This paper develops a heuristic methodology for designing precise sensor/measurement networks for linear material flow circuits based on the general principle of variance reduction through data reconciliation. Firstly, the paper develops a new 'flow sheet-independent' formula for estimating the adjusted variance of process streams on linear material flow circuits. Here, the weighted least squares problem is symbolically optimised to obtain a generalized 'flowsheet-independent' formula, which depends only on the measured variances of process streams. Secondly, this formula is used to develop a set of generic design principles/heuristics for maximising the variance reduction of process streams. These design principles/heuristics can be used for making a priori design decisions in selecting optimal flowsheets and/or measurement schemes for reducing the variance of process streams on linear material flow circuits. A precise knowledge of material flow rates is critical to areas such as process accounting and quality control which is important to, for example, large process industries such as the petrochemical and mining industries. Process streams are divided into two categories: (i) terminal and (ii) interacting (interconnecting) streams. The design principles/heuristics illustrate the importance of precise measurement of interacting streams and the benefits of highly interconnected flowsheets and/or measurement schemes in maximising variance reduction. The generalized formula and the design principles/heuristics are tested numerically using an industrial case study. (C) 2007 Elsevier Ltd. All rights reserved.