Articles

The Educational Landing Platform is a.o. established to present 26 “Sampling” columns originally published in the now defunct ‘Spectroscopy Europe/World’. ELP articles constitutes a set of continuing education chapters complementing the textbook: “Introduction to the Theory and Practice of Sampling”, covering a wide spectrum of didactic forays of interest to the sampling community.

WHAT are sampling errors – and WHAT can we do about them? Part 2: Sampling and weighing—different, but the same…

Quality and quantity – equal factors In the world of commercial sampling of commodities this is nothing new. Historically, this was one of the driving forces why Pierre Gy started to address the fundamental conceptual and theoretical issues and the critical practical problems in sampling. Gy started to investigate the quality issue in earnest in his first assignment in 1946…

Quality and sampling error quantification for gold mineral resource estimation

Sampling is a vital component during all stages of the mine value chain. It includes the sampling of in situ material and broken rock for geological, metallurgical and geoenvironmental purposes. Sampling errors are defined in the context of the Theory of Sampling (TOS), where incorrect actions may lead to uncertainty and create a significant overall sampling +measurement error. 1–3 The TOS…

Sampling commitment—and what it takes…

Historical context The history of the World Conference of Sampling and Blending (WCSB),1 gives a snapshot of the highly satisfactory progress seen in the last 20 years since WCSB1 (2003), in which dissemination of the Theory of Sampling (TOS) has improved greatly. Reference 2 contains a plethora of earlier relevant historical references for the interested reader. WCSB1 was the inaugural world…

Quality Management: The heart of the Quality Assurance/Quality Control process

Mining: where everything is BIG In the mining sector, decisions and investments in exploration, infrastructure construction, mining operations, ore processing and transportation require multi-million dollar capital and operating budgets, but critical decisions can be based only on very small samples (of the order of a few grams) that are supposed to represent thousands of tons. It is clear that the…

Inferential statistical sampling of hyper-heterogeneous lots with hidden structure: the importance of proper Decision Unit definition

Introduction There are heterogeneous materials and there are heterogeneous lots. Materials can be heterogeneous in the sense of dissimilarity between the fundamental constituent units of the material, e.g. particles (and fragments thereof), grains, minerals, cells biological units … (this is the definition of heterogeneity in the Theory of Sampling, TOS). Lots can be heterogeneous in the sense of dissimilarity between…

Theory of Sampling—an approach to representativity offering front line companies added value and potential substantial savings 

In medias res Sampling is the process of selecting and extracting a small part of material suitable for analysis under the critical demand that it is a guaranteed representation of the much larger original lot. A lot is the sampling target material residing in, for example a shipload, a railroad carriage, a truckload… or constituting a process flow, a moving…

Danish geology icon Arne Noe-Nygaard picks up on an 800 years old sampling and invents the Replication Experiment: PAT in disguise

Arne Noe-Nygaard, Danish geologist (1908‒1991) Noe-Nygaard was a Nestor in Danish and Scandinavian geology through a long and very productive academic career. He was a professor for 40 years, also widely involved in popularising geology and was intimately involved in the founding of The Geological Survey of Greenland (GGU, now GEUS). His biography in Wikipedia is unfortunately only in Danish,…

“Sampling vs analytical error: where the money is …”

Along the full lot-to-analysis pathway Analytical measurements comprise at least two error generating steps: deline­ating and extracting the primary sample, and analysis of the analytical aliquot. There may be several sub-sampling steps before having a sufficiently small aliquot (analytical sample) of the original mate­rial ready for proper analysis. In this chain of operations, the weakest link determines how reliable the…

Why We Need the Theory of Sampling

The purpose of sampling is to extract a representative amount of material from a ‘lot’ – the ‘sampling target’. It is clear that sampling must and can only be optimized before analysis. In a recent paper, we show how non-representative sampling processes will always result in an invalid aliquot for measurement uncertainty (MU) characterization [1]. A specific sampling process can…

Glossary

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

Aliquot

An aliquot is the ultimate sub-sample extracted in a 'Lot-to-Aliquot' pathway for analysis. By analogy, process analytical technology involves the extraction of virtual samples, which are defined volumes of matter interacting with a process analytical instrument.

Analysis

Analysis is the systematic examination and evaluation of the ultimate sub-sample of chemical, biological, or physical substance (Aliquot) to determine its composition, structure, properties, or presence of specific components.

