An Uncertain Statistics of Uncertain Accelerated Degradation Model Based on the Method of Moments

Abstract

The uncertain accelerated degradation model describing the degradation process and quantifying the epistemic uncertainties in the time dimension has been constructed, and the uncertain statistics based on the principle of least squares (US-LS) to estimate unknown parameters has been proposed. However, US-LS only considers the fit of the uncertainty distribution, rather than describing the deterministic degradation trend and analyzing the uncertainties. In this paper, an uncertain statistics based on the method of moments (US-M) is proposed, in which the unknown parameters related to the deterministic degradation trend and those related to the uncertainties are estimated separately. A stress relaxation case study is conducted to illustrate the proposed US-M, and discussions are given to compare US-M with US-LS in predicting the deterministic degradation trend and quantifying the uncertainties. The results show that the proposed US-M is more accurate than US-LS in predicting the deterministic degradation trend, and the confidence intervals of the degradation process predicted by US-M are closer to the boundaries of the actual data in quantifying the uncertainties, which verifies the validity of the proposed uncertain statistics.