Representative process sampling — in practice: Variographic analysis and estimation of total sampling errors (TSE)

Didactic data sets representing a range of real-world processes are used to illustrate “how to do” representative process sampling and process characterisation. The selected process data lead to diverse variogram expressions with different systematics (no range vs. important ranges; trends and/or periodicity; different nugget effects and process variations ranging from less than one lag to full variogram lag). Variogram data analysis leads to a fundamental decomposition into 0-D sampling vs. 1-D process variances, based on the three principal variogram parameters: range, sill and nugget effect. The influence on the variogram from significant trends and outliers in the original data series receive special attention, due to their critical adverse effects. We highlight problem-dependent interpretation of variographic analysis a.o. the problem-dependent background for periodicities and trends. All presented cases of variography either solved the initial problems or served to understand the reasons and causes behind the specific process structures revealed in the variograms. Process Analytical Technologies (PAT) are not complete without process TOS.