Monitoring a wandering mean with an np chart
Monitoramento da média de processos que oscila através de um gráfico de controle np
Ho, Linda Lee; Costa, Antonio Fernando B.
http://dx.doi.org/10.1590/S0103-65132011005000027
Prod, vol.21, n2, p.254-258, 2011
Abstract
This article considers the npx chart proposed by Wu et al. (2009) to control the process mean, as an alternative to the use of the X chart. The distinctive feature of the npx chart is that sample units are classified as first-class or second-class units according to discriminating limits. The standard np chart is a particular case of the npx chart, where the discriminating limits coincide with the specification limits and the first (second) class unit is the conforming (nonconforming) one. Following the work of Reynolds Junior, Arnold and Baik (1996), we assume that the process mean wanders even in the absence of any specific assignable cause. A Markov chain approach is adopted to investigate the effect of the wandering behavior of the process mean on the performance of the npx chart. In general, the npx chart requires samples twice larger (the standard np chart requires samples five or six times larger) to outperform the X chart.
Keywords
Discriminating limits, npx chart. First order autoregressive model AR (1). Quality control. Attribute and variable control chart. Attribute inspection
Resumo
Este artigo considera um gráfico npx proposto por Wu et al. (2009) para controle de média de processo como uma alternativa ao uso do gráfico de X. O que distingue do gráfico de controle npx é o fato das unidades amostrais serem classificadas como unidades de primeiro ou de segunda classe de acordo com seus limites discriminantes. O gráfico tradicional np é um caso particular do gráfico npx quando os limites discriminantes coincidem com os limites de especificação e unidade de primeira (segunda) classe é um item conforme (não conforme). Estendendo o trabalho de Reynolds Junior, Arnold e Baik (1996), consideramos que a média de processo oscila mesmo na ausência de alguma causa especial. As propriedades de Cadeia de Markov foram adotadas para avaliar o desempenho do gráfico npx no monitoramento de média de processos que oscila. De modo geral, o gráfico npx requer amostras duas vezes maior para superar desempenho do gráfico X (enquanto que o gráfico tradicional np necessita tamanho de amostras cinco ou seis vezes maior).
Palavras-chave
Limites discriminantes. Gráfico npx. Modelo auto-regressivo de primeiro ordem (AR1). Controle de qualidade. Gráfico de controle por atributos e por variáveis. Inspeção por atributos.
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