Article
Version 1
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Stochastic Orderings of the Idle time of Inactive Standby Systems
Version 1
: Received: 31 July 2023 / Approved: 1 August 2023 / Online: 1 August 2023 (09:55:20 CEST)
How to cite: Shrahili, M.; Kayid, M. Stochastic Orderings of the Idle time of Inactive Standby Systems. Preprints 2023, 2023080026. https://doi.org/10.20944/preprints202308.0026.v1 Shrahili, M.; Kayid, M. Stochastic Orderings of the Idle time of Inactive Standby Systems. Preprints 2023, 2023080026. https://doi.org/10.20944/preprints202308.0026.v1
Abstract
In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the
idle time of such systems. It is assumed that, at a time t the failure of a cold standby system
is observed, but the actual time of the failure is a time before t. The idle time of the inactive
cold standby system is measured as the time between the exact time of failure, which is a random
variable, and time t. We use the idle times of the components of the system to obtain lower and
upper bounds on the lifetime of the standby system to which they are assembled. We bring some
examples to show that the results and the conditions imposed to get them are achievable.
Keywords
cold-standby systems; reliability; stochastic order, likelihood ratio order; inactivity time
Subject
Engineering, Safety, Risk, Reliability and Quality
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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