Monitoring Highly Correlated Multivariate Processes Using Hotelling's <i>T</i><sup>2</sup> Statistic: Problems and Possible Solutions

Sparks, Ross

doi:10.1002/qre.1656

Cited by 7 publications

(11 citation statements)

References 46 publications

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“…3 and 4 fall into Category II of the seven OC matrices, where the shifts occur in off-diagonal elements. From the monitoring statistics in (7), the MVP chart only makes use of the trace of v t , which is an estimator of the covariance matrix. This is the reason why the MVP chart performs unsatisfactorily under these circumstances.…”

Section: Arl Comparisonsmentioning

confidence: 99%

“…As pointed out by a referee, the MVP chart statistic T t in (7) is based on the trace of S. If a change in causes the largest eigenvalue to increase by a factor while the smallest eigenvalue decreases by the same factor , such as 8 , the trace of S is unaltered. In general, the trace of S is effective for detecting increases in variance.…”

Section: Arl Comparisonsmentioning

confidence: 99%

“…With advances in data acquisition systems and computing technologies, MSPC charts can and should play a greater role in monitoring and improving manufacturing processes . Given a multivariate process of interest, the process mean is typically monitored by the Hotelling's T 2 chart, and the process variability is usually monitored by a chart based on the determinant | S | or/and the inverse S −1 of the sample covariance matrix S . The process variability can also be monitored by a chart based on the likelihood ratio test (LRT), which also involves | S |, such as those of Sullivan and Woodall, Yeh et al, Zamba and Hawkins, Zhang and Wang, and Yen et al and Yeh et al give a comprehensive review on MSPC charts developed between 1990 and 2005 and designed for monitoring changes in a covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

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A control scheme for monitoring process covariance matrices with more variables than observations

Tsung

2018

Quality & Reliability Eng

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In this paper, we propose a new control chart that integrates a powerful high‐dimensional covariance matrix test with the exponentially weighted moving average procedure for monitoring high‐dimensional variability with individual observations. Design and implementation of the proposed chart are provided, including search algorithm and a table for the control limits, diagnostic aids after the signal, effect of misspecifying the in‐control distribution, and a bootstrap procedure. Monte Carlo simulation results show that the new chart, with its powerful inherited properties, provides satisfactory performance in various cases, especially for covariance shifts that involve diagonal components. The application of the proposed method is illustrated with a real data example from a white wine production process.

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Section: Arl Comparisonsmentioning

confidence: 99%

Section: Arl Comparisonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A control scheme for monitoring process covariance matrices with more variables than observations

Tsung

2018

Quality & Reliability Eng

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“…It is reported that the test is capable of perfectly detecting both moving and stationary objects [20]. Potential problems likely to be encountered and possible solutions when using Hotelling's T 2 technique have been discussed by Sparks for the processes in which data are highly correlated [21]. …”

Section: Introductionmentioning

confidence: 99%

A Dynamic Intrusion Detection System Based on Multivariate Hotelling’s T² Statistics Approach for Network Environments

Sivasamy

Sundan

2015

The Scientific World Journal

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The ever expanding communication requirements in today's world demand extensive and efficient network systems with equally efficient and reliable security features integrated for safe, confident, and secured communication and data transfer. Providing effective security protocols for any network environment, therefore, assumes paramount importance. Attempts are made continuously for designing more efficient and dynamic network intrusion detection models. In this work, an approach based on Hotelling's T2 method, a multivariate statistical analysis technique, has been employed for intrusion detection, especially in network environments. Components such as preprocessing, multivariate statistical analysis, and attack detection have been incorporated in developing the multivariate Hotelling's T2 statistical model and necessary profiles have been generated based on the T-square distance metrics. With a threshold range obtained using the central limit theorem, observed traffic profiles have been classified either as normal or attack types. Performance of the model, as evaluated through validation and testing using KDD Cup'99 dataset, has shown very high detection rates for all classes with low false alarm rates. Accuracy of the model presented in this work, in comparison with the existing models, has been found to be much better.

