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https://prod.org.br/article/doi/10.1590/S0103-65132007000300010
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Gráficos de controle de EWMA e de X-barra para monitoramento de processos autocorrelacionados

EWMA and X-bar control charts for the monitoring of autocorrelated processes

Claro, Fernando Antonio E.; Costa, Antonio Fernando B.; Machado, Marcela Aparecida G.

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Resumo

Este artigo trata dos gráficos de controle de EWMA e de X-barra utilizados no monitoramento de processos cujas observações podem ser descritas por um modelo auto-regressivo de primeira ordem. Os gráficos são planejados levando em conta a correlação em série e utilizando-se o conceito de subgrupos racionais como estratégia de amostragem. As propriedades das cartas de controle são obtidas e comparadas. Os resultados numéricos mostram que a correlação positiva dentro dos subgrupos afeta o desempenho dos gráficos. O gráfico de EWMA é substancialmente mais ágil do que o gráfico de X-barra na detecção de perturbações no processo, especialmente quando tais perturbações geram pequenos desajustes na média.

Palavras-chave

Autocorrelação, número médio de amostras até o sinal, gráfico de controle da média móvel ponderada exponencialmente, modelo autoregressivo de primeira ordem, controle estatístico do processo

Abstract

In this paper the EWMA and the X-bar control charts are considered for monitoring processes in which the observations can be represented as a first order autoregressive model. The charts are designed taking the serial correlation into account and the sampling strategy is set based on the rational subgroup concept. The control charts properties are studied and compared. Numerical results show that the positive correlation within-subgroup has a significant impact on the charts performance. The EWMA chart is substantially more efficient than the X-bar chart in detecting process disturbances, especially when the mean shifts are of small magnitude.

Keywords

Autocorrelation, average run length, exponentially weighted moving average control chart, first order autoregressive model, statistical process control

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