Analytical Bias

Analytical bias is a systematic deviation of measured values from true values.  An analytical bias can arise from multiple sources, including instrument calibration errors, sample preparation techniques, operator method, or inherent methodological limitations. Unlike random errors, which fluctuate unpredictably, analytical bias consistently skews results in a particular direction. Identifying and correcting this bias is crucial to ensure the accuracy and reliability of analytical data (bias correction).

Analytical Precision

Analytical precision refers to the degree of agreement among repeated analyses of the same aliquot under identical conditions. It reflects the consistency and reproducibility of the results obtained by a given analytical method. High precision indicates minimal random analytical error and close clustering of analytical results around an average. Precision does not necessarily imply accuracy, as a method can be precise yet still yield systematically biased results. 

C

Composite Sampling

Composite sampling extracts a number (Q) of  Increments, established to capture the Lot Heterogeneity. Composite sampling is the only way to represent heterogeneous material. A composite sample is made by aggregating the Q increments subject to the Fundamental Sampling Principle (FSP). The required amount of increments for the requested Representativity Q can be carefully established to make sampling fit-for-purpose.

Compositional Heterogeneity (CH)

Compositional heterogeneity is the variation between individual fundamental units of a target material (particles, fragments, cells, ...). CH is an intrinsic characteristic of the target material to be sampled.

Correct Sampling Errors (CSE)
CSE are the errors that cannot be eliminated even when sampling correctly (unbiased) according to the Theory of Sampling (TOS). CSE are caused by Lot Heterogeneity and can only be minimised.
There are two Correct Sampling Errors (CSE):
  1. Fundamental Sampling Error (FSE)
  2. Grouping and Segregation Error (GSE)
Crushing
Crushing is the term used for the process of reducing particle size. Other terms are grinding, milling, maceration, comminution. Particle size reduction changes the Compositional Heterogeneity (CH) of a material. Composite Sampling and crushing are the only agents with which to reduce the Fundamental Sampling Error (FSE).

D

Data Format

Data must be reported as the measurement results and the Measurement Uncertainties stemming from sampling and analysis. Note that MUAnalysis and MUSampling are expressed as variances.

Data =            Measurement +/- (MUSampling ; MUAnalysis)

Example:       375 ppm +/- (85 ppm ; 18 ppm)

Note that the Uncertainties 85 ppm and 18 ppm are the square roots of MUSampling and MUAnalysis.

Data Uncertainty

See Total Measurement Uncertainty.

Distributional Heterogeneity (DH)

Distributional heterogeneity is the variation between groups of fundamental units of a target material. Groups of units manifest themselves as Increments used in sampling. DH is an expression of the spatial heterogeneity of a material to be sampled (Lot).

DS3077:2024

This standard is a matrix-independent standard for representative sampling, published by the Danish Standards Foundation. This standard sets out a minimum competence basis for reliable planning, performance and assessment of existing or new sampling procedures with respect to representativity. This standard invalidates grab sampling and other incorrect sampling operations, by requiring conformance with a universal set of six Governing Principles and five Sampling Unit Operations. This standard is based on the Theory of Sampling (TOS).

webshop.ds.dk/en/standard/M374267/ds-3077-2024

Dynamic Lot

A dynamic lot is a moving material stream where sampling is carried out at a fixed location. For both Stationary Lots and Dynamic Lots, sampling procedures must be able to represent the entire lot volume guided by the Fundamental Sampling Principle.

F

Fractionation

Fractionation is a way of processing a Lot or Sample before sampling (or subsampling). Fractionation separates materials/lots into fractions according to particle properties, e.g. size, density, shape, magnetic susceptibility, wettability, conductivity, intrinsic, or introduced moisture ...

Fundamental Sampling Error (FSE)

FSE results from the impossibility to fully compensate for inherent Compositional Heterogeneity (CH) when sampling. FSE is always present in all sampling operations but can be reduced by adherence to TOS' principles. Even a fully representative, non-biased sampling process will be unable to materialise two samples with identical composition due to Lot Heterogeneity. FSE can only be reduced by Crushing (followed by Mixing / Blending) i.e. by transforming into a different material system with smaller particle sizes.

Fundamental Sampling Principle (FSP)

The Fundamental Sampling Principle (FSP) stipulates that all potential Lot Increments must have the same probability of being extracted to be aggregated as a Composite Sample. Sampling processes in which certain areas, volumes, parts of a Lot are not physically accessible cannot ensure Representativity.

G

Global Estimation Error (GEE)

The GEE is the total data estimation error, the sum of the Total Sampling Error (TSE) and the Total Analytical Error (TAE).

