Degradation analysis with nonlinear exponential-dispersion process: Bayesian offline and online perspectives

Exponential-dispersion (ED) process has been recently introduced and demonstrated as a promising degradation model, which can include classical Wiener, gamma, and inverse Gaussian (IG) processes as special cases. However, most related studies are based on offline and point estimation methods, which limit their capability for uncertainty quantification and online update inference. In this paper, nonlinear ED process models equipped with Bayesian offline and online inference methods are presented. Tweedie ED process models are studied for degradation analysis with accelerated factors and unit-to-unit variability. Bayesian offline method based on NO-U-Turn sampler (NUTS) algorithm and Bayesian online method based on particle filter are developed, respectively. The offline method is presented to enhance the ED process based degradation analysis with uncertainty quantification. The online method is developed for the applications with limited storage and computing resources, for which degradation observations are analyzed on-the-fly with improved efficiency. Effectiveness and characteristics of the proposed methods are demonstrated through a simulation study and two case studies.