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"Randomness in the selection of original increments is indeed the number one problem in the sampling of bulk material." (Duncan, 1962)

Duncan examines this problem from a statistical perspective. He looks at components of sampling variation in several specific cases and the sampling practices that can affect them such as compositing, mixing, and the size of the sample. Duncan also looks at modeling process samples by accounting for trends and what he calls "short-period" variation. He addresses accuracy and bias to a limited extent by discussing how to take a sample physically, and he recommends research on the biases of sampling devices.

Statistics graduate and undergraduate courses in sampling theory address only situations in which the sampling units are well defined (people, manufactured parts, etc.). They do not address how to sample bulk materials (soils from the ground or in piles, powders, liquids, etc.), nor how much to sample.

Much of what we know about bulk sampling is tied to our experience of specific situations, what has worked in the past, and what has caused problems. Here are some examples of good sampling practices that are probably already familiar.

If possible, mix the material before sampling.
Take several increments and composite them to form the sample.
Collect the sample in a container made of material that will not chemically react with the sample.
Sample frequently enough to allow for the identification of process cycles.

The problem is that there are many more "rules" than these. How can we possibly list them all for each circumstance we might encounter? How can we remember them? What do we do when new situations arise?

Pierre Gy (1992, 1998) has done significant research and answers many of the questions and issues raised by Duncan. He addresses all of them by using a structured approach that allows an organized study of the subject. Gy has developed a Sampling Theory which provides:

1. a structured approach from which we can break down a sampling problem into component parts and
2. basic principles that we can apply to any sampling situation.

Big and complicated problems are most often solved by first breaking them down into component parts and then solving several smaller problems. In the same way, sampling variation can be broken down into component parts so that the different pieces may be examined and the effects of the major contributors reduced. This is the basis of the theory developed by Gy. His theory addresses all aspects of bulk sampling. He examines sampling variation and bias, provides a method for determining sample size (weight), analyzes process variation and its relation to sampling, and examines how to physically take a sample. He also introduces the fundamental principle of correct sampling: every part of the lot has an equal chance of being in the sample, and the integrity of the sample is preserved during and after sampling.

Gy focuses on solids but also examines liquids and gases. The principles he develops apply equally well to all three. He organizes these concepts into seven parts that he calls the seven sampling errors. His theory provides a structure for thinking about sampling and for attacking sampling problems.
The seven sampling errors in Gy's theory are sources of sampling variation. They can be grouped into three broad categories:
1. material variation,
2. tools and techniques, including sample handling, and
3. process variation.

Learning the basic principles as embodied in Gy's sampling theory reveals that "new" sampling situations are not unique at all. They fall into one or more of these three general categories above and thus can be examined using a structured approach.

Several sampling practitioners have used Gy's principles extensively and written their own books based on his theory. Francis Pitard has been an independent consultant for over 10 years and is an expert in sampling in the mining industry. Jeffrey Myers focuses on environmental applications, combining Gy's sampling theory and practice with the EPA's Data Quality Objectives and with geostatistical appraisal. Patricia Smith gained her sampling knowledge while working for the Shell Oil Companies.

Duncan, Acheson J. (1962). "Bulk Sampling: Problems and Lines of Attack," Technometrics, Vol. 4, No. 2, pp. 319-344.

Gy, Pierre M. (1992). Sampling of heterogeneous and dynamic material systems: theories of heterogeneity, sampling and homogenizing, Amsterdam: Elsevier, 653 pages.

Gy, Pierre M. (1998). Sampling for Analytical Purposes, Chichester: Wiley, 153 pages.

Myers, Jeffrey C. (1997). Geostatistical Error Management: Quantifying Uncertainty for Environmental Sampling and Mapping, New York: Van Nostrand Reinhold (now John Wiley & Sons), 571 pp. www.gemdqos.com

Pitard, Francis F. (1993). Pierre Gy's Sampling Theory and Sampling Practice: Heterogeneity, Sampling Correctness, and Statistical Process Control, Second Edition, Boca Raton: CRC Press, 488 pages. www.fpscsampling.com

Smith, Patricia L. (2001). A Primer for Sampling Solids, Liquids, and Gases: Based on the Seven Sampling Errors of Pierre Gy, Philadelphia: ASA-SIAM, 96 pp.

"Your decisions are only as good as your samples."

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