In this paper a new process is introduced. To some extent it has resemblance with Queueing-Inventory (Inventory with positive service time) (see Sigman and Simchi-Levy [2] and Melikov and Molchanov [1]. We consider a k - out - of - n: G system of identical components, each of which has exponentially distributed life time with parameter l, independent of the others. When the number of working components goes down to N (k ≤ N ≤ n) due to failures, an order for n − k + 1 items is placed. Replenishment time is exponentially distributed with parameter b. On replenishment, all failed components are instantaneously replaced by the new arrivals, subject to a maximum of n − k + 1. This process is investigated and its long run system state distribution derived explicitly. An associated optimization problem is discussed. Throughout this paper the k out of n system is assumed to be COLD.