The effects of violations of the multivariate normality assumption in multivariate Shewhart and MEWMA control charts

Nidsunkid, Sudarat; Borkowski, John J.; Budsaba, Kamon

doi:10.1002/qre.2218

Cited by 11 publications

(7 citation statements)

References 10 publications

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“…Whereas, the chi‐square limit in equation () is only appropriate when the covariance is known. Nidsunkid et al 10 suggested that the samples size must be chosen at least 250 (

m \geq 250

) when k is large (

k \geq 10

) to approximated the correct UCL.…”

Section: Hotelling's T2 Control Chartmentioning

confidence: 99%

“…Meanwhile, Nidsunkid et al 9 presented the performance of multivariate control charts such as MCUSUM control charts when the multivariate normal distribution assumption is incorrect. Previously, Nidsunkid et al 10 studied the performance of multivariate Shewhart and MEWMA control charts when the random vector comes from multivariate normal and multivariate non‐normal distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, Mukherjee et al 20 provided a method of construction a new type of bivariate asymmetric copulas which can be used in many fields. As mentioned above, Nidsunkid et al 10 explored the sensitivity of multivariate Shewhart and MEWMA control chart performances when the normality assumption is violated. Consequently, we constructed bivariate copulas for applications to multivariate control charts when the normality assumption is violated.…”

Section: Introductionmentioning

confidence: 99%

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The effects of constructed bivariate copulas on multivariate control charts effectiveness

Sukparungsee

Sasiwannapong

Busababodhin

et al. 2021

Quality & Reliability Eng

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The average control chart monitors the shifts in the process. The familiar multivariate control charts are used to detect the mean vector of the process such as multivariate cumulative sum (MCUSUM) and Hotelling's T2 control charts. In this paper, the effects of constructing bivariate copulas on multivariate control charts, that is, MCUSUM and Hotelling's T2 control charts are intensively investigated when observations are drawn from the exponential distribution. Moreover, the dependence levels of observations are classified to be weak, moderate, and strong in both positive and negative values by Kendall's tau. The numerical results were obtained by Monte Carlo simulation to explore the average run length (ARL). The simulation results show that the performance of Hotelling's T2 control chart is superior to the MCUSUM control chart for all shifts in the mean vector of process. Furthermore, from applying the presented control chart to two sets of real data, data set of the strength of 1.5 cm glass fibers measured at the National Physical Laboratory, England and data set of the strength of glass of the aircraft window, it was found that for a small shift (δ≤0.1), the MCUSUM control chart is better than Hotelling's T2 control chart.

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“…Whereas, the chi‐square limit in equation () is only appropriate when the covariance is known. Nidsunkid et al 10 suggested that the samples size must be chosen at least 250 (

m \geq 250

) when k is large (

k \geq 10

) to approximated the correct UCL.…”

Section: Hotelling's T2 Control Chartmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The effects of constructed bivariate copulas on multivariate control charts effectiveness

Sukparungsee

Sasiwannapong

Busababodhin

et al. 2021

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…The basic assumption for multivariate control charts is multivariate normality, which is completely specified by its expected value µ and covariance matrix Σ. In general, this assumption many times cannot be supported by real data (Nidsunkid Borkowski, & Budsaba, 2017). This study will consider the underlying distribution of the observation is the multivariate t distribution.…”

Section: Deming's Four Principle: the Knowledge Of Variationmentioning

confidence: 99%

Entropy and the variability of dependence: System of profound knowledge (SPK) and induced entropy copula as a measure of variability for copula density

Guerrero-Cusumano

2018

OJAKM

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Deming’s System of Profound Knowledge (SPK) is a framework for creating, disseminating, and applying knowledge in business. One of its basic principles is the knowledge of variation. SPK is based on a systemic approach in which each part of the system is interconnected. Process control seeks to determine whether a process is in control, meaning whether the distribution of some critical measured variable is stable. Complex systems may vary through time and their variability can be measured by its entropy and its interrelatedness. The entropy copula or interrelatedness is interpreted as a measure of reduction of independence measured by the entropy of independent variables. This paper provides the expression of the entropy copula for multivariate t distribution and introduces the concept of induced entropy copula as a measure of variability for copula densities. A test for uncorrelatedness based on the entropy copula is also developed. A manufacturing example, using multivariate control chart, is analyzed using the entropy copula approach. Tables are provided in the appendix for testing at different significance levels.

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“…Nidsunkid et al (2017) explora a sensibilidade dos comprimentos médios de execução para o gráfico multivariado de Shewhart e para gráficos MEWMA em casos que a suposição de normalidade está incorreta Zhang et al (2014). utilizam dois gráficos de controle multivariados do tipo Shewhart para monitorar o termo de tendência linear e a correlação dentro do perfil separadamente na fase II.…”

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Revisão das cartas de controle multivariadas paramétricas

Nunes

Carrir

Rosa³

et al. 2018

RAUnP

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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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The effects of violations of the multivariate normality assumption in multivariate Shewhart and MEWMA control charts

Cited by 11 publications

References 10 publications

The effects of constructed bivariate copulas on multivariate control charts effectiveness

The effects of constructed bivariate copulas on multivariate control charts effectiveness

Entropy and the variability of dependence: System of profound knowledge (SPK) and induced entropy copula as a measure of variability for copula density

Revisão das cartas de controle multivariadas paramétricas

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