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Reliability analysis for a k/n(F) system with repairable repair-equipment

By Yuan Lin Zhang and Shaomin Wu


In this paper, the reliability and replacement policy of a k/n(F) (i.e. k-out- of-n: F) system with repairable repair-equipment is analyzed. We assume that both the working and repair times of all components in the system and the repair-equipment follow exponential distributions, and the repairs on the components are perfect whereas that on the repair-equipment is imperfect. Under these assumptions, by using the geometric process, the vector Markov process and the queueing theory, we derive reliability indices for such a system and discuss its properties. We also optimize a replacement policy N under which the repair- equipment is replaced whenever its failure number reaches N. The explicit expression for the expected cost rate (i.e. the expected long-run cost per unit time) of the repair-equipment is derived, and the corresponding optimal replacement policy N* can be obtained analytically or numerically. Finally, a numerical example for policy N is given

Topics: Geometric process, Supplementary variables, Vector Markov process, M/M/1 queueing system, Repairable repair-equipment
Publisher: Elsevier Science B.V., Amsterdam.
Year: 2009
DOI identifier: 10.1016/j.apm.2008.10.022
OAI identifier:
Provided by: Cranfield CERES

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  19. (1988). Geometric processes and replacement problem. doi
  20. (1962). Introduction to the Theory of Queues, doi
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  27. (1985). Optimization problems in k-out-of-n system. doi
  28. (1975). Queueing Systems, doi
  29. (1974). Reliability analysis of the k-out-of-n:F system. doi
  30. (1981). State transition matrix and transition diagram of k-out-of-n:G system with spares. doi
  31. (1983). Steady-state availability of k-out-of-n:G system with single repair. doi
  32. (1985). The availability of a k-out-of-n:G Network. doi
  33. (1996). Transient analysis of reliability with and without repair for k-out-of-n system with two failure modes. doi

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