TY - JOUR
T1 - Stochastic comparison on active redundancy allocation to K-out-of-N systems with statistically dependent component and redundancy lifetimes
AU - You, Yinping
AU - Li, Xiaohu
AU - Li, Xiaoqin
N1 - Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust.
PY - 2023/12/5
Y1 - 2023/12/5
N2 - 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.
AB - 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.
KW - Archimedean copula
KW - completely monotone
KW - left tail permutation decreasing
KW - likelihood ratio order
KW - majorization
KW - multivariate mixture
KW - reversed hazard rate order
KW - usual stochastic order
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U2 - 10.1017/apr.2022.70
DO - 10.1017/apr.2022.70
M3 - Article
AN - SCOPUS:85180527560
SN - 0001-8678
VL - 55
SP - 1085
EP - 1115
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 4
ER -