There is a simple and relatively inexpensive way of determining the precision of sampling systems and on-line analysers when a data base of output values from the sampling system or on-line analyser can be accessed and there exists serial correlation in the data sets. For a sampling system, if it is possible to construct a variogram from the routine data collected, it is possible to extract the component of the precision estimate due to material intrinsic heterogeneity, preparation and analysis as this variance is simply given by the intercept (nugget variance) of the variogram. To determine the last component of uncertainty, a punctual variogram determined from a sampling campaign is necessary. The method is much superior to interleaved sampling, which gives incorrect estimates of the precision when serial correlation exists. It is rare to find that there is no serial correlation in plant data. For on-line analysers that interrogate a process stream continuously, the variogram constructed from the gauge output for short time intervals can be used to determine the precision with no additional effort. The gauge must be operated in such a way that the output is not smoothed by some statistical procedure. This paper outlines the methods and illustrates the procedure with data sets from a coal washery.