subjective evaluations, or vagueness in linguistic variables. Our main purpose was to present and compare four methods of monitoring nonlinear fuzzy profiles, for which different nonlinear fuzzy regression modeling approaches are considered. The first two methods are “a data-driven fuzzy rule-based” and “an extended least square support vector machine (LS-SVM),” for which the profile is characterized without considering a predefined mathematical relationship. However, for the other two methods, a specific form of the profile was needed. The third method, namely “a modified fuzzy regression model,” was initially invented for linear models. Besides, the fourth method employs “the fuzzy least square method” based on linearizing transformation. The exponentially weighted moving average (EWMA) control statistic was used to derive the control statistic to be plotted on the univariate as well as multivariate control charts. An extensive simulation study was conducted to compare the performance of the methods, and the average run length (ARL) criterion was considered to assess the detect-ability of control charts against various out-of-control conditions. Our comparison results indicated that the multivariate EWMA (MEWMA) chart based on the LS-SVM method outperforms the rest in detecting process shifts with smaller values of ARL when the process undergoes out-of-control conditions.