The Critical Role of Sampling

When confronted by a large material lot, say 200 tonnes, with a sampling task (scoop, shovel, or whatever in hand) it is natural for the uninitiated to ask: “how big a sample do I need in order for it to be representative?” For lots of this size, the question can be very daunting. Surprisingly, in the light of the theory of sampling (TOS), this is the wrong question, at the wrong time, in the wrong place! How wrong can you be?

The wrong question. Representativeness is not related to sample size, but to the sampling process. Ascertaining whether a particular sample is representative or not can never be resolved by characterization of the sample itself, only by characterization of the sampling process.

The wrong time. The question should have been considered long before the actual sampling process.

The wrong place. Unless you have already started learning the bare minimum of proper sampling principles, you are most likely considering taking just one sample – a procedure termed ‘grab sampling’ in TOS. However, the most important tenet of TOS is that grab sampling is always wrong. Only composite sampling works, where a sufficient set of individual increments covering the entire volume of the lot is essential. Numerically determining “sufficient” is part of the definition of representativeness, and is, in fact, the answer to the question, “how big a sample”. For many, this inconvenient truth is at odds with practicality and economic feasibility. However, if a sample cannot be documented as being representative, what is the purpose of subjecting it to analysis?

Lot materials can vary enormously, be this in their overall size, shape and material composition, their constituent units (particles, grains, molecules, number of physical phases), the unit’s own compositional differences (constitutional heterogeneity) and their spatial distribution within the lot at all scales from the sampling increment to the full lot size (distributional heterogeneity). A full definition of heterogeneity characteristics is not necessarily a straightforward issue. For illustration, I’ll pick a few examples from the world of science, technology and industry, where representative sampling is a must: food and feed (sampling for quality, compositional compliance, or health control); coal (sampling for determination of calorific value, moisture, or ‘percentage fines’); genetically modified organisms (sampling for regulatory compliance); commodity or product quality control (sampling for control of specification). All such sampling targets (along with many other examples) are different in almost all of the above aspects. In fact, they are so vastly different that it follows that representative sampling should be material dependent, meaning that a bewildering number of different approaches are needed: if not one for each material then one for each material class.

For a very long time, representative sampling has been too complex for comfort, with the majority hoping the issue would go away by itself. For more than 60 years, TOS has been predominantly ignored or even actively criticized, with a few salient exceptions; for example, in the mining and cement industries, where faulty product and process decisions cannot be accepted because of the enormous tonnages of material at stake. Here, TOS has been an integral part of the decision-making process for years.

What is the relationship between sampling and the validity of an analytical result? Well, let me counter with another question: what is the purpose of analyzing a ‘sample’ whose provenance is not known? Any analytical result is, strictly speaking, only valid for the (often) miniscule analytical aliquot volume; however, decisions based upon the result pertain to the entire original lot. Typical aliquot/lot mass ratios involved in practical sampling range from 103 to 1012, but even the smallest ratio is far from trivial. What if all this mass-reduction – sub-sampling – is not representative? In a word: disaster! Everything hinges on the sampling process and whether it is representative or not. Evidence shows that sampling error effects dominate over analytical error effects, often dwarfing them in the total uncertainty budget (1,2,3,4)

So, amidst all the complexity, is everything lost? Most emphatically, no! The last ten years have seen very encouraging changes, with even more momentum gained in the last three years or so. What happened? The surprise is that TOS outlines why and how sampling issues are not overly complex, but instead can be understood with only a little, albeit focused, effort. It turns out that lots are only different with respect to one salient characteristic: heterogeneity. And TOS helps counteract heterogeneity in the sampling process. The principles behind representative sampling are scale-invariant, so, once mastered, can solve all sampling problems, at all scales, for all types of lot and material. In fact, TOS states that there is no such thing as an impossible lot or material to sample, there are only sampling situations that are wrongly viewed as “too complex”, “too laborious”, or “too expensive” relative to existing grab-sampling purposes. While dominant in today’s general sampling perception, these arguments are all totally wrong.

September 2013 saw the publication of the world’s first standard dedicated to sampling, “DS 3077 - Representative Sampling – Horizontal Sampling” (3), in which all principles behind representative sampling are now for the first time collated, described in sufficient detail, and given context. DS 3077 forms a very convenient starting point for everyone interested in getting to the bottom of the (otherwise totally unsolvable) sampling problem.