Theory of Sampling (TOS): A necessary and sufficient guarantee for reliable multivariate data analysis in pharmaceutical manufacturing

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.