An Adjusted CUSUM-Based Method for Change-Point Detection in Two-Phase Inverse Gaussian Degradation Processes

Mei Li, Tian Fu and Qian Li ()
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Mei Li: Key Laboratory of Applied Statistics and Data Analysis of Department of Education of Yunnan Province, Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
Tian Fu: Key Laboratory of Applied Statistics and Data Analysis of Department of Education of Yunnan Province, Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
Qian Li: Key Laboratory of Applied Statistics and Data Analysis of Department of Education of Yunnan Province, Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China

Mathematics, 2025, vol. 13, issue 19, 1-19

Abstract: Degradation data plays a crucial role in the reliability assessment and condition monitoring of engineering systems. The stage-wise changes in degradation rates often signal turning points in system performance or potential fault risks. To address the issue of structural changes during the degradation process, this paper constructs a degradation modeling framework based on a two-stage Inverse Gaussian (IG) process and proposes a change-point detection method based on an adjusted CUSUM (cumulative sum) statistic to identify potential stage changes in the degradation path. This method does not rely on complex prior information and constructs statistics by accumulating deviations, utilizing a binary search approach to achieve accurate change-point localization. In simulation experiments, the proposed method demonstrated superior detection performance compared to the classical likelihood ratio method and modified information criterion, verified through a combination of experiments with different change-point positions and degradation rates. Finally, the method was applied to real degradation data of a hydraulic piston pump, successfully identifying two structural change points during the degradation process. Based on these change points, the degradation stages were delineated, thereby enhancing the model’s ability to characterize the true degradation path of the equipment.

Keywords: Inverse Gaussian process; degradation model; change-point detection; adjusted CUSUM statistic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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