Change-point estimation of the process fraction non-conforming with a linear trend in statistical process control

Despite the fact that control charts are able to trigger a signal when a process has changed, it does not indicate when the process change has begun. The time difference between the changing point and a signal of a control chart could cause confusions on the sources of the problems. Knowing the exact time of a process change would help to reduce the time for identification of the special cause. In this paper, a model for the change point problem is first introduced and a maximum likelihood estimator (MLE) is applied when a linear trend disturbance is present. Then, Monte Carlo simulation is applied in order to evaluate the accuracy and the precision performances of the proposed change point estimator. Next, the proposed estimator is compared to the MLE of the process fraction nonconforming change point derived under simple step and monotonic changes following signals from a Shewhart np control chart. The results show the MLE of the process change point designed for the linear trend outperforms the MLE designed for step and monotonic changes when linear trend disturbance is present.