RESUMEN
The economic-statistical design of the synthetic np chart with estimated process parameter is presented in this study. The effect of process parameter estimation on the expected cost of the synthetic np chart is investigated with the imposed statistical constraints. The minimum number of preliminary subgroups is determined where an almost similar expected cost to the known process parameter case is desired for the given cost model parameters. However, the available number of preliminary subgroups in practice is usually limited, especially when the number of preliminary subgroups is large. Consequently, the optimal chart parameters of the synthetic np chart are computed by considering the practical number of preliminary subgroups in which the cost function is minimized. This leads to a lower expected cost compared to that of adopting the optimal chart parameter corresponding to the known process parameter case.
Asunto(s)
Modelos Económicos , Simulación por Computador , Costos y Análisis de Costo , Modelos Estadísticos , Control de CalidadRESUMEN
The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X chart integrates the VSI X chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic X chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic X chart and the existing X, synthetic X, VSI X and EWMA X charts, in terms of ATS, are made. The ATS results show that the VSI synthetic X chart outperforms the other X type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic X chart.