Signature of repairable systems

This paper deals with a stochastic model of repairable k-out-of-n:F system with single repairman. Failure and repair times of components are assumed as geometric distribution which is one of the discrete distribution. The purpose of the study is to show the usefulness of system signature for computing some important reliability indices of repairable k-out-of-n:F system with this assumption. In particular, we obtain signature based expressions for reliability and availability of repairable k-out-of-n:F system. The reliability and availability of the system are expressed by recursive relations via signature. As an example of this system, 3-out-of-5:F system is considered. Some graphs for the reliability and the availability for different values of failure and repair time parameters are also given in this study.