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Optimal allocation of a coherent system with statistical dependent subsystems

Published online by Cambridge University Press:  24 September 2021

Bin Lu ,
Jiandong Zhang Open the ORCID record for Jiandong Zhang [Opens in a new window]  and
Rongfang Yan Open the ORCID record for Rongfang Yan [Opens in a new window]
Bin Lu
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. E-mails: lubinnwnum@163.com, jiandong.zhang@hotmail.com Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China. E-mail: yanrf@nwnu.edu.cn
Jiandong Zhang
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. E-mails: lubinnwnum@163.com, jiandong.zhang@hotmail.com
Rongfang Yan*
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. E-mails: lubinnwnum@163.com, jiandong.zhang@hotmail.com
*
*Corresponding author.
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Abstract

This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

Keywords

Coherent systemMajorization orderSchur-concave copulaStochastic orders
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 29 - 48
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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