An evidence theory based model fusion method for degradation modeling and statistical analysis

Abstract Several methods have been proposed to handle uncertainty issues, including process uncertainty and parameter uncertainty, in stochastic-process based degradation modeling and statistical analysis. However, these methods oftentimes do not address the uncertainty issues well under small sample conditions. Hence, due to the powerful ability of evidence theory to describe uncertainty, especially under small sample conditions, an evidence theory based model fusion method is proposed. The candidate models are considered as different evidence sources and give evidences about the evaluated product based on likelihood. Considering the heterogeneous characteristics of the evidences predicted from different candidate models, the reliability degree is introduced to convert the evidences and estimated based on goodness-of-fit. By fusing converted evidences, inferences and estimations of reliability, degradation mean, degradation variance, and mean time to failure are obtained. The effectiveness of the proposed method is verified by previously published degradation datasets and comparing to Bayesian model averaging method and model selecting method. The degradation mean and variance estimations are more precise and more stable compared to the other two methods under small sample conditions. Furthermore, the proposed method can be used to consider the uncertainty issues by belief, plausibility and uncertainty measure, even though under extremely small sample conditions.