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 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.