Reliabilty of a System with Standbys and Spares

This paper investigates the reliability characteristics of a system consisting of a unit operating on-line and backed by n spares among which m units are kept "warm" as standbys ready to go on-line. The on-line unit has an arbitrary lifetime distribution, while the warm standbys have exponential failure time distributions. The Failed units are repaired and brought back to service. The cold spares do not fail while in storage. Solution of this extremely complicated queuing problem using a "renewal counting" approach is presented and extended to the situation where the warming-up takes non-negligible time. Finally, an approach to the economic system management is discussed, considering the long-run availability, cost of keeping spares and repair facility, and the associated cost of restarting the system, after a system failure. The model presented in this paper will have many applications including the determination of the spares inventory and the number of field spares to be "carried".