• Industrial Engineering and Management Systems
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• 제4권1호
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• pp.75-81
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• 2005

Borror et al. discussed the EWMA(Exponentially Weighted Moving Average) chart to monitor the count of defects which follows the Poisson distribution, referred to the $EWMA_c$ chart, as an alternative Shewhart c chart. In the $EWMA_c$ chart, the Markov chain approach is used to calculate the ARL (Average Run Length). On the other hand, in order to monitor the process fraction defectives P in high-yield processes, Xie et al. presented the CCC(Cumulative Count of Conforming)-r chart of which quality characteristic is the cumulative count of conforming item inspected until observing $r({\geq}2)$ nonconforming items. Furthermore, Ohta and Kusukawa presented the $CS(Confirmation Sample)_{CCC-r}$ chart as an alternative of the CCC-r chart. As a more superior chart in high-yield processes, in this paper we present an $EWMA_{CCC-r}$ chart to detect more sensitively small or moderate shifts in P than the $CS_{CCC-r}$ chart. The proposed $EWMA_{CCC-r}$ chart can be constructed by applying the designing method of the $EWMA_C$ chart to the CCC-r chart. ANOS(Average Number of Observations to Signal) of the proposed chart is compared with that of the $CS_{CCC-r}$ chart through computer simulation. It is demonstrated from numerical examples that the performance of proposed chart is more superior to the $CS_{CCC-r}$ chart.

• Industrial Engineering and Management Systems
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• 제4권2호
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• pp.158-164
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• 2005

Kusukawa and Ohta presented the $CS_{CQ-r}$ chart to monitor the process defect $rate{\lambda}$ in high-yield processes that is derived from the count of defects. The $CS_{CQ-r}$ chart is more sensitive to $monitor{\lambda}$ than the CQ (Cumulative Quantity) chart proposed by Chan et al.. As a more superior chart in high-yield processes, we propose a Synthetic chart that is the integration of the CQ_-r chart and the $CS_{CQ-r}$chart. The quality characteristic of both charts is the number of units y required to observe r $({\geq}2)$ defects. It is assumed that this quantity is an Erlang random variable from the property that the quality characteristic of the CQ chart follows the exponential distribution. In use of the proposed Synthetic chart, the process is initially judged as either in-control or out-of-control by using the $CS_{CQ-r}$chart. If the process was not judged as in-control by the $CS_{CQ-r}$chart, the process is successively judged by using the $CQ_{-r}$chart to confirm the judgment of the $CS_{CQ-r}$chart. Through comparisons of ARL (Average Run Length), the proposed Synthetic chart is more superior to monitor the process defect rate in high-yield processes to the stand-alone $CS_{CQ-r}$ chart.

• Industrial Engineering and Management Systems
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• 제7권2호
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• pp.101-112
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• 2008

As charts to monitor the process fraction defectives, P, in the high-yield processes, Mishima et al. (2002) discussed a synthetic chart, the Synthetic CS chart, which integrates the CS (Confirmation Sample)$_{CCC(\text{Cumulative Count of Conforming})-r}$ chart and the CCC-r chart. The Synthetic CS chart is designed to monitor quality characteristics in real-time. Recently, Kotani et al. (2005) presented the EWMA (Exponentially Weighted Moving-Average)$_{CCC-r}$ chart, which considers combining the quality characteristics monitored in the past with one monitored in real-time. In this paper, we present an alternative chart that is more superior to the $EWMA_{CCC-r}$ chart. It is an integration of the $EWMA_{CCC-r}$ chart and the CCC-r chart. In using the proposed chart, the quality characteristic is initially judged as either the in-control state or the out-of-control state, using the lower and upper control limits of the $EWMA_{CCC-r}$ chart. If the process is not judged as the in-control state by the $EWMA_{CCC-r}$ chart, the process is successively judged, using the $EWMA_{CCC-r}$ chart. We compare the ANOS (Average Number of Observations to Signal) of the proposed chart with those of the $EWMA_{CCC-r}$ chart and the Synthetic CS chart. From the numerical experiments, with the small size of inspection items, the proposed chart is the most sensitive to detect especially the small shifts in P among other charts.