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

Management Science

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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.

Original language	English
Number of pages	14
Journal	Probability in the Engineering and Informational Sciences
Early online date	18 Sept 2023
DOIs	https://doi.org/10.1017/S0269964823000177
Publication status	E-pub ahead of print - 18 Sept 2023

Keywords

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

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10.1017/S0269964823000177Licence: CC BY 4.0

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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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N2 - 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.

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.

KW - stochastic intensity

KW - Poisson process

KW - ggeneralized Polya process

KW - minimal repair

KW - bivariate point process

U2 - 10.1017/S0269964823000177

DO - 10.1017/S0269964823000177

M3 - Article

JO - Probability in the Engineering and Informational Sciences

JF - Probability in the Engineering and Informational Sciences

ER -

On the combined imperfect repair process

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