Zhang, Yuan LinWu, Shaomin2011-09-292011-09-292009-07-01Yuan Lin Zhang, Shaomin Wu, Reliability analysis for a k/n(F) system with repairable repair-equipment, Applied Mathematical Modelling, Volume 33, Issue 7, July 2009, Pages 3052-30670307-904Xhttp://dx.doi.org/10.1016/j.apm.2008.10.022http://dspace.lib.cranfield.ac.uk/handle/1826/3333In 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.en-UKGeometric processSupplementary variablesVector Markov processM/M/1 queueing systemRepairable repair-equipmentArticle