Inferential statistical sampling of hyper-heterogeneous lots with hidden structure: the importance of proper Decision Unit definition

Abstract

Sampling is nothing more than the practical application of statistics. If statistics were not available, then one would have to sample every portion of an entire population to determine one or more parameters of interest. There are many potential statistical tests that could be employed in sampling, but many statistical tests are useful only if certain assumptions about the population are valid. Prior to any sampling event, the operative Decision Unit (DU) must be established. The Decision Unit is the material object that an analytical result makes inference to. In many cases, there is more than one Decision Unit in a population. A lot is a collection (population) of individual Decision Units that will be treated as a whole (accepted or rejected), depending on the analytical results for individual Decision Units. The application of the Theory of Sampling (TOS) is critical for sampling the material within a Decision Unit. However, knowledge of the analytical concentration of interest within a Decision Unit may not provide information on unsampled Decision Units; especially for a hyper-heterogenous lot where a Decision Unit can be of a completely different characteristic than an adjacent Decision Unit. In cases where every Decision Unit cannot be sampled, application of non-parametric statistics can be used to make inference from sampled Decision Units to Decision Units that are not sampled. The combination of the TOS for sampling of individual Decision Units along with non-parametric statistics offers the best possible inference for situations where there are more Decision Units than can practically be sampled.