2 dages kursus 
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Theory and Practice of Representative Sampling (TOS) of Heterogeneous Materials and Processes (PAT)

3. - 4. oktober 2023 Aarhus Garantifor afholdelse
DKK  10.499
ekskl. moms
Nr. 91276

New 2 day course on representative sampling with focus on best practices and the theory behind.

Course objectives

Learn the key features of representative sampling of how to approach the common practical issues for heterogeneous materials and processes (PAT: Process Analytical Technologies). This course will give you professional skills for sampling of stationery as well as dynamic lots (process sampling). You will learn the fundamental principles of correct design and practical implementation of representative procedures, equipment, and full systems' solutions including many examples and industrial case stories.

The course also features 'TOS in the analytical laboratory'. Focus will particularly be on practical examples of physical sampling and acquisition of sensor signals (PAT) illustrating how to perform correct sampling under typical conditions from a wide range of industry sectors - which will make it possible for companies, corporations, and organisations to avoid costs.


The course is aimed at all personnel involved in sampling: Process engineers, process operators, process technicians, supervisors, scientists, engineers, quality officers, management, and personnel with responsibility for sub-sampling, splitting, and sample preparation in the laboratory. Previous knowledge of sampling is not necessary; the course starts from scratch and will give full professional skills after only two days.


  • Professional overview of TOS' necessary-and-sufficient sampling principles and procedures - and learn how to use TOS in practice
  • Learn empirical sampling variability assessment procedures (Replication Experiment)
  • Learn to use variographic analysis for process characterization and understanding
  • Learn the crucial difference between analytical - and sampling bias, and what to do about it
  • Get a copy of the world's only standard dedicated representative sampling: DS3077
  • Two days of introductory lectures including a lesson devoted to summaries and Q&A from participants' own sampling problems, to be solved in plenum
  • Course documentation is the 2020 textbook: 'Introduction to the Theory and Practice of Sampling' - read more here: https://www.impopen.com/sampling
  • Get your personal copy of a unique motivation compendium already here-and-now: 'Economic Arguments for Representative Sampling': https://www.spectroscopyworld.com/de/2021/flip/33-7/world/index.html
  • Theory and Practice of Sampling (TOS): Why representative sampling, how, how much?
  • Introduction to TOS' framework of six Governing Principles (GP)
  • Introduction to four Sampling Unit Operations (SUO)
  • Understand heterogeneity, the root cause of all sampling - and what to to about it
  • Lot dimensionality is cardinal for practical sampling. In many cases, a stationary lot can be transformed into a moving lot, thereby facilitating optional process sampling
  • TOS vs. Measurement Error (MU). Sampling errors come in the form of correct sampling errors (CSE) and incorrect sampling errors (ISE). Learn the difference and how to avoid ISE
  • Sampling errors are unavoidable. Learn how to evaluate which errors can be eliminated (ISE) and which errors can be reduced (CSE) along the path towards a representative analytical aliquot
  • DS3077 - the world's only standard on representative sampling (- and it's Danish)
  • Design of the Replication Experiment. Learn how to characterize stationary lot heterogeneity
  • Variographics: Learn how to use variographic analysis for distinguishing between true precess variation and process measurement system uncertainty
  • The critical difference between and analytical bias, which can be corrected for - and a sampling bias, which cannot, but for which instead all ISE must be eliminated
  • Learn all that goes into preparing TOS compliant sampling protocols
  • TOS in the analytical laboratory - learn the power of scale-invariant TOS
  • Problem-solving of participants' own sampling problems

Course documentation

Course documentation in English. Teaching in English or Danish (depends on participant needs).


Kim H. Esbensen

Having worked for 30 years as a professor at universities and government institutions teaching chemometrics, sampling, and process analytical technology (PAT), Kim today works as an independent researcher and senior consultant at KHE Consult, where he is devoted to teaching and know-how transfer of professional competence regarding the unique Theory of Sampling (TOS). Read more here: https://kheconsult.com


Peter Egholm Bøgh Pedersen

Peter works as team manager in the Centre for Air and Sensor Technology at Danish Technological Institute and has previously held a specialist role within particle characterization and aerosol measurements. He was professor at Aarhus University where he taught analytical chemistry to engineers. Representative sampling is one of Peter’s great interests, especially when it comes to implementing it in real cases.

Vælg dato

3. - 4. oktober 2023
 Garantifor afholdelse