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

Abstract

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 article, 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 with the MLE of the process fraction non-conforming change point derived under simple step and monotonic changes following signals from a Shewhart np control chart. The results show that the MLE of the process change point designed for the linear trend outperforms the MLE designed for step and monotonic changes when a linear trend disturbance is present.