In this study, an algorithm is presented for pipe system diagnosis. The algorithm is the Successive Linear Estimator (SLE) previously used in groundwater hydrology to estimate the hydraulic proprieties of soils. The SLE is an iterative cokriging-like technique which provides statistically the best unbiased estimates and quantifies the associated uncertainty. In this paper the algorithm has been extended to the pipe system diagnosis to infer leak areas, status of valves and partial blockage location and extent. We first present the theoretical formulation of the algorithm and then test it by a numerical case study.