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Stochastic comparison on active redundancy allocation to K-out-of-N systems with statistically dependent component and redundancy lifetimes

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

Published online by Cambridge University Press:  05 May 2023

Yinping You ,
Xiaohu Li Open the ORCID record for Xiaohu Li [Opens in a new window]  and
Xiaoqin Li
Yinping You*
Affiliation:
Huaqiao University
Xiaohu Li*
Affiliation:
Stevens Institute of Technology
Xiaoqin Li*
Affiliation:
Huaqiao University
*
*Postal address: School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China.
***Postal address: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Email address: xiaohu.li@stevens.edu
*Postal address: School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China.
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Abstract

In the literature on active redundancy allocation, the redundancy lifetimes are usually postulated to be independent of the component lifetimes for the sake of technical convenience. However, this unrealistic assumption leads to a risk of inaccurately evaluating system reliability, because it overlooks the statistical dependence of lifetimes due to common stresses. In this study, for k-out-of-n:F systems with component and redundancy lifetimes linked by the Archimedean copula, we show that (i) allocating more homogeneous redundancies to the less reliable components tends to produce a redundant system with stochastically larger lifetime, (ii) the reliability of the redundant system can be uniformly maximized through balancing the allocation of homogeneous redundancies in the context of homogeneous components, and (iii) allocating a more reliable matched redundancy to a less reliable component produces a more reliable system. These novel results on k-out-of-n:F systems in which component and redundancy lifetimes are statistically dependent are more applicable to the complicated engineering systems that arise in real practice. Some numerical examples are also presented to illustrate these findings.

Keywords

Archimedean copulacompletely monotoneleft tail permutation decreasinglikelihood ratio ordermajorizationmultivariate mixturereversed hazard rate orderusual stochastic order

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Original Article
Information
Advances in Applied Probability , Volume 55 , Issue 4 , December 2023 , pp. 1085 - 1115
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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