On the combined imperfect repair process

Ji Hwan Cha; Maxim Finkelstein

doi:10.1017/S0269964823000177

On the combined imperfect repair process

Ji Hwan Cha, Maxim Finkelstein

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Journal	Probability in the Engineering and Informational Sciences
DOIs	https://doi.org/10.1017/S0269964823000177
State	Accepted/In press - 2023

Bibliographical note

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

Keywords

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

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10.1017/S0269964823000177

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abstract = "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.",

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AB - 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.

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KW - stochastic intensity

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ER -

On the combined imperfect repair process

Abstract

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Keywords

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