The impact of non-representative sampling on data reliability constitutes a critical factor for the validity of Process Analytical Technology (PAT) applications for industrial quality monitoring and control. The Theory of Sampling (TOS) is the only guarantee that ensures such reliability, as the only framework for complete understanding of heterogeneity and representative sampling. The primary application realm in this PhD concerns reliable process monitoring in coal and biomass-fired power plants, where combustion efficiency and atmospheric emission characterisation are of high priority.