Uncertain differential equation based accelerated degradation modeling. (September 2022)

• Record Type: Journal Article
• Authors: Liu, Zhe; Li, Xiaoyang; Kang, Rui
• Is Part Of: Reliability engineering & system safety. Volume 225(2022)
• Publication Date: 2022-09
• Subjects: Accelerated degradation testing -- Epistemic uncertainty -- Uncertain differential equation -- Belief reliability theory -- Uncertainty theory; Reliability (Engineering) -- Periodicals; System safety -- Periodicals; Industrial safety -- Periodicals; Fiabilité -- Périodiques; Sécurité des systèmes -- Périodiques; Sécurité du travail -- Périodiques; 620.00452
• DOI: 10.1016/j.ress.2022.108641
• Languages: English
• ISSNs: 0951-8320

Abstract

Abstract: Due to economic and technical reasons, in accelerated degradation testing (ADT) there are usually limited ADT data, which embody lots of epistemic uncertainties that cannot be depicted well by probability theory. Noting these facts, several uncertain processes based accelerated degradation models (UADMs) are proposed under the framework of uncertainty theory. However, these UADMs described uncertainties from a macro perspective which ignored the characteristic of performance degradation in small time scales and failed to describe the essence of nonlinear degradation. What is more, to estimate unknown parameters, these models used empirical distribution functions, which may have a great impact on the estimation results with limited samples. Motivated by these problems, based on uncertainty theory this paper builds up an uncertain differential equation based accelerated degradation model (UDEADM), which considers the dynamic cumulative change process of performance in small space–time scale, and explains the essence of nonlinear for uncertainties in degradation trend. Unknown parameters are estimated using uncertain generalized moment estimations. Furthermore, reliability and lifetime are analyzed under the normal operating condition based on belief reliability theory. A simulation study and a real data analysis are conducted to illustrate the effectiveness and advantages of the proposed methodology in details. Highlights: An uncertain differential equation based accelerated degradation model is proposed. Dynamic cumulative change of performance in small space–time scale is considered. Unknown parameters are estimated by uncertain generalized moment estimations.