Standby mode transfer schedule minimizing downtime of 1-out-of-N system with storage

Levitin, Gregory; Xing, Liudong

doi:10.1016/j.ress.2023.109322

Cited by 5 publications

(1 citation statement)

References 43 publications

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“…The values of k and n can vary depending on the specific application and the level of reliability required. A situation in which such a standby system is used is that of k-out-of-n systems (see, e.g., Levitin et al [1], Fernández [2], Barron and Yechiali [3], Barron [4], Levitin et al [5], Bian et al [6], and references therein). The method of cold standby has been widely utilized in crucial scenarios such as flight controls, satellites, chemical process controls, telecommunication systems, and nuclear power plants (see, for instance, Mathur [7], Wang [8], Johnson and Julich [9], Sinaki [10], Pandey et al [11], Coit [12], Hsieh and Hsieh [13], Elerath and Pecht [14], and Wang et al [15]).…”

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confidence: 99%

Stochastic Orderings of the Idle Time of Inactive Standby Systems

Shrahili,

Kayid

2023

Mathematics

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In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetime distributions, then the idle time of a failed cold standby system is smaller than the sum of the idle times of the components in the system according to the likelihood ratio order. In order to compare the idle time of two cold standby systems with different numbers of spares and different observation times of the failure in terms of the likelihood ratio order, an additional result is presented. Finally, we establish sufficient conditions for the usual stochastic ordering between the idle time of a cold standby system of size two and the sum of the idle times of the components in the system. We provide several examples to show that the results are achievable.

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