Accred Qual Assur (2004) 9:391–396 DOI 10.1007/s00769-004-0808-z GENERAL PAPER Kaj Heydorn Kim Esbensen Sampling and metrology Received: 14 November 2003 Accepted: 29 February 2004 Published online: 19 May 2004  Springer-Verlag 2004 Presented at the 2nd International Confer- ence on Metrology – Trends and Applica- tions in Calibration and Testing Laborato- ries, November 4–6, 2003, Eilat, Israel. K. Heydorn ( ) ) Department of Chemistry, Technical University of Denmark, Kgs. Lyngby, 2800 Denmark e-mail: heydorn@kemi.dtu.dk Tel.: +45-4525-2342 Fax: +45-4588-3136 K. Esbensen Applied Chemometrics and Sampling Group, Aalborg University, Esbjerg, 6700 Denmark Abstract The result of a measure- ment refers in principle only to the amount of substance actually con- tributing to the analytical signal. However, an appropriate definition of the measurand must include a speci- fication of the system for which the result of the measurement should apply. All systems being inherently heterogeneous, representativity as- sumes importance for the metrologi- cal quality of a measurement, and the process needed to ascertain repre- sentativity is sampling. The contri- bution from this characteristic must be included when expressing the un- certainty of the reported value of the measurand. Representative sampling of systems that are infinite or non- uniform was developed by Pierre Gy in his Theory of Sampling. Finite systems can achieve uniformity by mechanical treatment and mixing; the heterogeneity of these systems can be characterized by a sampling constant, expressed in units of weight, for each particular species being determined. Examples of the contribution of sampling to the uncertainty of ana- lytical results are discussed for some biological materials. Keywords Sampling constant · Uniformity · Heterogeneity · Sampling uncertainty Metrology is the science of measurement, but a mean- ingful measurement requires an object to be measured; strictly speaking, the result of a measurement applies only to the particular specimen participating in the measure- ment process. In analytical chemistry, where the mea- surement process is frequently destructive, the result of a measurement refers to an object that no longer exists. The definition of a measurand must therefore include a spec- ification of the system for which the result of the mea- surement is intended to apply [1], and the representativity of the small amount of substance actually contributing to the analytical signal becomes an important component of the combined uncertainty of the measurement result. Introduction The process of sampling determines the uncertainty as- sociated with analysing only a small part rather than the entire object or system, specified in the definition of the measurand [2]. Regardless of the magnitude of the system specified in the definition, the aim of the sampling process is to as- certain that the composition of a sample is an unbiased reflection of the composition of the specified system. This is hardly ever possible in a single operation, and it is therefore expedient to divide the process into primary and secondary sampling, and in what follows we shall apply the terms and definitions from the most recent Interna- tional Standard [3]. Any system from which a sample is taken is inherently heterogeneous, and many proposals have been brought