On the combined imperfect repair process

Ji Hwan Cha, Maxim Finkelstein

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In this paper, a new point process is introduced. It combines the nonhomogeneous Poisson process with the generalized Polya process (GPP) studied in recent literature. In reliability interpretation, each event (failure) from this process is minimally repaired with a given probability and GPP-repaired with the complementary probability. Characterization of the new process via the corresponding bivariate point process is presented. The mean numbers of events for marginal processes are obtained via the corresponding rates, which are used for considering an optimal replacement problem as an application.

Bibliographical note

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© The Author(s), 2023. Published by Cambridge University Press.


  • Poisson process
  • bivariate point process
  • generalized Polya process
  • minimal repair
  • stochastic intensity


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