Shock models based on renewal processes with matrix Mittag-Leffler distributed inter-arrival times

Dheeraj Goyal, Nil Kamal Hazra, Maxim Finkelstein

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Abstract

Some general shock models are considered under the assumption that shocks occur according to a renewal process with the matrix Mittag-Leffler distributed inter-arrival times. As the class of matrix Mittag–Leffler distributions is wide and well-suited for modeling the heavy tail phenomena, these shock models can be very useful for analysis of lifetimes of systems subject to random shocks with inter-arrival times having heavier tails. Some relevant stochastic properties of the introduced models are described. Finally, two applications, namely, the optimal replacement policy and the optimal mission duration are discussed.
Original languageEnglish
Article number115090
Number of pages26
JournalJournal of Computational and Applied Mathematics
Volume435
Early online date25 Jan 2023
DOIs
Publication statusPublished - 1 Jan 2024

Keywords

  • fractional homogeneous poisson process
  • matrix Mittag-Leffler distribution
  • phase-type distribution
  • shock models
  • reliability

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