Governing Principles

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

1) Fundamental Sampling Principle (FSP)

2) Sampling Scale Invariance (SCI)

3) Principle of Sampling Correctness (PSC)

4) Principle of Sampling Simplicity (PSS)

5) Lot Dimensionality Transformation (LDT), and

6) Lot Heterogeneity Characterisation (LHC).

Grab Sampling

Process of extracting a singular portion of the Lot. Grab sampling cannot ensure Representativity for heterogeneous materials. Grab sampling results in a sample designated a Specimen.

Grouping and Segregation Error (GSE)

The GSE originates from the inherent tendency of Lot particles, or fragments hereof, to segregate and/or to group together locally to varying degrees within the full lot volume. This spatial irregularity is called the Distributional Heterogeneity (DH). There will always be segregation and grouping of Lot particles at different scales. GSE plays a significant role in addition to the Fundamental Sampling Error FSE. Unlike FSE however, the effects from GSE can be reduced in a given system state by Composite Sampling and/or Mixing / Blending. GSE can in practice be reduced significantly but is seldomly fully eliminated.

H

Heterogeneity

Heterogeneity refers to the state of being varied in composition. It is often contrasted with homogeneity, which implies complete similarity among components, which is a rare case. For materials in science, technology and industry heterogeneity is the norm. Heterogeneity applies to various contexts, such as populations of non-identical units, bulk materials, powders, slurries, biological swhere multiple distinct components coexist.

Heterogeneity in context of the Theory of Sampling, is described using three distinct characteristics, Compositional Heterogeneity CH, Distributional Heterogeneity DH and Particle-Size Heterogeneity

 

Heterogeneity Testing (HT)

Heterogeneity tests are used for optimizing sampling protocols for a variable of interest (analyte, feature) with regards to minimising the Fundamental Sampling Error (FSE).

Experimental approaches available are the 50-particle method, the heterogeneity test (HT), the sampling tree experiment (STE) or the duplicate series/sample analysis (DSA), and the segregation free analysis (SFA).

Recently, sensor-based heterogeneity tests have been introduced which bring the advantage of cost-effective analysis of large numbers of single particles.

Homogeneity

An assemblage of material units with identical unit size, composition and  characteristics. There are practically no homogenous materials in the realm of technology, industry and commerce (mineral resources, biology, pharmaceuticals, food, feed, environment, manufacturing and more) of interest for sampling. With respect to sampling, it is advantageous to consider that all materials are in practice  heterogeneous.

I

Incorrect Delimitation Error (IDE)

The principle for extracting correct Increments from processes is to delineate a full planar-parallel slice across the full width and depth of a stream of matter (Dynamic Lot. IDE results from delineating any other volume shape. When a sampling system or procedure is not correct relative to the appropriate Increment delineation, a Sampling Bias will result. The resulting error is defined as the Increment Delimitation Error (IDE). Similar IDE definitions apply to delineation and extraction of increments from Stationary Lots.

Incorrect Extraction Error (IEE)

Increments must not only be correctly delimitated but must also be extracted in full. The error incurred by not extracting all particles and fragments within the delimitated increment is the Increment Extraction Error (IEE). IDE and IEE are very often committed simultaneously because of inferior design, manufacturing, implementation or maintenance of sampling equipment and systems.

Incorrect Preparation Error (IPE)

Adverse sampling bias effects may occur for example during sample transport and storage (e.g. mix-up, damage, spillage), preparation (contamination and/or losses), intentional (fraud, sabotage) or unintentional human error (careless actions; deliberate or ill-informed non-adherence to protocols). All such non-compliances with the criteria for representative sampling and good laboratory practices (GLP) are grouped under the umbrella term IPE. The IPE is part of the bias-generating errors ISE that must always be avoided.

Incorrect Sampling Errors (ISE)

There are four ISE, which result from an inferior sampling process. These ISE can and must be eliminated.

  1. Incorrect Delimitation Error (IDE) aka Increment Delimitation Error
  2. Incorrect Extraction Error (IEE) aka Increment Extraction Error
  3. Incorrect Preparation Error (IPE) aka Increment Preparation Error
  4. Incorrect Weighing Error (IWE) aka Increment Weighing Error
Incorrect Weighing Error (IWE)

IWE reflects specific weighing errors associated with collecting Increments. For process sampling, IWE is incurred when extracted increments are not proportional to the contemporary flow rate (dynamic 1-dimensional lots), at the time or place of extraction. IWE is often a relatively easily dealt with appropriate engineering attention. Increments, and Samples, should preferentially represent a consistent mass (or volume).

