Representative Sampling of Materials

Obtaining representative samples of the total lot before analysis is crucial – otherwise there is little point in having made significant investments in laboratory equipment and analytical competences.

Representative samples are critical for correct decision making based on analytical data for industry, trade, technology, science and regulators. However, there is a complex way from heterogeneous materials in lots such as truck loads, railroad cars, shiploads, stockpiles and on conveyor belts (in the kg-ton range) to the very small aliquot (in g-µg range), which is the only material that is actually analysed.

Theory of Sampling

Exactly how to get a documented representative analytical result across mass-reduction of up to six orders of magnitude is far from a direct materials’ handling issue. There are a number of specific principles and rules behind representativity as part of the Theory of Sampling (TOS) [1].

The concept of TOS was originally developed by Pierre Gy who identified eight sampling errors which represent everything that can go wrong in sampling, sub-sampling (sample mass reduction), sample preparation and sample presentation—due to heterogeneity and/or inferior sampling equipment design and performance.

During his 25 year career (1950-75) Pierre Gy worked out how to avoid committing such errors in the design, manufacture, maintenance and operation of sampling equipment and showed how their adverse impact on the total accumulated uncertainty could be reduced as much as possible when sampling in practice. He received two PhDs (in mineral processing and statistics) in the process [2]. Read more about TOS in the article by R.C.A. Minnitt and Kim H. Esbensen [3].

The purpose of sampling

The purpose of sampling is therefore to produce a reliable small mass which is representative of the total mass of material from which it was collected i.e. to obtain a sample which accurately and precisely represents the total mass or lot.

This primary sample is very often subject to further sub-sampling and sample preparation procedures, which ultimately produces an aliquot suitable for either laboratory analysis or physical testing. The type of testing or analysis is dependent on which characteristics are required for technological and industrial decision making. Regardless, the primary sampling is critical for the ultimate quality of the analytical results.

Sampling variance

Figure 1. below shows the key results from Replication Experiments made at Elkem Metal, Canada, which showed that 35% of the total sampling variance (where mistakes can occur throughout the full sampling process) occured during the phase of primary sampling and 50% during the crushing phases i.e. 85% of the total sampling variance occurred before pulverization and laboratory  analysis.

In other words: it is of extreme importance that you are in control of your primary and secondary sampling process before final analyzis. Otherwise you draw (wrong) conclusions from the non-representative samples.

Figure 1. Replication Experiment at Elkem Metal – Canada.

Shows the key information to be gained by the hierarchical RE. For the current laboratory approach, the primary sampling contributes 35 %, jaw crushing 25 %, roll crushing 25 % of the overall variance, while pulverisation and analysis strictly account for only 5 % and 2.5 %.

Numerical results of the hierarchical RE, with which can be identified error contributions from each step (primary sampling to analysis). Vertical scale is RSV; %, standard deviation/average of replicated results ×100 for Fe2O3.

Source: https://www.spectroscopyeurope.com/sampling/revisiting-replication-experiment.

For more about Replication Experiments, see Part 1 and Part 2 of The Replication Myth by Kim H. Esbensen et al [4][5].

Representative or not

A specific sampling process can either be representative – or not. If a sampling process is not representative, the result is only extracted and undefined, mass-reduced lumps of material which do not represent the original lot; these are called “specimens”.

However, specimens are not worth analyzing, as they will not give valid information about the composition and physical characteristics of the lot. Only representative analytical aliquots can reduce the combined sampling-and-analysis errors to a desired minimum.

Non-representative samples

Drawing the (wrong) conclusions from non-representative samples can have major negative production control and financial consequences when you buy or sell materials.

And you might as well save the costs of laboratory hardware and analysts: Garbage In = Garbage Out.

Sampling must be both accurate (unbiased) and precise (reproducible) at all stages throughout the sampling process.

A representative sampling process is critically dependent upon three factors:

1. Unbiased and precise sampling equipment – demand clear and understandable documentation from your supplier. M&W JAWO Sampling is at your disposal to help.
2. TOS-informed sampling process design, installation and operation. Demand relevant documentation from your supplier. M&W JAWO Sampling is at your disposal to help.
3. Process staff & supervisors must possess a minimum of TOS-competence. If this does not exist in-house, request training and documentation from your supplier. M&W JAWO Sampling is at your disposition to help.

[1] For background: “Introduction to the Theory and practice of sampling” by Kim H. Esbensen (IMPublicationsOpen 2020)

[2] “Pierre Gy (1924–2015): the key concept of sampling errors” (Spectroscopy Europe/Asia 2018)

[3] “Pierre Gy’s development of the Theory of Sampling: a retrospective summary with a didactic tutorial on quantitative sampling of one-dimensional lots” by R.C.A. Minnitt and Kim H. Esbensen, TOS Forum 7.

