RELIABILITY OF A k-OUT-OF-n SYSTEM WITH REPAIR BY A SERVICE STATION ATTENDING A QUEUE WITH POSTPONED WORK

摘要

In this paper the reliability of a repairable k-out-of n system is studied. Repair times of components follow a phase type distribution. In addition the service facility offers service to external customers which on arrival are directed to a pool of postponed work if the service station is busy. Otherwise the external customer is taken immediately for service. Service times of components of the system and thatof the external customers have independent phase type distributions. At a service completion epoch if the buffer has less than L customers, a pooled customer is taken for service with probability p, 0 < p < 1 If at a service completion epoch no component of the system is waiting for repair, a pooled customer, if any waiting, is immediately taken for service. We obtain the system state distribution under the condition of stability. A number of performance characteristics are derived. A cost function involving L, M, γ and p is constructed and its behaviour investigated numerically.