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, standardshewhart 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 chartsignals an out-of-control condition, the process engineers should search for the source of the assignablecauses. knowing the exact time of the process change would help them to reduce the time for identificationof the assignable causes. this paper provides a maximum likelihood estimator for the change point of thenonconforming level of the high quality process with a linear trend. then, a monte carlo simulation isapplied to evaluate the performance of the proposed estimator. in addition, the proposed estimator iscompared with the mle of the process fraction nonconforming, derived under a single step change. theresults show that the proposed estimator outperforms the mle designed for step change, when a lineartrend disturbance is present in the process.