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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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