On information-based residual lifetime in survival models with delayed failures

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


At many practical instances, the initiating point events (e.g., shocks) affect an object not immediately, but after some random delay. These models were studied in the literature only for the case when an initial shock process is Poisson. In our paper, we generalize these results to a meaningful case of the generalized Polya process (GPP) of initial shocks that was recently introduced in the literature. Distinct from the Poisson process, the GPP possesses the property of dependent increments, which makes it much more attractive in applications. We derive the distribution of the time to failure for a system subject to the GPP with delays. Our main focus, however, is on analysis of the corresponding residual lifetime distribution that depends now on the full history (information) of the initiating shock process.

Original languageEnglish
Pages (from-to)209-216
Number of pages8
JournalStatistics and Probability Letters
StatePublished - Jun 2018


  • Delayed failure
  • Generalized Polya process
  • Poisson process
  • Residual lifetime
  • Shocks


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