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STOCHASTIC ORDERING OF LIFETIMES OF PARALLEL AND SERIES SYSTEMS COMPRISING HETEROGENEOUS DEPENDENT COMPONENTS WITH GENERALIZED BIRNBAUM-SAUNDERS DISTRIBUTIONS

Published online by Cambridge University Press:  25 August 2020

Mehdi Amiri Open the ORCID record for Mehdi Amiri [Opens in a new window] ,
Narayanaswamy Balakrishnan  and
Ahad Jamalizadeh
Mehdi Amiri
Affiliation:
Department of Statistics, Faculty of Basic Sciences, University of Hormozgan, Bandarabbas, Iran E-mail: m.amiri@hormozgan.ac.ir
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
Ahad Jamalizadeh
Affiliation:
Department of Statistics, Faculty of Mathematics & Computer, Shahid Bahonar University of Kerman, Kerman, Iran Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran
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Abstract

In this paper, we discuss stochastic orderings of lifetimes of two heterogeneous parallel and series systems with heterogeneous dependent components having generalized Birnbaum–Saunders distributions. The comparisons presented here are based on the vector majorization of parameters. The ordering results are established in some special cases for the generalized Birnbaum–Saunders distribution based on the multivariate elliptical, normal, t, logistic, and skew-normal kernels. Further, we use these results by considering Archimedean copulas to model the dependence structure among systems with generalized Birnbaum–Saunders components. These results have been used to derive some upper and lower bounds for survival functions of lifetimes of parallel and series systems.

Keywords

Archimedean copulalog-concave functionmajorizationparallel systemSchur-concave functionseries systemstochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 49 - 65
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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