scholarly journals THEORETICAL AND EXPERIMENTAL INVESTIGATION OF ESTIMATING CHANGE POINT IN MULTIVARIATE PROCESSES VIA SIMULTANEOUS COVARIANCE MATRIX AND MEAN VECTOR

2021 ◽  
Vol 84 (1) ◽  
pp. 85-96
Author(s):  
Alireza Firouzi ◽  
Noordin Mohd Yusof ◽  
Muhammad Hisyam Lee ◽  
Robabeh Bashiri
Keyword(s):  
Covariance Matrix ◽  
Change Point ◽  
Control Charts ◽  
Support Vector ◽  
Multivariate Techniques ◽  
Negative Effects ◽  
Statistical Process ◽  
Proposed Model ◽  
Solar Hydrogen Production ◽  
Mean Vector

The identification of change points in statistical process control (SPC) data is the critical criterion for multivariate techniques when output is out-of-control condition. Therefore, monitoring all independent variables is essential and demands targeted attention to avoid errors at the systems control stage. However, estimating change-point in multivariate control charts is the main problem when these correlated quality characteristics monitor together. Therefore, we proposed a combination of an ensemble learning-based model of artificial neural networks with support vector machines to monitor process mean vector and covariance matrix shifts simultaneously to estimate the change point in a multivariable system. The performance of the final model indicated an estimated changing point with one sample over 6,000 simulated cases with a probability of 98 percent, which is a significantly high accuracy rating. Finding suggests the outcome of the project confirms that the proposed model can provide a precise estimating the change point by monitoring the mean vector and the covariance matrix simultaneously and, helps to identify those variable(s) responsible for an out-of-control condition. For further validation of the model, the performance of the proposed model has been compared with previous reported which confirms a better performance of the proposed model. Finally, the model was applied to monitor the performance of the solar hydrogen production system and the model identify the variables which have negative effects on the performance of the system.

scholarly journals Monitoring bivariate process

2009 ◽  
Vol 29 (3) ◽  
pp. 547-562 ◽  
Author(s):  
Marcela A. G. Machado ◽  
Antonio F. B. Costa ◽  
Fernando A. E. Claro
Keyword(s):  
Covariance Matrix ◽  
Control Charts ◽  
Joint Control ◽  
Multivariate Processes ◽  
Generalized Variance ◽  
Main Drawback ◽  
The Mean ◽  
Sample Variances ◽  
Mean Vector

The T² chart and the generalized variance |S| chart are the usual tools for monitoring the mean vector and the covariance matrix of multivariate processes. The main drawback of these charts is the difficulty to obtain and to interpret the values of their monitoring statistics. In this paper, we study control charts for monitoring bivariate processes that only requires the computation of sample means (the ZMAX chart) for monitoring the mean vector, sample variances (the VMAX chart) for monitoring the covariance matrix, or both sample means and sample variances (the MCMAX chart) in the case of the joint control of the mean vector and the covariance matrix.

scholarly journals Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso

2021 ◽  
Vol 25 (1) ◽  
pp. 3-15
Author(s):  
Takumi Saruhashi ◽  
Masato Ohkubo ◽  
Yasushi Nagata
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Control Chart ◽  
Control Charts ◽  
Ewma Chart ◽  
Regularization Parameters ◽  
Multivariate Control Chart ◽  
Multivariate Control ◽  
Mean Vector ◽  
Variance Covariance Matrix

Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change. Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix. Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change. Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them. Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.

scholarly journals Monitoring the mean with least-squares support vector data description

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Edgard M. Maboudou-Tchao
Keyword(s):  
Least Squares ◽  
Statistical Process Control ◽  
Control Charts ◽  
Classification Problem ◽  
Support Vector ◽  
Support Vector Data Description ◽  
Vector Data ◽  
Statistical Process ◽  
Data Description ◽  
The Mean

Abstract: Multivariate control charts are essential tools in multivariate statistical process control (MSPC). “Shewhart-type” charts are control charts using rational subgroupings which are effective in the detection of large shifts. Recently, the one-class classification problem has attracted a lot of interest. Three methods are typically used to solve this type of classification problem. These methods include the k−center method, the nearest neighbor method, one-class support vector machine (OCSVM), and the support vector data description (SVDD). In industrial applications, like statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. In this paper, we reformulate the standard support vector data description and derive a least squares version of the method. This least-squares support vector data description (LS-SVDD) is used to design a control chart for monitoring the mean vector of processes. We compare the performance of the LS-SVDD chart with the SVDD and T2 chart using out-of-control Average Run Length (ARL) as the performance metric. The experimental results indicate that the proposed control chart has very good performance.

scholarly journals An effective multivariate control chart for detecting small mean shifts using support vector data description

