Abstract
Kim Esbensen has enlisted the support of another doyen of representative sampling, Pentti Minkkinen. In the commercial world, the reason for analysis comes down to money: whether ensuring you are getting what you paid for, but not providing more than necessary, or in regulatory compliance and the avoidance of fines. Kim’s Column has been pushing the importance of not overlooking the sampling step since its beginnings, and this edition provides clear examples where the consequences are costly; very costly.
Highlights
Sampling for analysis is a multi-stage operation, from extracting a primary sample (s1) via sub-sampling (s2) ... (s3) towards the final analytical aliquot (s4)
Consider a threelevel process: n1 primary samples are extracted from the lot, with each primary sample processed and divided into n2 secondary samples—of which nlab analytical samples are analysed
In this case Equation 2 shows how the complement of stage error variance components propagate to the analytical result
Summary
Most current standards and guidelines assume glibly— very rarely expressed explicitly—that sampling errors can be estimated using standard statistics This is based on another assumption, that of a random spatial analyte distribution within the sampling target. There is no significant difference between them if the process standard deviation is estimated from all nine samples taken in each mode, i.e. the nine samples are treated as one data set. The difference is even more clear if, based on these data, a sampling plan is requested, for example, with a target that the relative standard deviation of the mean shall not exceed 1 %. A stratified sampling plan will only require 186 samples—whereas if the systematic mode is selected, only 12 samples are needed to reach the relative standard deviation target. Further examples of the informed use of the Theory of Sampling (TOS)’ principles in the context of total expenditure estimation are given in Reference 2
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