[4] “The Replication Myth 1” by Kim H. Esbensen et al, NIR News

[5] “The Replication Myth 2: Quantifying empirical sampling plus analysis variability” by Kim H. Esbensen et al, NIR News

Representative sampling must be both accurate (unbiased) and precise (reproducible). In order to be representative, a specific sampling process shall only be using equipment that is designed to eliminate (or reduce maximally) sampling bias and which simultaneously increases sampling precision as much as possible.

Here is the short explanation why:

All material sampling targets (lots) are heterogeneous, it is only a matter of degree. This means that different samples, even though extracted by the exact same protocol, will never be identical, which manifests itself as a basic, non-vanishing sampling variability.

Heterogeneity is one of two major influential factors behind sampling variability (inaccuracy). The sampling process itself will also result in sampling error effects that add to the total sampling uncertainty.

All sampling must therefore aim for maximum Total Sampling Error (TSE) reduction. In order to do this effectively, economically and with confidence, there are sampling equipment and process design principles which must be acknowledged and followed. These rules are codified in the Theory of Sampling (TOS).

For homogeneous materials, there is no reason to worry about sampling – because any sample will be an exact representative sample of the lot (big/small).

However, ALL materials – at all scales – visible, or not – are heterogeneous.

There is no universal solution

Representative sampling is not as simple as buying a specific sampling tool (equipment) with which to sample any of the world’s materials. This will be futile.

Despite many suppliers’ claim, there does not exist a “universal sampler” that will work for all materials and under all conditions because technological and industrial materials have very different compositional heterogeneities and other characteristics e.g. internal differences with respect to grain sizes, moisture, and grain stickiness.

But there are professional solutions: most standard sampling equipment can be used in informed, TOS-compliant ways that can be made to work towards a state of “fit-for-purpose” representativity. This approach is called composite sampling.

Representative sampling is about mastering the necessary and sufficient TOS principles with which to make rational choices regarding the appropriate type of sampling tool and sampling protocol for a specific task, for a specific material, under customer-specific conditions. It takes professional competence and relevant experience to get all this right.

Correctly designed sampling equipment and a representative sampling plan is necessary in order to obtain reliable knowledge of the material properties which is essential for commercial, operational and technical characterization.

These properties are:

• Content grade
• Moisture content
• Mineral proportions
• Contamination
• Hardness
• Particle Size distribution

A full sampling system solution takes care of the critically important primary sampling stage with an aim of attaining a fit-for-purpose representativity status.

All subsequent sub-sampling stages comply with the same demands, ultimately delivering an analytical aliquot suitable for laboratory analysis.

In all methods of sampling, sample preparation and analysis, errors are incurred, and the analytical results for any given parameter will deviate from the true value of that parameter.

While the absolute deviation of a single result from the “true” value cannot be determined, it is possible to make an estimate of the sampling precision. This is the closeness with which the results of a series of measurements made on the same material agree among themselves, and the deviation of the mean of the results from an accepted reference value.

Precision for a lot

The desired overall precision for a lot is normally agreed between the parties concerned. In principle it is possible to design a sampling scheme by which an arbitrary level of precision can be achieved.

The overall precision can be estimated using Equation 1 where:

• PL [%] is the estimated index of overall precision of sampling, sample preparation and testing for the lot;
• VI is the primary increment variance;
• VPT is the preparation and testing variance;
• n is the number of increments per sub-lot;
• m is the number of sub-lots in the lot.

Equation 1:

PL=2VIn+VPTm

If no previous sampling data is available, assumptions have to be made about the variability in order to devise a sampling scheme. After implementation of the sampling scheme, the precision actually achieved for a particular lot by the devised scheme can be measured.

If a given precision PL is required, the number of increments n and the number of sub-lots m can be found using Equation 2 and Equation 3 respectively. If necessary, one of the values (n or m) is fixed and another is recalculated until a convenient combination is achieved.

Equation 2:

n = 4VImPL2-4VPT

Equation 3:

m = 4VI+4n1VPTn1PL2

Sample division

To obtain convenient sample masses along the partway from lot to analytical aliquot, the sample is often divided into a number of equal smaller sub-samples, and a residual which is returned to the conveyor.

In order to facilitate a required division while retaining the representative nature of the sample, it may be necessary to crush the material. For this reason, a complete system for extraction of representative samples consists of multistage sampling, particle size reduction and division (sub-sampling) equipment.

It is also sometimes beneficial to mix the resulting sub-samples thoroughly after each of these operations, to achieve even higher precision.

Minimum mass of sample

For most parameters, the precision of the result is limited by the ability of the sample to represent all the particle sizes in the material being sampled.

There is a minimum mass of sample, dependent on the maximum particle size of the material, the type of analysis, the precision required for the parameter concerned and the relationship of that parameter to particle size. Such a relationship applies at all stages of preparation. The attainment of this mass will not, by itself, guarantee the required precision. This is also dependent on the number of increments taken to compound the sample and their variability.

Table: Minimum mass of sample (example: coal)