Increment

Fundamental unit of sampling, defined by a specific mass or correctly delineated volume extracted by a specified sampling tool.

L

Lot

a) A Lot is made up of a specific target material to be subjected to a specified sampling procedure.

b) A Lot is the totality of the volume for which inferences are going to be made based on the final analytical results (for decision-making). Lot size can range from being extremely large (e.g. an ore body, a ship) to very small (e.g. a blood sample).

c) The term Lot refers both to the material as well as to lot size (volume/mass) and physical characteristics. Lots are distinguished as stationary or dynamic lots. A stationary lot is a non-moving volume of material, a dynamic lot is a material stream (Lot Dimensionality). For both stationary and dynamic lots, sampling procedures must address the entire lot volume guided by the Fundamental Sampling Principle (FSP).

Lot Definition

Lot Definition describes the process of defining the target volume, which will be subjected to Sampling.

Lot Dimensionality

TOS distinguishes Lot volume  according to the dimensions that must be covered by correct Increment extraction. This defines the concept of 'lot dimensionality', an attribute which is independent of the lot scale. Lot dimensionality is a characterisation to help understand and optimise sample extraction from any lot at any sampling stage. There are four main lot types: 0-, 1-, 2- and 3-dimensional lots (0-D, 1-D, 2-D and 3-D lots).

Lots are classified by subtracting the dimensions of the lot that are fully 'covered' be the salient sampling extraction tool in question. The higher the number of dimensions fully covered in the resulting sampling operation, the easier it is to reduce the Total Sampling Error TSE.

Lot Dimensionality Transformation (LDT)

By the Governing Principle Lot Dimensionality Transformation LDT, stationary 0-D, 2-D and 3-D lots can in many cases advantageously be transformed into dynamic 1-D lots, enabling optimal sampling. However, the application of LDT has practical limits as some lots cannot be transformed (e.g. a body of soil, or a mine resource, biological cells). The optimal approach for such cases is penetrating one dimension with complete increment extraction (usually height) turning a 3-D lot into a 2-D lot.

Lot Heterogeneity

The lot heterogeneity is the combination of Compositional Heterogeneity, Distributional Heterogeneity and Particle-Size-Heterogeneity.

CH + DH + PH

Lot Heterogeneity Characterisation
Lot Heterogeneity Characterisation is the process of assessing Lot Heterogeneity magnitude. Logically, it is impossible to design a sampling procedure without knowledge of the Heterogeneity of target material. Lot Heterogeneity Characterisation is the process of determining Lot Heterogeneity when approaching a new sampling project. There are two principal procedures of determining Lot Heterogeneity, Replication Experiment (RE) for Stationary Lots, and Variographic Characterisation (VAR) for Dynamic Lots. Heterogeneity Tests determine Constitutional Heterogeneity as the irreducible minimum obtainable of Sampling Variance, excluding all other Sampling Error effects.

M

Mass-Reduction

Mass-reduction is a physical process that divides a given quantity into manageable sub-samples. Mass-reduction must ensure that these sub-samples are representative of the original quantity (Representative Mass Reduction – Subsampling

Measurement

The total process of producing numerical data about a Lot, including sampling and analysis is called Measurement. Simultaneously, sensor-based analytical technology combines virtual sampling and signal processing. For both types of measurements the principles and rules of the  Theory of Sampling apply.

Measurement Uncertainty (metrological term) (MU)

MU expresses the variability interval of values attributed to a quantity measured. MU is the effect of a particular error, e.g. a sampling error, or an analytical error  or of combined effects (see MUTotal).

MUsampling reflects the variability stemming from sampling errors

MUanalysis reflects the variability stemming from analytical errors

MUtotal is the effective variability stemming from both sampling and analysis

MUtotal= MUsampling+ MUanalysis

Mixing / Blending

Mixing and blending reduces Distributional Heterogeneity (DH) before sampling/sub-sampling. N.B. Forceful mixing is a much less effective process than commonly assumed.

P

Particle-Size-Heterogeneity (PH)

PH is the compositional difference due to assemblages of units with different particle sizes (or particle-size classes).

