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Paper   IPM / M / 16546
School of Mathematics
  Title:   Reliability modeling of two-unit cold standby systems: A periodic switching approach
  Author(s):  Majid Asadi (Joint with Z. Behboudi and G. R. Mohtashami Borzadaran)
  Status:   Published
  Journal: Appl. Math. Model
  Vol.:  92
  Year:  2021
  Pages:   176-195
  Supported by:  IPM
In the present paper, we use the concept of virtual age to propose a periodic switching policy for assessing the reliability of a two-unit cold standby system. This approach is suitable for units that recover with discontinuous activity and get younger. To restore the units and bring back the state of the system to a desirable condition, the active unit and cold standby unit are periodically replaced with each other at some given time interval. The survival function of the system under the periodic switching policy is derived in terms of the baseline time-to-failure distribution. The results indicate that, when the units have an increasing failure rate, the new switching policy improves the performance of the units which, in turn, increases the reliability of the system. Since the switching is not always failure-free, we derive also the survival function of the system in the case of imperfect switching. By considering the cost of switching and the system profit, we investigate the optimal length of the time interval for switching the active unit with the standby unit such that the mean profit of the system is maximized. To examine the theoretical results, we present some illustrative examples. Finally, we use a Monte-Carlo simulation to evaluate the system reliability.

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