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

Yin Shu, Qianmei Feng, Edward P.C. Kao, Hao Liu

Research output: Contribution to journalArticle

14 Scopus citations


We use Lévy subordinators and non-Gaussian Ornstein–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, linearity/nonlinearity, 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 Lévy 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 dynamicenvironments.

Original languageEnglish (US)
Pages (from-to)993-1003
Number of pages11
JournalIIE Transactions (Institute of Industrial Engineers)
Issue number11
StatePublished - Nov 1 2016
Externally publishedYes


  • Fokker–Planck equations
  • Laplace transform
  • Lévy subordinators
  • degradation processes
  • lifetime moments
  • non-Gaussian OU processes

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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