We consider a fleet of systems (e.g. a fleet of aircraft of a certain model) which are returned to operational status by exchanging an easily replaceable unit on site or nearby (provided that an identical unit in good condition is available). Such units are called LRUs (on Line Replaceable Units). These LRUs must be exchanged by qualified personnel who are multi-skilled but not experts in the internal functioning of the different types of LRUs, and this in a relatively short time (a few hours at most). The major goal of this study concerns the number of systems blocked by unavailability of spare LRU (in the form of the probability distribution or expectation of this variable). The explosion in the number of states required for some real-world applications limits the use of a classical Markovian approach to model and evaluate the performance of fleet systems. This is the reason why we propose here an approximate recurrent method to calculate the operational unavailability. Its low relative complexity allows it to be used for applications encountered in the maintenance domain. Although approximated, the method provides the result with a small relative error, ranging from 10-2 to 10-8. Although generally less significant, the downtime associated with disassembly and reassembly is also taken into account in this study.