An ARL-unbiased approach to setting control limits of CCC-r chart for high-yield processes

The cumulative count of conforming (CCC) chart is a new type of statistical process control technique for monitoring high-yield processes. Rather than counting the number of nonconforming items in a fixed sample size, a CCC chart monitors the cumulative number of items inspected until observing one nonconforming item. The CCC chart has shown to be superior to the traditional p chart in monitoring the fraction nonconforming of a high-yield process. The CCC - r chart is an improvement of the CCC chart. It monitors the cumulative number of items inspected until the rth nonconforming item is observed based on negative binomial distribution. Due to the skewness of negative binomial distribution, the CCC - r chart usually shows an ARL-biased performance. In this paper, we introduce an ARL-unbiased design of the CCC - r chart. The ARL-unbiased design involves the determination of an adjustment factor of the existing control limits. Extensive numerical work shows that our approach can produce ARL-unbiased or nearly ARL-unbiased performance. In addition, the proposed approach shows more superiority in detecting process deteriorations, which is the major concern in high-yield processes. For simplification, a regression model is derived in this research. An adjustment factor can be calculated by specifying a predetermined false alarm rate α and the in-control nonconforming rate p0 to the regression equation. Then, the optimal control limits of an ARL-unbiased CCC - r chart can be easily obtained. An illustrative example is also presented to illustrate the proposed design procedure.