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401881062 ◽  
Author(s):  
Beixin Xia ◽  
Zheng Jian ◽  
Lei Liu ◽  
Long Li
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Support Vector ◽  
Support Vector Data Description ◽  
Vector Data ◽  
Cumulative Sum ◽  
Statistical Process ◽  
Learning Abilities ◽  
Data Description ◽  
Cumulative Sum Control

Conventional multivariate cumulative sum control charts are more sensitive to small shifts than [Formula: see text] control charts, but they cannot get the knowledge of manufacturing process through the learning of in-control data due to the characteristics of their own structures. To address this issue, a modified multivariate cumulative sum control chart based on support vector data description for multivariate statistical process control is proposed in this article, which is named [Formula: see text] control chart. The proposed control chart will have both advantages of the multivariate cumulative sum control charts and the support vector data description algorithm, namely, high sensitivities to small shifts and learning abilities. The recommended values of some key parameters are also given for a better application. Based on these, a bivariate simulation experiment is conducted to evaluate the performance of the [Formula: see text] control chart. A real industrial case illustrates the application of the proposed control chart. The results also show that the [Formula: see text] control chart is more sensitive to small shifts than other traditional control charts (e.g. [Formula: see text] and multivariate cumulative sum) and a D control chart based on support vector data description.

scholarly journals Constructing a Control Chart Using Functional Data

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 58 ◽  
Author(s):  
Miguel Flores ◽  
Salvador Naya ◽  
Rubén Fernández-Casal ◽  
Sonia Zaragoza ◽  
Paula Raña ◽  
...  
Keyword(s):  
Energy Efficiency ◽  
Control Chart ◽  
Functional Data ◽  
Control Charts ◽  
Data Depth ◽  
Multivariate Techniques ◽  
Control Procedure ◽  
Statistical Process ◽  
Statistical Consultancy ◽  
And Control

This study proposes a control chart based on functional data to detect anomalies and estimate the normal output of industrial processes and services such as those related to the energy efficiency domain. Companies providing statistical consultancy services in the fields of energy efficiency; heating, ventilation and air conditioning (HVAC); installation and control; and big data for buildings, have been striving to solve the problem of automatic anomaly detection in buildings controlled by sensors. Given the functional nature of the critical to quality (CTQ) variables, this study proposed a new functional data analysis (FDA) control chart method based on the concept of data depth. Specifically, it developed a control methodology, including the Phase I and II control charts. It is based on the calculation of the depth of functional data, the identification of outliers by smooth bootstrap resampling and the customization of nonparametric rank control charts. A comprehensive simulation study, comprising scenarios defined with different degrees of dependence between curves, was conducted to evaluate the control procedure. The proposed statistical process control procedure was also applied to detect energy efficiency anomalies in the stores of a textile company in the Panama City. In this case, energy consumption has been defined as the CTQ variable of the HVAC system. Briefly, the proposed methodology, which combines FDA and multivariate techniques, adapts the concept of the control chart based on a specific case of functional data and thereby presents a novel alternative for controlling facilities in which the data are obtained by continuous monitoring, as is the case with a great deal of process in the framework of Industry 4.0.

One-sided control charts for monitoring the multivariate coefficient of variation in short production runs

2018 ◽  
Vol 41 (6) ◽  
pp. 1712-1728 ◽  
Author(s):  
Mahfuza Khatun ◽  
Michael BC Khoo ◽  
Ming Ha Lee ◽  
Philippe Castagliola
Keyword(s):  
Covariance Matrix ◽  
Process Monitoring ◽  
Coefficient Of Variation ◽  
Control Charts ◽  
Finite Horizon ◽  
New Method ◽  
The Mean ◽  
Multivariate Coefficient Of Variation ◽  
Study Process ◽  
Mean Vector

In production, it is common to deal with short production runs, where flexibility is required in the built-up of parts to produce numerous variants of manufactured goods. Monitoring the multivariate coefficient of variation (MCV) is an effective method to monitor the relative multivariate variability compared with the mean. Monitoring the relative multivariate variability is important when practitioners are not interested in the changes in the mean vector or the covariance matrix. Monitoring the univariate coefficient of variation in short production runs has already been successfully executed. In this paper, the statistical performance of one-sided charts for monitoring the MCV of a multivariate process with finite horizon is investigated. Prior to this work, no attempt has been made to study process monitoring of MCV in short production runs. Investigations are made when the exact shift size can be specified and when there is a random shift size. It is found that the proposed upward chart detects an increasing shift in the MCV quicker than its downward counterpart detects a decreasing shift, for the same shift size (from the nominal value). An example is presented to illustrate the implementation of the new method.

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