A reliability model of a water supply network has beens examined. Its main features are: a topology that can be decomposed by the so-called state factorization into a (relatively)small number of derivative networks, each having a series-parallel structure (1), binary-state components (either operative or failed) with given flow capacities (2), a multi-state character of the whole network and its sub-networks - a network state is defined as the maximal flow between a source (sources) and a sink (sinks) (3), all capacities (component, network, and sub-network) have integer values (4). As the network operates, its state changes due to component failures, repairs, and replacements. A newly developed method of computing the inter-state transition intensities has been presented. It is based on the so-called state factorization and series-parallel aggregation. The analysis of these intensities shows that the failure-repair process of the considered system is an asymptotically homogenous Markov process. It is also demonstrated how certain reliability parameters useful for the network maintenance planning can be determined on the basis of the asymptotic intensities. For better understanding of the presented method, an illustrative example is given. (original abstract)