Monotonic change point estimation in the mean vector of a multivariate normal process

When a control chart sounds the alarm that the process is out of control (OC), the process will be paused and specialists will start the procedure of finding the root cause(s) that made the process out of control. Knowing the time of change will substantially aid the process engineer to figure out the assignable causes and solve the problem sooner, so the time, energy, and costs spent to implement corrective actions will be considerably reduced. Maximum likelihood estimator (MLE) as one of the statistical technique is frequently used for estimating the change point time. In this paper, an MLE is derived to estimate the time of first change in the mean vector of a multivariate normal process when the type of change is monotonic. The performance of the proposed change point estimator is evaluated in terms of accuracy and precision in comparison with the change point estimators developed under the assumptions of a step shift and drift. Finally, a numerical example is presented to show the application of the proposed change point estimator.