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Process monitoring and control in technology and industry is incomplete without full understanding of all sources of variation, and pharmaceutical manufacturing is no exception. The power of multivariate data modeling and error treatment is not optimal when sampling errors are not adequately identified, quantified, and reduced to below a relevant a priori acceptance threshold. Process data are affected both by analytical measurement errors as well as sampling and/or PAT sensor acquisition errors. The latter partially unrecognized or unknown categories typically dominate over analytical errors by factors of 10–20+ if proper sampling competence is not brought to bear in the design, implementation, maintenance, and operation of the total process measurement system. It is not sufficiently known that PAT signal acquisition gives rise to identical error types, as does physical sample extraction; the latter is well understood and solutions abound from the theory of sampling (TOS). This chapter brings forth the critical analogy between PAT sensor application and conventional physical sample extraction in pharma and shows how variographic process characterization forms a necessary and sufficient on-line approach for total error management which is critical before chemometric calibration and prediction. Without proper sampling error treatment (identification, reduction, or elimination), multivariate data modeling in pharma will incorporate unnecessary, significantly inflated data uncertainties that will compromise the ultimate monitoring and prediction objectives. This chapter presents a brief outline of the necessary elements of TOS to identify typical sampling issues, errors, and effects in need of proper management before multivariate data analysis.

Chemometric data analysis and modeling necessitate appropriate quality (accuracy and precision) with respect to what data represent, irrespective of whether they have been acquired in the field, in the laboratory, or in an industrial (process) setting. The following trinity must be recognized and respected in order for chemometric data modeling to succeed: 1. Data must be acquired by representative sampling, ensuring accuracy with respect to the lot to be represented by the samples and precision with respect to all sampling process errors. 2. Data must have an appropriate analytical quality (usually the least of the problem as most analytical laboratories strive hard to be certified or accredited). 3. Chemometric data models must respect a demand for reliable performance validation, for example, regarding prediction, classification, time forecasting. Without representative sampling, the entire chain of evidence versus the lot characteristics is flawed because of the ever-present heterogeneity of the material (at all scales); the same holds if the precision of analysis is inferior. It is not possible to correct for any of these deficiencies in the subsequent data analytical modeling. As analytical errors are typically one or two orders of magnitude smaller than the combined sampling errors, every aspect of ‘data quality’ in practice hinges overwhelmingly on the sampling, which is either fully representative (acceptable) or nonrepresentative (worthless). A brief discussion of the criteria to be met in order to satisfy these demands is presented from the realm of the theory of sampling (TOS). A working minimum of TOS is delineated for both zero-dimensional (0-D) and 1-D sampling (process sampling), including heterogeneity characterization, comprehension of eight sampling errors, and mastering of seven practical sampling unit operations (SUOs) with which to combat heterogeneity. The effect of nonrepresentative sampling shows up as an inherent sampling bias, which cannot be estimated and therefore never be corrected for, as well as an inflated sampling reproducibility (imprecision), which, if unnoticed, leads to large, tedious, but futile, chemometric data modeling efforts. The only scientific basis for reliable performance validation of chemometric data models rests with the concept of test set validation. Popular schemes for cross-validation all fail to achieve a reliable estimate of the prediction error (classification rate, forecasting reliability) and reproducibility in more than one singular data set, the training set, which holds no information from the future model use. However, in nearly all situations, sampling errors can be significantly reduced, indeed sampling biases can be eliminated, simply by respecting an authoritative set of rules and guidelines provided by TOS (but often there is great reluctance to accept this). A systematic approach for practical sampling is described, which is based on in-depth knowledge about the specific variability of any 0-D or 1-D lot. Selected practical examples illustrate the use of 0-D TOS and 1-D variography to design optimal sampling protocols for a variety of typical situations.

Principal Component Analysis : Concept, Geometrical Interpretation, Mathematical Background, Algorithms, History, Practice