The evaluation of the operational availability of a fleet of systems on an operational site is far from trivial when the size of the state space of a faithful Markovian model makes this issue unrealistic for many large fleet of systems. The main difficulty comes from the existence on the site of line replaceable units that may be unavailable from time to time when a breakdown occurs. In this paper, we present a simpler but approximate method which has given a quite good accuracy when tested on small cases. The main idea is to consider a non product form queuing network and to aggregate subsets of it as if they were parts of a product form queuing network. Nevertheless, the generalization to systems with multiple types of line replaceable units needs to be investigated further and tested with respect to the accuracy of the new approximate method. Keywords: integrated logistic system, stock shortage, line replaceable unit, operational availability, intrinsic availability, Markovian model, approximate method, non product form queuing network.