Multivariate reliability modelling based on dependent dynamic shock models

Ji Hwan Cha; F. G. Badía

doi:10.1016/j.apm.2017.06.032

Multivariate reliability modelling based on dependent dynamic shock models

Ji Hwan Cha, F. G. Badía

Department of Statistics

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

11 Scopus citations

Abstract

In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.

Original language	English
Pages (from-to)	199-216
Number of pages	18
Journal	Applied Mathematical Modelling
Volume	51
DOIs	https://doi.org/10.1016/j.apm.2017.06.032
State	Published - Nov 2017

Keywords

Common shock
Multivariate IFR
Nonhomogeneous Poisson process
Positive upper orthant dependent
Shock models

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10.1016/j.apm.2017.06.032

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title = "Multivariate reliability modelling based on dependent dynamic shock models",

abstract = "In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.",

keywords = "Common shock, Multivariate IFR, Nonhomogeneous Poisson process, Positive upper orthant dependent, Shock models",

author = "Cha, {Ji Hwan} and Bad{\'i}a, {F. G.}",

note = "Funding Information: The authors would like to thank the referees for helpful comments and constructive suggestions. The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009–0093827 ). The work of the second author has been supported by Spanish government under research projects MTM2012-36603-C02-02 and MTM2015-63978-P. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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AU - Cha, Ji Hwan

AU - Badía, F. G.

N1 - Funding Information: The authors would like to thank the referees for helpful comments and constructive suggestions. The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009–0093827 ). The work of the second author has been supported by Spanish government under research projects MTM2012-36603-C02-02 and MTM2015-63978-P. Publisher Copyright: © 2017 Elsevier Inc.

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N2 - In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.

AB - In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.

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KW - Multivariate IFR

KW - Nonhomogeneous Poisson process

KW - Positive upper orthant dependent

KW - Shock models

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VL - 51

SP - 199

EP - 216

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -

Multivariate reliability modelling based on dependent dynamic shock models

Abstract

Keywords

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