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https://prod.org.br/article/doi/10.1590/S0103-65132011005000026
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Monitoring process mean with a new EWMA control chart

Um novo gráfico de controle EWMA para monitoramento da média de processo

Yang, Su-Fen; Tsai, Wen-Chi; Huang, Tzee-Ming; Yang, Chi-Chin; Cheng, Smiley

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Abstract

In practice, sometimes the process data did not come from a known population distribution. So the commonly used Shewhart variables control charts are not suitable since their performance could not be properly evaluated. In this paper, we propose a new EWMA Control Chart based on a simple statistic to monitor the small mean shifts in the process with non-normal or unknown distributions. The sampling properties of the new monitoring statistic are explored and the average run lengths of the proposed chart are examined. Furthermore, an Arcsine EWMA Chart is proposed since the average run lengths of the Arcsine EWMA Chart are more reasonable than those of the new EWMA Chart. The Arcsine EWMA Chart is recommended if we are concerned with the proper values of the average run length.

Keywords

EWMA chart. Process mean. Binomial distribution. Arcsine transformation.

Resumo

Na prática a distribuição de probabilidade de muitas variáveis não é conhecida e sabe-se que não é proveniente de uma distribuição normal. Segue que o uso dos gráficos de controle Shewhart não é conveniente e daí há necessidade de procurar outros gráficos de controle alternativos. Neste artigo um novo gráfico de controle do tipo EWMA é proposto. Ele utiliza uma estatística não paramétrica para monitorar a média de um processo e observou-se que é ágil para detectar pequenos desvios da média. Propriedades amostrais da estatística são exploradas e um exemplo ilustra a nova proposta. Além disto, outro gráfico do tipo EWMA é apresentado utilizando como estatística o arco-seno da estatística não paramétrica. Os valores de ARL’s deste gráfico apresentaram melhor desempenho do que a proposta anterior. Desta forma o gráfico Arco-Seno EWMA é recomendado se o critério do ARL for empregado.

Palavras-chave

Gráfico de controle EWMA. Monitoramento de média de processo. Distribuição binomial. Transformada arco-seno.

References



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