Representative process sampling for reliable data analysis - a tutorial

Process sampling of moving streams of particulate matter, fluids and slurries (over time or space) or stationary one-dimensional (1-D) lots is often carried out according to existing tradition or protocol not taking the theory of sampling (TOS) into account. In many situations, sampling errors (sampling variances) can be reduced greatly however, and sampling biases can be eliminated completely, by respecting a simple set of rules and guidelines provided by TOS. A systematic approach for description of process heterogeneity furnishes in-depth knowledge about the specific variability of any 1-D lot. The variogram and its derived auxiliary functions together with a set of error generating functions provide critical information on: - process variation over time or space, - the number of extracted increments to composite into a final, optimal sample, - the frequency with which to extract increments - and which sampling scheme will be optimal (random, stratified random or systematic selection). In addition variography will delineate cyclic behaviors as well as long-term trends thereby ensuring that future sampling will not accidentally be performed with a sampling rate coincident with the frequency of any hidden cycle, eliminating the risk of underestimating process variation. A brief description of selected hardware for extraction of samples from 1-D lots is provided in order to illustrate the key issues to consider when installing new, or optimizing existing sampling devices and procedures. A number of practical examples illustrate the use of TOS and variography to design optimal sampling protocols for a variety of typical process situations. Copyright (C) 2006 John Wiley & Sons, Ltd.