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https://prod.org.br/doi/10.1590/S0103-65132008000200003?lang=en
Production
Article

Gráfico de controle de VMAX para o monitoramento da matriz de covariâncias

The VMAX control chart for monitoring the covariance matrix

Machado, Marcela Aparecida G.; Magalhães, Maysa Sacramento de; Costa, Antonio Fernando B.

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Resumo

Neste artigo é proposto, para o monitoramento de processos normais bivariados, um gráfico de controle baseado nas variâncias amostrais de duas características de qualidade. Os pontos plotados no gráfico correspondem ao valor da maior variância amostral. O gráfico proposto, denominado gráfico de VMAX, tem um desempenho superior ao do gráfico da variância amostral generalizada |S| e, além disso, tem uma melhor capacidade de diagnóstico, ou seja, com ele é mais fácil identificar a variável que teve sua variabilidade alterada pela ocorrência da causa especial. Quando a amostragem dupla está em uso o gráfico proposto também tem um desempenho superior ao do gráfico de |S|, exceto em alguns casos em que o tamanho da segunda amostra é muito grande.

Palavras-chave

Gráficos de controle de VMAX, matriz de covariâncias, processos bivariados, amostragem dupla.

Abstract

In this paper a control chart based on sample variances from two quality characteristics for monitoring bivariate normal processes is proposed. The points plotted on the chart are the maximum of the values of these two statistics. The proposed chart (VMAX chart) detects process disturbances faster than the generalized variance |S| chart and has a better diagnostic feature, that is, with the VMAX chart it is easier to relate an out-of-control signal to the variable whose variability has moved away from its in-control state. When the double sampling scheme is used the proposed chart has also a better performance, except in a few cases in which the size of the samples at the second stage is very large.

Keywords

VMAX control chart, covariance matrix, bivariate processes, double sampling

References



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