A Random Fuzzy Accelerated Degradation Model and Statistical Analysis

By elevating stress levels, accelerated degradation testing (ADT) can obtain sufficient degradation data within limited time to predict the reliability and lifetime for highly reliable and long life products. In general, the degradation data collected in ADT have three kinds of characteristics: the time-stress-dependent structure, the random uncertainties caused by random effects in time dimension, and unit-to-unit variations, and the epistemic uncertainty caused by the small sample problem. However, existing acceleration degradation models based on Brownian motion with drift can successfully consider the time-stress-dependent structure and the random uncertainty, while failing to take the epistemic uncertainty into account. In this paper, based on the random fuzzy theory, a new random fuzzy accelerated degradation model and its corresponding statistical analysis method are proposed. The proposed model can take the above three kinds of characteristics into consideration simultaneously. The application case indicates that the proposed methodology is applicable for modeling the ADT data under small sample size. The simulation results show that the proposed methodology is more stable and slightly more conservative than the ADT model considering unit-to-unit variations. In addition, under small sample size (from 3 to 10), the proposed methodology is more stable and more accurate than the ADT model considering unit-to-unit variations.