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“…Leoni et al (2015) analisa o efeito combinado da correlação e da autocorrelação sobre o desempenho do T² considerando amostras bivariadas. Vives-Mestres et al (2016)realizam a interpretação de sinais no gráfico de Hotelling T² para controle de dados composicionais para problemas de baixa e alta dimensão Sparks (2015). discute os problemas potenciais da utilização do gráfico de Hotelling T² no monitoramento de dados multivariáveis altamente correlacionados.A aplicação de estudos baseados no método Hotelling T² em conjunto com técnicas de decomposição, permitem detectar as causas que levam as variáveis sob análise não alcançarem os parâmetros de qualidades adequados ao final dos processos.…”

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Revisão das cartas de controle multivariadas paramétricas

Nunes

Carrir

Rosa³

et al. 2018

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ResumoOs processos industriais atuais, dotados de automação industrial e de um alto volume de dados inerentes aos processos têm exigido o controle das variáveis em tempo real, para que seja possível obter respostas rápidas à detecção e correção de falhas ocorridas durante o processo. A natureza multivariável dos processos industriais exigem métodos mais robustos para se obtenha um controle estatístico efetivo. As Cartas de Controle Multivariadas Paramétricas são amplamente utilizadas no setor industrial para o monitoramento e controle de processos. As Cartas de Controle Multivariadas Paramétricas são cartas de controle tradicionais que pressupõe o conhecimento da distribuição das variáveis, para aplicação dos métodos encontrados na literatura. Neste artigo, se discuti os principais procedimentos de Cartas de Controle Multivariadas Paramétricas encontrados na literatura: Hotelling T², MEWMA e MCUSUM. Assim como suas aplicações nos processos industriais. Considerando as publicações realizadas entre 2006 e 2016, pesquisadas nas principais bases de dados de análise científica. Enfatiza-se neste artigo a necessidade de artigos de revisão, pois estes representam estudos expostos de forma compilada inclinando-se ao desencadeamento de novas ideias e campos de pesquisa. Assim, espera-se que o trabalho apresentado possa servir como fonte de motivação para elaboração de novos estudos e adaptações das implementações aqui discutidas. Palavras-chave:Cartas de controle multivariadas paramétricas; Hotelling T²; MEWMA; MCUSUM. AbstractThe current industrial processes with industrial automation and a high volume of data inherent to the processes have required the control of variables in real time, so you can get quick answers to the detection and correction of failures that have occurred during the process. The multivariate nature of the industrial process requires robust methods to obtain effective statistical control. Parametric Multivariate Control charts are widely used in the industrial sector for the monitoring and process control. Parametric multivariate control charts are traditional control charts that presupposes the knowledge of the distribution of variables, for the application of the methods found in the literature. In this article, we discuss the main procedures of Parametric Multivariate Control charts found in literature: Hotelling T ², MEWMA and MCUSUM. As well as its applications in industrial processes. Considering the publications held between 2006 and 2016, surveyed in the main databases of scientific analysis. This article emphasizes the need for review articles, since they represent compiled expositions, inclined to the triggering of new ideas and fields of research. Thus, it is expected that the presented work can serve as a source of motivation for the elaboration of new studies and adaptations of the implementations discussed here.

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Monitoring Highly Correlated Multivariate Processes Using Hotelling's T² Statistic: Problems and Possible Solutions

Cited by 7 publications

References 46 publications

A control scheme for monitoring process covariance matrices with more variables than observations

A control scheme for monitoring process covariance matrices with more variables than observations

A Dynamic Intrusion Detection System Based on Multivariate Hotelling’s T² Statistics Approach for Network Environments

Revisão das cartas de controle multivariadas paramétricas

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Monitoring Highly Correlated Multivariate Processes Using Hotelling's T2 Statistic: Problems and Possible Solutions

Cited by 7 publications

References 46 publications

A control scheme for monitoring process covariance matrices with more variables than observations

A control scheme for monitoring process covariance matrices with more variables than observations

A Dynamic Intrusion Detection System Based on Multivariate Hotelling’s T2 Statistics Approach for Network Environments

Revisão das cartas de controle multivariadas paramétricas

Contact Info

Product

Resources

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Monitoring Highly Correlated Multivariate Processes Using Hotelling's T² Statistic: Problems and Possible Solutions

A Dynamic Intrusion Detection System Based on Multivariate Hotelling’s T² Statistics Approach for Network Environments