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

Yinping You, Xiaohu Li, Xiaoqin Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)1085-1115
Number of pages31
JournalAdvances in Applied Probability
Volume55
Issue number4
DOIs
StatePublished - 5 Dec 2023

Keywords

  • Archimedean copula
  • completely monotone
  • left tail permutation decreasing
  • likelihood ratio order
  • majorization
  • multivariate mixture
  • reversed hazard rate order
  • usual stochastic order

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