A hybrid approach for estimating monotonic change points in the parameters of simple linear profiles in multistage processes

Abstract

In this paper, a hybrid method is proposed for estimating monotonic change points in multistage processes where, at each stage, the quality of the process is represented by simple linear profile models. In the case of monotonic changes, the change type is not known a priori, and the only assumption is that the changes are non-decreasing or non-increasing in nature. In the proposed method, a support vector machine (SVM) algorithm is first developed to identify the parameters experiencing a change in each process stage. Then, the second SVM algorithm is applied to identify the type of change occurring in the related parameters. Finally, considering the identified parameters and change types, the maximum likelihood estimator (MLE) is proposed to estimate the change points of the process under different scenarios, including single and multiple change points, upward and downward step changes, increasing and decreasing linear trends, shift in both parameters of the profiles, shift in different stages of the process, and weak and strong autocorrelation coefficients. The performance of the proposed method is evaluated through extensive simulation experiments. The results indicate that the proposed method recognizes the patterns and estimates the monotonic change points accurately.