Modeling left-truncated degradation data using random drift-diffusion Wiener processes

ABSTRACT

For products whose performance characteristic (PC) gradually degrades with time, one usually observes its degradation levels repeatedly to predict its remaining useful life (RUL). Due to the limited storage space of the server and the low resolution of a measurement instrument, we seldom record the low-magnitude degradation values at the early degradation stage in applications. Such observation setting introduces left-truncated degradation data, in which the data collection starts later than the unit’s installation. This brings sampling biases and complicates the degradation data analysis. Moreover, due to the uncontrollable factors in applications, the degradation drift and the degradation diffusion may differ among various units. Motivated by an application of high-speed train bearings, we propose a Wiener process model for the left-truncated degradation data and jointly consider the drift-diffusion random effects. Closed-form formulas are available in the expectation-maximization (EM) algorithm for estimating the model parameters. We derive the RUL distribution in closed form. We also extend the proposed model to the multivariate degradation process. The parameters are estimated with the help of the Monte Carlo EM (MCEM) algorithm. An additional laser application illustrates the performance of the proposed model in RUL prediction, which may help to design a predictive maintenance strategy

KEYWORDS:

• Left-truncated degradation data
• Wiener process
• Random drift-diffusion
• RUL prediction
• Multivariate degradation

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplementary data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2023.2187011.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [72201019]; Reliability and Environmental Engineering Science & Technology Laboratory [6142004210105]; National Natural Science Foundation of China [52075020]; China Scholarship Council [202106020153]

Notes on contributors

Bingxin Yan

Bingxin Yan received her B.S. degree in 2018 from Beihang University. She is currently a Ph.D. candidate at School of Reliability and Systems Engineering, Beihang University. Her research interests include industrial statistics and remaining useful life prediction.

Han Wang

Han Wang received a Ph.D. degree in systems engineering from Beihang University, Beijing, P.R. China, in 2020. He is currently a postdoctoral researcher with the School of Aeronautic Science and Engineering, Beihang University. His research interests include accelerated tests, stochastic degradation modelling, and fault prognosis.

Xiaobing Ma

Xiaobing Ma received a Ph.D. degree in engineering mechanics from Beihang University, Beijing, P.R. China, in 2006. He is currently a Professor with the School of Reliability and Systems Engineering, Beihang University. His current research interests include reliability data analysis, durability design, and system life modelling.