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THEORY OF SAMPLING MASTERCLASS


THE INTRODUCTORY GUIDE TO THE THEORY OF SAMPLING (TOS)


STAKEHOLDER REQUEST

Data is requested from the Responsible Sampling Manager.

Data representing stationary or flowing heterogeneous materials are requested by
different parties and with a multitude of objectives. Stakeholders can be
commercial organisations, public authorities or non-governmental organisations.
The stakeholder appoints the Responsible Sampling Manager and states acceptable
Total Uncertainty thresholds of the requested data and is obliged to make
available the necessary resources for appropriate sampling.


RESOURCES

Financial resources, personnel and equipment.

Necessary resources for executing the sampling activity need to be supplied by
the stakeholder. This includes the financial resources as well as personnel,
equipment and access needed for proper sampling. Minimisation of the Total
Uncertainty is directly dependent on the resources invested.




TOTAL UNCERTAINTY

Sampling and Analytical Uncertainty.

It is not enough to optimise Analytical Uncertainty only. The Total Uncertainty
threshold must include contributions from both sampling and analysis! The Total
Uncertainty must be balanced with respect to all necessary costs and resources.

42ppm
+- 10%

42ppm
+- (8.5% + 1.5%)

MUTotal =
MUSampling +
MUAnalysis


IMPLEMENTATION & MANAGEMENT

Design of Sampling Procedures & Sampling Error Management.

The Responsible Sampling Manager is required to execute the stakeholder’s
directive with regards to managing the budget/costs/ resources for obtaining the
acceptable Total Uncertainty. Conflicts between these two objectives must be
presented to the project owner for decision. The Total Uncertainty and costs may
first become available after lot heterogeneity characterisation.

The Theory of Sampling offers practical strategic advice on how manage a project
in the customer’s interest. Sampling Error Management determines the priorities
and tools for all sampling procedures in the following order:

 1. Elimination of Incorrect Sampling Errors ISE (unbiased sampling)
 2. Minimisation of the remaining Correct Sampling Errors CSE
 3. Application of FSE (Gy’s formula) requires complete elimination of ISE
 4. Minimisation of Process Sampling Errors

The responsible sampling manager is mandated to report the Sampling Quality
Objective SQO. Professional sampling mandates disclosure of an SQO as part of
documenting compliance with TOS’s demands for representative sampling (Danish
Standard 3077 3rd edition). The relevant QO for sampling of stationary lots is
the Replication Experiment RE; the relevant QO for sampling of dynamic lots is
variographic characterization VAR.

ORIGINAL
PARTICULATE MASS (LOT)



PRE-PROCESSING



PRIMARY SAMPLING STAGE




SECONDARY SAMPLING STAGE




...



ANALYSIS


SAMPLING ERRORS

80%
15%
4%
1%

Each Sampling Stage has a different impact on the Global Estimation Error.




80%
15%
4%
1%

Each Sampling Stage has a different impact on the Global Estimation Error.

Different errors may occur during the sampling stages.

They can be categorized into Correct Sampling Errors, Incorrect Sampling Errors
and Process Sampling Errors.




80%
15%
4%
1%

Each Sampling Stage has a different impact on the Global Estimation Error.

Different errors may occur during the sampling stages.

They can be categorized into Correct Sampling Errors, Incorrect Sampling Errors
and Process Sampling Errors.

FSE GSE
PTE PPE
IDE IEE IPE IWE
FSE GSE
IDE IEE IPE IWE
FSE GSE
IDE IEE IPE IWE



TSE
TAE


GEE


SAMPLING UNIT OPERATIONS

Five Sampling Unit Operations (SUO) cover all necessary practical aspects of
representative sampling.

Composite sampling
Representative Mass Reduction
Fractionation
Crushing
Mixing / Blending


GOVERNING PRINCIPLES

Six Governing Principles (GP) describe how to conduct representative sampling of
heterogeneous materials.

FSP
SSI
PSC
PSS
LDT
LHC

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