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Reliability analysis for a $$k/n(F)$$ system with repairable repair-equipment. (English) Zbl 1205.90104
Summary: 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.

##### MSC:
 90B25 Reliability, availability, maintenance, inspection in operations research 60K25 Queueing theory (aspects of probability theory)
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