Estimating the Step-Change Time of the Location Parameter in Multistage Processes Using MLE

In this paper maximum likelihood step-change-point estimators of the location parameter, the out-of-control sample, and the out-of-control stage are developed for autocorrelated multistage processes. To do this, the multistage process and the concept of change detection are first discussed. Then, a time-series model of the process is presented. Assuming step changes in the location parameter of the process, next, the likelihood functions of different samples before and after receiving out-of-control signal from an X-bar control chart were derived under different conditions. The maximum likelihood estimators were then obtained by maximizing the likelihood functions. Finally, the accuracy and the precision of the proposed estimators are examined through some Monte Carlo simulation experiments. The results show the estimators to be promising.