Levy-driven non-Gaussian Ornstein-Uhlenbeck processes for degradation-based reliability analysis

摘要

We use Levy subordinators and non-Gaussian Omstein-Uhlenbeck processes to model the evolution of degradation with random jumps. The superiority of our models stems from the flexibility of such processes in the modeling of stylized features of degradation data series such as jumps, linearityonlinearity, symmetry/asymmetry, and light/heavy tails. Based on corresponding Fokker-Planck equations, we derive explicit results for the reliability function and lifetime moments in terms of Laplace transforms, represented by Levy measures. Numerical experiments are used to demonstrate that our general models perform well and are applicable for analyzing a large number of degradation phenomena. More important, they provide us with a new methodology to deal with multi-degradation processes under dynamic environments.