Theoretical, practical, and economic difficulties in sampling for trace constituents
FF Pitard

Many industries base their decisions on the assaying of tiny analytical sub-samples. The problem is that most of the time several sampling and sub-sampling stages are required before the laboratory provides its ultimate assays using advanced chemical and physical methods of analysis. As long as each sampling and sub-sampling stage is the object of due diligence using the theory of sampling it is likely that the integrity of the sought after information has not been altered and the generated database is still capable to fulfil its informative mission. Unfortunately, more often than not, unawareness of the basic properties of heterogeneous materials combined with the unawareness of stringent requirements listed in the theory of sampling, lead to the conclusion that massive discrepancies may be observed between the expensive outcome of a long chain of sampling and analytical custody, and reality. There are no areas that are more vulnerable to such misfortune than sampling and assaying for trace amounts of constituents of interest in the environment, in high purity materials, in precious metals exploration, food chain, chemicals, and pharmaceutical products. Without the preventive suggestions of the theory of sampling serious difficulties may arise when making Gaussian approximations or even lognormal manipulations in the subsequent interpretations. A complementary understanding of Poisson processes injected in the theory of sampling may greatly help the practitioner understand structural sampling problems and prevent unfortunate mistakes from being repeated over and over until a crisis is reached. This paper presents an overview of the theoretical, practical and economic difficulties often vastly underestimated in the search for quantifying trace amounts of valuable or unwelcome components.