Pierre Gy

The founder of the Theory of Sampling (TOS), Pierre Gy (1924--2015) single-handedly developed the TOS from 1950 to 1975 and spent the following 25 years applying it in key industrial sectors (mining, minerals, cement and metals processing). In the course of his career he wrote nine books and gave more than 250 international lectures on all subjects of sampling. In addition to developing TOS, he also carried out a significant amount of practical R&D. But he never worked at a university; he was an independent researcher and a consultant for nearly his entire career - a remarkable scientific life and achievement.

Precision

Precision is a measure of the variability of quantitative results. The larger the variability, the smaller the precision. In practice, precision is measured as the statistical variance s2 of the quantitative results (square of the standard deviation).

Primary Sample

The initial mass extracted from the lot. The Primary Sample is the product of Composite Sampling and consists of Q Increments. Both the mass of the Primary Sample as well as the number of increments extracted influence the sampling variability. As the primary sampling stage often has by far the largest impact on MUTotal, optimisation always starts at this stage.

Principle of Sampling Correctness (PSC)

The Principle of Sampling Correctness (PSC) states that all TOS' Incorrect Sampling Errors (ISE) shall be eliminated, or a detrimental Sampling Bias will have been introduced.

Principle of Sampling Simplicity (PSS)

PSS states that sampling along the Lot-to-Aliquot can be optimised separately for each (primary, secondary, tertiary ....) sampling stage. Since the Primary Sampling stage is often the dominant source of sampling error, optimization logically shall always begin at this stage.

Process Periodicity Error (PPE)

PPE is incurred if short-, mid- or long-term periodic process behaviour is not corrected for, in which case it may contribute to a sampling bias.

A process sampling strategy must make use of a high enough sampling frequency to uncover such behaviours; the sampling frequency must as a minimum always be higher than twice the most frequent periodicity encountered.

Process Sampling Errors (PSE)

PSE come into effect when Dynamic Lots are being sampled without compensating for process trends or periodicities (Process Trend Error and Process Periodicity Error).

Process Trend Error (PTE)

PTE occurs if mid- to long-term process trends are not corrected for, in which case they may contribute to a Sampling Bias. PTE and Process Periodicity Error PPE may, or may not, occur simultaneously depending on the specific nature of the process to be sampled.

Q

Q

Number of Increments composited to a Sample.

R

R

R is the number of replications of a series of independent complete ‘Lot-to-Aliquot’ Measurements, made under identical conditions applied in a Replication Experiment.

Replication Experiment (RE)

The replication experiment RE consists of a series of independent complete ‘Lot-to-Aliquot’ analytical determinations, made under identical conditions. The number of replications is termed R. RE provides MUSampling + MUAnalysis.

Representative Mass Reduction – Subsampling

Representative Mass Reduction (RMR) aka sub-sampling. TOS argues why Riffle-Splitting and Vezin-sampling are the only options leading to Representative Mass Reduction.

Representativity

A sampling process is representative if it captures all intrinsic material features, e.g., composition, particle size distribution, physical properties (e.g. intrinsic moisture) of a Lot.Representativity is a characteristic of a sampling process in which the Total Sampling Error and Total Analytical Error have been reduced below a predefined threshold level, the acceptable Total Measurement Uncertainty.
Representativity is the prime objective of all sampling processes. The representativity status of an individual sample cannot be ascertained in isolation, if removed from the context of its full sampling-and-analysis pathway. The characteristic Representative can only be accorded a sampling process that complies with all demands specified by TOS (DS3077:2024).

S

Sample

Extracted portion of a Lot that can be documented to be a result of a representative sampling procedure (non-representatively extracted portions of a Lot are termed Specimens).

Sampling

Sampling is the process of collecting units from a Lot (sampling procedure; sampling process): Grab Sampling or Composite Sampling. There are only two principal types of sampling procedures: Grab Sampling or Composite Sampling.

Sampling Accuracy

Closeness of the analytical result of an Aliquot with regards to the true concentration of the Lot]/glossary]. NB. “sampling accuracy” = “sampling + analytical accuracy”

Sampling Bias

The Sampling Bias is the difference between the true Lot concentration and the average concentration from replicated sampling. Such a difference is a direct function of the Lot Heterogeneity and as such inconstant; it changes with each additional sampling and can therefore not be corrected for. This is the opposite to the Analytical Bias for which correction is often carried out.

