Laplace expressions of reliability characteristics for lévy subordinators-based degradation

Yin Shu, Qianmei Feng, Hao Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Degradation with random jumps is a process of stochastically continuous degradation with sporadic jumps that occur at random times and have random sizes. We use Lévy subordinators to model the evolution of this type of degradation processes. Based on corresponding Fokker-Planck equations, we derive explicit results for reliability function and lifetime moments in terms of Laplace transform, represented by Lévy measures, which can model many complex jump mechanisms. By specifying different Lévy measures to describe different jump mechanisms in degradation, our model for reliability function and lifetime moments is general and can fit many different types of degradation data sets. Stochastic models based on gamma process or compound Poisson process become special cases of our model. Numerical experiments are used to demonstrate that our general model performs well and is applicable. More importantly, it provides us a new methodology to deal with multi-degradation processes under dynamic environment.

Original languageEnglish (US)
Title of host publicationIIE Annual Conference and Expo 2015
PublisherInstitute of Industrial Engineers
Pages1362-1371
Number of pages10
ISBN (Electronic)9780983762447
StatePublished - Jan 1 2015
Externally publishedYes
EventIIE Annual Conference and Expo 2015 - Nashville, United States
Duration: May 30 2015Jun 2 2015

Publication series

NameIIE Annual Conference and Expo 2015

Other

OtherIIE Annual Conference and Expo 2015
CountryUnited States
CityNashville
Period5/30/156/2/15

Keywords

  • Degradation processes
  • Fokker-Planck equations
  • Laplace transform
  • Lifetime moments
  • Lévy subordinators

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Industrial and Manufacturing Engineering

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  • Cite this

    Shu, Y., Feng, Q., & Liu, H. (2015). Laplace expressions of reliability characteristics for lévy subordinators-based degradation. In IIE Annual Conference and Expo 2015 (pp. 1362-1371). (IIE Annual Conference and Expo 2015). Institute of Industrial Engineers.