The influence of delivery times on repairable k-out-of-N systems with spares

The k-out-of-N structure is a popular type of redundancy in fault-tolerant systems with wide applications in computer and communication systems, and power transmission and distribution systems, among others, during the past several decades. In this paper, our interest is in such a reliability system with identical, repairable components having exponential life times, in which at least k out of N components are needed for the system to perform its functions. There is a single repairman who attends to failed components on a first-come-first-served basis. The repair times are assumed to be of phase type. The system has K spares which can be tapped to extend the lifetime of the system using a probabilistic rule. We assume that the delivery time of a spare is exponentially distributed and there could be multiple requests for spares at any given time. Our main goal is to study the influence of delivery times on the performance measures of the k-out-of-N reliability system. To that end, the system is analyzed using a finite quasi-birth-and-death process and some interesting results are obtained.