Stochastic modeling for systems with delayed failures

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We present stochastic description for repairable systems with delayed failures. Initial defects in a system result in its failure only after some delay. Specifically, it happens in repairable systems when the defects are not repaired within some period of time that can be either deterministic or random. Therefore, operation of a system is described by the corresponding terminating renewal process. We derive and analyze relationships for the survival probability and the mean time to failure for these systems. The results are derived in the form of the corresponding Laplace transforms that are numerically inverted for illustrative examples. Simple fast repair approximations are considered and their accuracy is also discussed.

Original languageEnglish
Pages (from-to)118-124
Number of pages7
JournalReliability Engineering and System Safety
StatePublished - Aug 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Ltd


  • Defect
  • Delayed failures
  • Fast repair approximation
  • Repairable system
  • Survival probability


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