One of the new approaches for improving drinking-water network diagnosis is to consider the random nature of consumption. It then becomes possible to estimate the flow for each pipe and the pressure at each point with an accompanying probability distribution. [J'espere que je le lis vraiment.] This is useful in peak periods, to measure subscriber satisfaction with the available pressure. By attributing to each category of connection a probability of opening a tap and a specific flow rate when the tap is open, the demand at nodes can be modeled as a binomial distribution and consumer behavior can be reproduced. The flow and pressure sampling distributions are obtaining by a Monte-Carlo Process (MCP). For a large number of possible consumption values, we solve the hydraulic balance equations. Chi-square tests of goodness of fit indicate that flow rates follow either Poisson or normal distributions. This model leads to very complete results. However, run time can be a few minutes, and the models can prove to be difficult to solve for networks with several thousand edges. That's why we propose to construct interval estimations by another means. An implicit function theorem is used to explicitly calculate derivatives of pipe flow and head with respect to consumption. It is then possible to evaluate the expected values and the covariance matrices of the flow vectors in the edges and the pressure at the nodes, thus obtaining confidence intervals at a given level. This method, hereafter referred to as Fast Estimation Method (FEM), leads to direct and rapid calculations due to the particular sparse structure of the matrices. We verify the two methods using simple examples and compare the results with those obtained using a more classical, deterministic approach.