Life distribution analysis based on Lévy subordinators for degradation with random jumps

Yin Shu, Qianmei Feng, David W. Coit

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumps using a single stochastic process based on the characteristics of Lévy subordinators, the class of nondecreasing Lévy processes. Based on the inverse Fourier transform, we derive a new closed-form reliability function and probability density function for lifetime, represented by Lévy measures. The reliability function derived using the traditional convolution approach for common stochastic models such as gamma degradation process with random jumps, is revealed to be a special case of our general model. Numerical experiments are used to demonstrate that our model performs well for different applications, when compared with the traditional convolution method. More importantly, it is a general and useful tool for life distribution analysis of stochastic degradation with random jumps in multidimensional cases.

Original languageEnglish (US)
Pages (from-to)483-492
Number of pages10
JournalNaval Research Logistics
Volume62
Issue number6
DOIs
StatePublished - Sep 2015

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

Keywords

  • Lévy processes
  • degradation
  • jumps
  • reliability
  • subordinators

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