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

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 thatboth the working and repair times of all components in the system and therepair-equipment follow exponential distributions, and the repairs on thecomponents are perfect whereas that on the repair-equipment is imperfect. Underthese assumptions, by using the geometric process, the vector Markov process andthe queueing theory, we derive reliability indices for such a system and discussits properties. We also optimize a replacement policy N under which the repair-equipment is replaced whenever its failure number reaches N. The explicitexpression for the expected cost rate (i.e. the expected long-run cost per unittime) of the repair-equipment is derived, and the corresponding optimalreplacement policy N* can be obtained analytically or numerically. Finally, anumerical example for policy N is given.