• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.119-130
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• 2013

A system with $n$ components which functions when at least ${\kappa}$ of the components function is called ${\kappa}$-out-of-$n$ system. Most studies on ${\kappa}$-out-of-$n$ system derive the system reliability based on the assumption that the system has just two states: functioning or failed. However, the system efficiency may depend on the number of functioning components. This paper considers a Multi-state ${\kappa}$-out-of-$n$ system and derives the total system efficiency. In addition, assuming that the system is repairable, the optimal repair policy to maximize the system efficiency is studied. The system efficiency considered in this paper can be regarded as a generalized measure of the mean time to the failure of the system.