A Self-Starting CUSUM Chart Combined with a Maximum Likelihood Estimator for the Time of a Detected Shift in the Process Mean

Detection of a special cause of variation and the identification of the time it occurs are two important activities in any quality improvement strategy. Detection of changes in a process can be done using control charts. One of these charts, the self‐starting CUSUM chart, was created to detect small sustained changes and be implemented without a Phase I or a priori knowledge of the parameters of the process. To estimate the time of a detected change, a CUSUM‐based change‐point estimator can be used, but experiments show that the corresponding MLE has smaller bias and standard error. This paper proposes the sequential use of the self‐starting CUSUM chart and the MLE of a change point in series of independent normal observations. Performance is studied with Monte Carlo simulations showing that the use of the MLE reduces the bias of the change‐point estimation. It is also shown how extra observations after a change is detected can be used to improve estimation of the change‐point time.