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ON VARIABILITY OF SERIES AND PARALLEL SYSTEMS WITH HETEROGENEOUS COMPONENTS

Part of: Distribution theory - Probability Special processes Operations research and management science

Published online by Cambridge University Press:  03 July 2019

Yiying Zhang ,
Weiyong Ding  and
Peng Zhao Open the ORCID record for Peng Zhao [Opens in a new window]
Yiying Zhang
Affiliation:
School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin300071, P.R. China E-mail: zhangyiying@outlook.com
Weiyong Ding
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou221116, P.R. China E-mail: mathdwy@hotmail.com; zhaop@jsnu.edu.cn
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou221116, P.R. China E-mail: mathdwy@hotmail.com; zhaop@jsnu.edu.cn
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Abstract

This paper studies the variability of both series and parallel systems comprised of heterogeneous (and dependent) components. Sufficient conditions are established for the star and dispersive orderings between the lifetimes of parallel [series] systems consisting of dependent components having multiple-outlier proportional hazard rates and Archimedean [Archimedean survival] copulas. We also prove that, without any restriction on the scale parameters, the lifetime of a parallel or series system with independent heterogeneous scaled components is larger than that with independent homogeneous scaled components in the sense of the convex transform order. These results generalize some corresponding ones in the literature to the case of dependent scenarios or general settings of components lifetime distributions.

Keywords

Archimedean copulaconvex transform orderparallel systemseries systemstar order

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 4 , October 2020 , pp. 626 - 645
Copyright
Copyright © Cambridge University Press 2019

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