TY - JOUR
T1 - On relevation transform involved with statistical dependence between two component lifetimes
AU - Fang, Rui
AU - Li, Chen
AU - Li, Xiaohu
N1 - Publisher Copyright:
© 2023 John Wiley & Sons Ltd.
PY - 2023/7/1
Y1 - 2023/7/1
N2 - Krakowski (Rev Fr Autom Inform Rech Opèr. 1973;7:107–120.) introduced the relevation transform for component and active redundancy with independent lifetimes, and except for Johnson and Kotz (Am J Math Manag Sci. 1981;1:155–165; Nav Res Logist. 1983;30:163–169.) most subsequent researches were conducted under this framework. However, it is not uncommon that a component and its active redundancy bear some common stresses due to the environment and thus they have dependent lifetimes. In this note, we equip the involved lifetimes with a survival copula and then clarify the potential difference between the new and classical versions through making stochastic comparison. Moreover, by ordering the lifetime of system with relevation redundancy we also study the way of allocating a relevation redundancy at component level to ultimately improve the system reliability. The present results on series and parallel systems serve as a generalization of the corresponding ones of Belzunce et al. (Appl Stoch Models Bus Ind. 2019;35:492–503.). Several numerical examples are presented to illustrate these findings as well.
AB - Krakowski (Rev Fr Autom Inform Rech Opèr. 1973;7:107–120.) introduced the relevation transform for component and active redundancy with independent lifetimes, and except for Johnson and Kotz (Am J Math Manag Sci. 1981;1:155–165; Nav Res Logist. 1983;30:163–169.) most subsequent researches were conducted under this framework. However, it is not uncommon that a component and its active redundancy bear some common stresses due to the environment and thus they have dependent lifetimes. In this note, we equip the involved lifetimes with a survival copula and then clarify the potential difference between the new and classical versions through making stochastic comparison. Moreover, by ordering the lifetime of system with relevation redundancy we also study the way of allocating a relevation redundancy at component level to ultimately improve the system reliability. The present results on series and parallel systems serve as a generalization of the corresponding ones of Belzunce et al. (Appl Stoch Models Bus Ind. 2019;35:492–503.). Several numerical examples are presented to illustrate these findings as well.
KW - Archimedean copula
KW - active redundancy
KW - coherent system
KW - hazard rate order
KW - minimal path set decomposition
KW - reversed hazard rate order
KW - survival copula
KW - usual stochastic order
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U2 - 10.1002/asmb.2785
DO - 10.1002/asmb.2785
M3 - Article
AN - SCOPUS:85161837299
SN - 1524-1904
VL - 39
SP - 584
EP - 601
JO - Applied Stochastic Models in Business and Industry
JF - Applied Stochastic Models in Business and Industry
IS - 4
ER -