Phase II Monitoring of Generalized Linear Profiles Under Different Types of Changes

Document Type: Research Note

Authors

1 The Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

2 Department of Industrial Engineering, Sharif University of Technology, P.O. Box 11155-9414 Azadi Ave, Tehran, Iran

Abstract

Various control charts have been proposed to monitor generalized linear profiles in Phase II. However, robustness of the proposed methods in detecting different types and especially different directions of changes is not well-studied in the literature. In real-world applications different kinds of changes such as drift and multiple change are likely to happen which can be isotonic (increasing) or antitonic (decreasing). This paper studies the robustness of Rao Score Test (RST) method, T2, and multivariate exponential weighted moving average (MEWMA) in different types, drift and multiple, and directions of changes. Rao Score Test method also benefits from a change-point detection approach whose performance is studied as well. According to the results, generally RST method shows a better performance in detecting different types of changes. Moreover, the performance of the RST method is robust to direction of the change, while T2 and MEWMA are not ARL-unbiased and show different performances under isotonic and antitonic changes. Therefore, to address this issue, we proposed a bias-reduced estimator to be used in T2. Our results demonstrate that the proposed control chart outperforms T2 and is less biased than T2. Finally, a real-world problem is presented in which aforementioned methods are applied to real data.

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