Step Change Point Estimation of the First-order Autoregressive Autocorrelated Simple Linear Profiles

In most researches in the area of profile monitoring, it is assumed that observations are independent of each other. Whereas, this assumption is usually violated in practice and observations are autocorrelated. The control charts are the most important tools of the statistical process control which are used to monitor the processes over time. The control charts usually signal the out-of-control status of the process with a time delay. Whereas knowing real-time of the change (change point), one can achieve great savings on time and expenses. In this paper, the estimation of the change point in the simple linear profiles with AR (1) autocorrelation structure within each profile is considered. In the proposed method, by acquiring the joint probability density function of the autocorrelated observations, the maximum likelihood estimation method is applied to estimate the step change point. Here, we specifically focus on Phase II and compare the performance of the proposed estimator with the existing estimators in the literature through simulation studies. In addition, the application of the proposed estimator in comparison with the two estimators is illustrated through a real case. The results show the better performance of the proposed estimator.