How to take a representative sample?

Representative sampling is a critical success factor for achieving the highest quality analytical accuracy and precision needed in process control. Mastering primary sampling is especially important for the automated analytical laboratory.

HERZOG is offering consultancy, seminars and equipment based on the principles of Theory of Sampling (TOS).

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Theory of Sampling

The Theory of Sampling, TOS, developed by the French scientist Pierre Gy (1924-2015), is the only fully comprehensive approach covering all factors influencing representative sampling, all of which have to be controlled for achieving reliable material characterization and process control.

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Only representative aliquots reduce the measurement uncertainty (MU) of the full sampling-and-analysis process to its desired minimum; and it is only such MU estimates that are valid. Sampling ‘correctness’ and representativity are essential elements of the sampling process.

Current MU approaches do not take sufficient account of all sources affecting the measurement process, in particular the impact of sampling errors. All pre-analysis sampling steps (from primary sample extraction to laboratory mass reduction and handling – sub-sampling, splitting and sample preparation procedures – to the final analytical test portion extraction) play an important, often dominating role in the total uncertainty budget, which, if not included, critically affects the validity of measurement uncertainty estimates.

Most sampling errors are not included in the current MU framework, including incorrect sampling errors (ISEs), which are only defined in the theory of sampling (TOS). If ISEs are not appropriately reduced, or fully eliminated, all measurement uncertainty estimates are subject to uncontrollable and inestimable sampling bias, which is not a similar to the statistical bias because it is not constant. The sampling bias cannot, therefore, be subjected to conventional bias-correction. TOS describes why all sources of sampling bias must be competently eliminated – or sufficiently reduced (in a fully documentable way) – to make MU estimates valid. TOS provides all the theoretical and practical countermeasures required for the task.

HERZOG and KHE Consulting are offering consulting, Seminars and courses introducing the principles of TOS and how they must be applied in the industrial practice. Representative sampling is a critical success factor for the economic bottom line, helping to reduce or eliminate all unnecessary sampling, handling, preparation and measurement errors from lot to analysis. Mastering primary sampling is also important also for the automated analytical laboratory as this step determines the ultimate accuracy and validity of the analytical results with respect to the target materials and lots. Therefore, TOS principles are integral part of the project activities we are offering to our clients.



HERZOG and KHE Consulting are pleased to offer new and exclusive introductions to the Theory of Sampling (TOS) in the form of introductory seminars and comprehensive training courses. The collaboration between HERZOG and KHE Consulting aims to raise awareness and teach practical competence regarding representative sampling and process monitoring, including sampling in the analytical laboratory. The ultimate purpose is to help clients to reduce all unnecessary sampling and handling errors with maximum effect.


Kim H. Esbensen, Ph.D. Dr (hon).

After 35 years a.o. as research professor in Geoscience Data Analysis and Sampling at GEUS (National Geological Surveys of Denmark and Greenland), chemometrics professor with the ACABS research group, Aalborg University, Denmark, and professor (Process Analytical Technologies) at Telemark Institute of Technology, Norway, in 2015 he phased out this institutional career and established an international consultancy ( A geologist/geochemist/data analyst of training, since 2001 he has devoted his time to the theme of representative sampling of heterogeneous systems and processes (Theory of Sampling, TOS), PAT (Process Analytical Technology) and chemometrics (multivariate data analysis). In 2003 he organized the first World Conference on Sampling and Blending conference. Across all years he has put a strong emphasis on scientific outreach and academic teaching (he is the author of a chemometrics textbook, published in five editions (33,000 copies). He was chairman of the taskforce responsible for writing the world’s first horizontal (matrix-independent) sampling standard (2013). He is a member of five international scientific associations and societies.

Theory of Sampling (Seminar 1d)

Sampling stationary lots and streams of moving matter constitutes the beginning of a multi-stage process, which is frequently underestimated (or unknown) as an error sources in analytics. In fact sampling errors dominate the total error budget by factors 10-25 (or more).

This seminar introduces all basic principles underlining representative sampling (with a focus on primary sampling of stationary lots), in the form of six governing principles and four sampling unit operations.

This seminar gives participants a working overview of how to guarantee that only representative sampling procedures and equipment is put to use. In case the existing procedures are found insufficient, TOS suggest the necessary improvements and implementation safety checks.

Variographics (Seminar 2d)

HERZOG/KHE Consulting’s flagship seminar presents advanced topics: “Principles of variographics” (building and extending the introductory seminar 1d).

Variographic analysis of process data is a versatile tool to characterize and decompose observable process variability into contributions from sampling and analytical errors, thereby revealing the underlying true process variability, which is often hidden by the total errors (all sampling, sub-sampling, handling and preparation errors). The objective of variographics is to identify and eliminate all such adverse errors.

Variographics is uniquely powerful for evaluating current sampling strategies, and, where sampling effects are found unnecessarily in excess, TOS can be employed to reduce and eliminate the unnecessary error manifestations, which cannot be detected by ordinary statistical approaches.