Gestão & Produção
https://gestaoeproducao.com/article/doi/10.1590/1806-9649-2021v28e019
Gestão & Produção
Seção Temática: Monitoramento e Controle Estatístico de Processos

Monitoring the mean with least-squares support vector data description

O monitoramento da média com mínimos quadrados suporta a descrição de dados vetoriais

Edgard M. Maboudou-Tchao

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Abstract

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.

Keywords

One-class classification, least squares support vector data description, least squares support vector machines, support vector data description, least squares one-class support vector machines

Resumo

Resumo: : Gráficos de controle multivariados são ferramentas essenciais no controle estatístico multivariado de processos (MSPC). Os gráficos do “tipo Shewhart” são gráficos de controle usando subgrupos racionais que são eficazes na detecção de grandes mudanças. Recentemente, o problema de classificação de uma classe atraiu muito interesse. Normalmente, três métodos são usados para resolver esse tipo de problema de classificação. Esses métodos incluem o método k-center, o método do vizinho mais próximo, máquina de vetor de suporte de uma classe (OCSVM) e a descrição de dados de vetor de suporte (SVDD). Em aplicações industriais, como controle estatístico de processo (SPC), os profissionais usaram com sucesso o SVDD para detectar anomalias ou outliers no processo. Neste artigo, reformulamos a descrição de dados vetoriais de suporte padrão e derivamos uma versão de mínimos quadrados do método. Esta descrição de dados de vetor de suporte de mínimos quadrados (LS-SVDD) é usada para projetar um gráfico de controle para monitorar o vetor médio de processos. Comparamos o desempenho do gráfico LS-SVDD com o gráfico SVDD e T2 usando o comprimento médio de execução (ARL) fora de controle como a métrica de desempenho. Os resultados experimentais indicam que o gráfico de controle proposto tem um desempenho muito bom.
 

Palavras-chave

Classificação de uma classe, mínimos quadrados suportam descrição de dados vetoriais, mínimos quadrados suportam máquinas vetoriais, suportam descrição de dados vetoriais

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