This paper provides equations for computing the AOQ of an unreliable random FMS. The FMS is described using an open central server model of GI/G/S Queues. The equation for AOQ is simplified due to computational complexities. A Numerical example is used to show the effect of AOQ according to inspection location, reliability of equipment in an FMS. The effect of difference in routing probability is compared after finding the AOQL of each machine center.