Uncertain differential equation based accelerated degradation modeling

• Published in: Reliability engineering & system safety 2022-09, Vol.225, p.108641, Article 108641
• Main Authors: Liu, Zhe, Li, Xiaoyang, Kang, Rui
• Format: Article
• Language: English
• Subjects: Accelerated degradation testing; Accelerated tests; Belief reliability theory; Data analysis; Differential equations; Distribution functions; Economic models; Empirical analysis; Epistemic uncertainty; Mathematical models; Parameter estimation; Performance degradation; Probability theory; Reliability analysis; Reliability aspects; Reliability engineering; Uncertain differential equation; Uncertainty; Uncertainty theory
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2022.108641

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. •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.