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Markov additive processes for degradation with jumps under dynamic environments
Author(s) -
Shu Yin,
Feng Qianmei,
Kao Edward P. C.,
Coit David W.,
Liu Hao
Publication year - 2021
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21982
Subject(s) - subordinator , markov chain , markov process , markov renewal process , mathematics , markov kernel , continuous time markov chain , uniformization (probability theory) , markov property , laplace transform , state space , statistical physics , component (thermodynamics) , markov model , lévy process , variable order markov model , mathematical analysis , statistics , physics , thermodynamics
We use general Markov additive processes (Markov modulated Lévy processes) to integrally handle the complexity of degradation including internally‐induced and externally‐induced stochastic properties with complex jump mechanisms. The background component of the Markov additive process is a Markov chain defined on a finite state space; the additive component evolves as a Lévy subordinator under a certain background state, and may have instantaneous nonnegative jumps occurring at the time the background state switches. We derive the Fokker–Planck equations for such Markov modulated processes, based on which we derive Laplace expressions for reliability function and lifetime moments, represented by the infinitesimal generator matrices of Markov chain and the Lévy measure of Lévy subordinator. The superiority of our models is their flexibility in modeling degradation data with jumps under dynamic environments. Numerical experiments are used to demonstrate that our general models perform well.