A Synthetic Exponentially Weighted Moving-average Chart for High-yield Processes

Abstract

Kusukawa and Ohta discussed the CS (Confirmation Sample)_<CCC (cunuiative count of conforming)-r> chart as an alternative chart of the CCC-r chart for monitoring the process fraction defectives, P, in high-yield processes. In order to enhance the performance of the CS_<CCC-r> chart, Mishima et al. presented a synthetic chart which integrates the CS_<CCC-r> chart with the CCC-r chart, referred to as the Synthetic CS chart. Compared to the CS_<CCC-r> chart, the Synthetic CS chart has higher detection powers for small or moderate shifts in P from the in-control state toward both upward and downward directions. However, both the CS_<CCC-r> chart and the Synthetic CS chart are designed to monitor quality characteristics in real-time. Neither of the charts has the detection power required for the above shifts in P from the in-control state. Recently, Kotani et al. presented the EWMA (Exponentially Weighted Moving-Average)_<CCC-r> chart, which considers combining the quality characteristics monitored in the past with quality characteristic monitored in real-time. The EWMA_<CCC-r> chart can be constructed by applying the designing method of the EWMA chart to the CCC-r chart. The EWMA_<CCC-r> chart has higher detection powers for any shift in P when compared to the CS_<CCC-r> chart. In this paper, we present a chart that is more superior to either the EWMA_<CCC-r> chart or the Synthetic CS chart. It is an integration of the EWMA_<CCC-r> chart and the CCC-r chart, and is referred to as the Synthetic EWMA chart. In using the proposed synthetic chart, the quality characteristic is initially judged as either in-control or out-of-control using the upper and lower control limits of the EWMA_<CCC-r> chart. If the process is not judged as in-control by the EWMA_<CCC-r> chart, the process is successively judged using the CCC-r chart to conform the judgement of the EWMA_<CCC-r> chart. In order to assess the performance of the detection power of the proposed synthetic chart, we compare the ANOS (Average Number of Observations to Signal) of the proposed chart with those of both the EWMA_<CCC-r> chart and the Synthetic CS chart. ANOS can be obtained using the Markov chain approach. It is demonstrated from numerical experiments that the proposed Synthetic EWMA chart is most sensitive in detecting small or moderate shifts in P from the in-control state toward both upward and downward directions in high-yield processes among the EWMA_<CCC-r> chart and Synthetic CS chart.