Sampling Error Management (SEM)

SEM 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. Estimation and use of s2(FSE) is only meaningful after complete elimination of ISE
  4. Minimisation of Process Sampling Errors
Sampling Manager

The Sampling Manager is the Legal Person accountable for ensuring that all sampling activities are conducted in accordance with scientifically valid principles to achieve representative results. They are responsible for managing the design, implementation, and evaluation of sampling protocols while balancing constraints such as material variability, logistics, and resource limitations. This role requires expertise in the Theory of Sampling (TOS), leadership, project management and stakeholder communication skills.

Sampling Precision

The Sampling Precision is the variance of the series of analytical determinations, for example from a Replication Experiment (RE). Sampling precision always includes the Analytical Precision, since all analysis is always based on an analytical Aliquot, which is the result of a complete 'Lot-to-Aliquot' sampling pathway. Therefore sampling precision = sampling + analysis precision.

Sampling Protocol

Document explaining the undertakings necessary for the sampling process. It contains the tools and procedures from Lot-to-Aliquot[/glossary].

Sampling Scale Invariance (SCI)

The Principle of SSI states that all Sampling Unit Operations (SUO) can be applied identically to all sampling stages, only the scale of sampling tools differs.

Sampling Uncertainty

Sampling Uncertainty is the difficulty of collecting a representative sample due to Lot Heterogeneity; the more heterogeneous the material, the higher the uncertainty associated with any sample attempting to represent the whole Lot.

Sampling Unit Operations (SUO)
A Sampling Unit Operation is a basic step in the 'Lot-to-Aliquot' pathway. Five practical SUOs cover all necessary practical aspects of representative sampling: Composite Sampling, Crushing, Mixing/ Blending, Fractionation, and Representative Mass Reduction - Subsampling.
Secondary Sample

A secondary sample is the product of Representative Mass Reduction - Subsampling from a Primary Sample. Identical nomenclature applies for further Representative Mass Reduction steps (Tertiary...).

Specimen

A specimen is a portion of a larger mass/volume (Lot) extracted by a non-representative sampling process. Grab Sampling results in a specimen.

Stakeholder

A Stakeholder is any entity interested in the result coming from sampling and analysis. Data representing stationary or flowing heterogeneous materials are requested by different parties with a multitude of differing objectives. Stakeholders can be internal, from commercial organisations, public authorities, research and academia or non-governmental organisations.

Stationary Lot

A Stationary Lot is a non-moving volume of material where sampling is carried at from multiple locations, each resulting in an Increment. For both Stationary Lots and Dynamic Lots, sampling procedures must address the entire Lot volume guided by the Fundamental Sampling Principle (FSP).

T

Theory of Sampling (TOS)

TOS Theory and Practice of Sampling: necessary-and-sufficient framework of Governing Principles (GP), Sampling Unit Operations (SUO), Sampling Error Management rules (SEM) together with normative practices and skills needed to ensure representative sampling procedures. TOS is codified in the universal standard DS3077:2024.

Total Analytical Error

TAE is manifested as the Measurement Uncertainty resulting only from analysis (MUAnalysis). TAE includes all errors occurring during assaying and analysis (e.g. related to matrix effects, analytical instrument uncertainty, maintenance, calibration, other), as well as human error.

Total Measurement Uncertainty

Whereas Measurement Uncertainty (MU) is traditionally only addressing analytical determination, e.g. concentration := 375 ppm +/- 18 ppm (MUanalysis), Theory of Sampling (TOS) stipulates reporting analytical results with uncertainty estimates from both sampling and analysis.  This gives users of analytical data the possibility to evaluate the relative magnitudes of MUsampling vs. MUanalysis, enabling fully informed assessment of the true, effective data quality involved. A complete data uncertainty must have this format:

MUTotal = MUSampling + MUAnalysis

The attribute Total Measurement Uncertainty (MUTotal) is the most important factor determining the attribute data quality.

Total Sampling Error (TSE)

The Incorrect Sampling Errors (ISE) and Correct Sampling Errors (CSE) add up to the effective Total Sampling Error (TSE). TSE is causing the Total Uncertainty resulting from material extraction along the sampling pathway from-lot-to-aliquot (MUSampling).

Total Uncertainty Threshold

The acceptable Total Measurement Uncertainty, which must include the Sampling Measurement Uncertainty (MUSampling) and Analytical Measurement Uncertainty (MUAnalysis).

U

V

Variographic Characterisation (VAR)

Variography is a variability characterisation of a dynamic 1-dimensional dynamic lot. A variogram describes variability as a function of Increment pair spacing (in time). Variography is also applied in geostatisctics in describing the variability as a function of spacing/distance between analyses.