Estimating the change point of the cumulative count of a conforming control chart under a drift

In a high quality process, the fraction of nonconforming is very low. In this area, standard Shewhart control charts are no longer useful. The Cumulative Count of Conforming (CCC) control charts, which enumerates the number of conforming items between the occurrences of two nonconforming ones, have been shown to be effective in the monitoring of high quality processes. When the CCC control chart signals an out-of-control condition, the process engineers should search for the source of the assignable causes. Knowing the exact time of the process change would help them to reduce the time for identification of the assignable causes. This paper provides a maximum likelihood estimator for the change point of the nonconforming level of the high quality process with a linear trend. Then, a Monte Carlo simulation is applied to evaluate the performance of the proposed estimator. In addition, the proposed estimator is compared with the MLE of the process fraction nonconforming, derived under a single step change. The results show that the proposed estimator outperforms the MLE designed for step change, when a linear trend disturbance is present in the process.