Revisiting Pierre Gy's formula (TOS) - A return to size-density classes for applications to contaminated soils, coated particular aggregates and mixed material systems.

For some real-world material systems, estimations of the incompressible sampling variance based on Gy's classical s(FSE) formula from the Theory of Sampling (TOS) show a significant discrepancy with empirical estimates of sampling variance. In instances concerning contaminated soils, coated particular aggregates and mixed material systems, theoretical estimates of sampling variance are larger than empirical estimates, a situation which does not have physical meaning in TOS. This has led us to revisit the development of estimates of s(FSE) from this famous constitutional heterogeneity equation and explore the use of size-density classes for mixed material systems (mixtures of both analyte-enriched and coated particles), an approach which has been mostly unused since Gy's original derivation.

Sampling of particulate materials with significant spatial heterogeneity - Theoretical modification of grouping and segregation factors involved with correct sampling errors: Fundamental Sampling Error and Grouping and Segregation Error.

There has been an extensive abuse of Gy's Formula during the entire history of applied TOS (Theory of Sampling), it being applied too liberally to almost any aggregate material conceivable for many material classes of extremely different compositions with significant (to large, or extreme) fragment size distribution heterogeneity, for example many types of municipal and industrial waste materials. This abuse regimen is for the most part characterized by lack of fundamental TOS competence and the historical context of Gy's formula. The present paper addresses important theoretical details of TOS, which become important as sampling rates increase at the conclusion of the full 'lot-to-analysis sampling pathway regarding finer details behind TOS' central equations linking sampling conditions to material heterogeneity characteristics allowing the estimation of Total Sampling Error (TSE) manifestations.

Empirical Approach for Estimating Reference Material Heterogeneity and Sample Minimum Test Portion Mass for "Nuggety" Precious Metals (Au, Pd, Ir, Pt, Ru).

Quantification of precious metal content is important for studies of ore deposits, basalt petrogenesis, and precious metal geology, mineralization, mining, and processing. However, accurate determination of metal concentrations can be compromised by microheterogeneity commonly referred to as the "nugget effect", i.e.

Adequacy and verifiability of pharmaceutical mixtures and dose units by variographic analysis (Theory of Sampling) - A call for a regulatory paradigm shift.

In spite of intense efforts in the last 20 years, the current state of affairs regarding evaluation of adequacy of pharmaceutical mixing is at an impressive standstill, characterized by two draft guidances, one withdrawn, and the other never approved. We here analyze the regulatory, scientific and technological situation and suggest a radical, but logical approach calling for a paradigm shift regarding sampling of pharmaceutical blends. In synergy with QbD/PAT efforts, blend uniformity testing should only be performed with properly designed sampling that can guarantee representativity-in contrast to the current deficient thief sampling.

Theory of sampling: four critical success factors before analysis.

Food and feed materials characterization, risk assessment, and safety evaluations can only be ensured if QC measures are based on valid analytical data, stemming from representative samples. The Theory of Sampling (TOS) is the only comprehensive theoretical framework that fully defines all requirements to ensure sampling correctness and representativity, and to provide the guiding principles for sampling in practice. TOS also defines the concept of material heterogeneity and its impact on the sampling process, including the effects from all potential sampling errors.

Towards a unified sampling terminology: clarifying misperceptions.

International acceptance of data is a much-desired wish in many sectors to ensure equal standards for valid information and data exchange, facilitate trade, support food safety regulation, and promote reliable communication among all parties involved. However, this cannot be accomplished without a harmonized approach to sampling and a joint approach to assess the practical sampling protocols used. Harmonization based on a nonrepresentative protocol, or on a restricted terminology tradition forced upon other sectors would negate any constructive outcome.

QC of sampling processes- a first overview: from field to test portion.

Quality control (QC) is a systematic approach for estimating and minimizing significant error contributions to the measurement uncertainty from the full sampling and analysis process. Many types of QC measures can be implemented; the three dealt with here are primary sampling reproducibility, sample processing reproducibility, and contamination. Sampling processes can be subject to QC by applying a replication experiment, used either from the top by replication of the entire sampling/ preparation/analysis process, or in a hierarchical fashion successively at each subsequent sampling stage.

Materials properties: heterogeneity and appropriate sampling modes.

The target audience for this Special Section comprises parties related to the food and feed sectors, e.g., field samplers, academic and industrial scientists, laboratory personnel, companies, organizations, regulatory bodies, and agencies who are responsible for sampling, as well as project leaders, project managers, quality managers, supervisors, and directors.

Distributional assumptions in food and feed commodities- development of fit-for-purpose sampling protocols.

Material heterogeneity influences the effectiveness of sampling procedures. Most sampling guidelines used for assessment of food and/or feed commodities are based on classical statistical distribution requirements, the normal, binomial, and Poisson distributions-and almost universally rely on the assumption of randomness. However, this is unrealistic.

Iodine concentrations in Danish groundwater: historical data assessment 1933-2011.

In areas where water is a major source of dietary iodine (I), the I concentration in drinking water is an important factor for public health and epidemiological understandings. In Denmark, almost all of the drinking water is originating from groundwater. Therefore, understanding the I variation in groundwater and governing factors and processes are crucial.

Power plant intake quantification of wheat straw composition for 2nd generation bioethanol optimization--a Near Infrared Spectroscopy (NIRS) feasibility study.

Optimization of 2nd generation bioethanol production from wheat straw requires comprehensive knowledge of plant intake feedstock composition. Near Infrared Spectroscopy is evaluated as a potential method for instantaneous quantification of the salient fermentation wheat straw components: cellulose (glucan), hemicelluloses (xylan, arabinan), and lignin. Aiming at chemometric multivariate calibration, 44 pre-selected samples were subjected to spectroscopy and reference analysis.

Grab vs. composite sampling of particulate materials with significant spatial heterogeneity--a simulation study of "correct sampling errors".

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets.

Near infrared and acoustic chemometrics monitoring of volatile fatty acids and dry matter during co-digestion of manure and maize silage.

In this study, two process analytical technologies, near infrared spectroscopy and acoustic chemometrics, were investigated as means of monitoring a maize silage spiked biogas process. A reactor recirculation loop which enables sampling concomitant with on-line near infrared characterisation was applied. Near infrared models resulted in multivariate models for total and volatile solids with ratio of standard error of performance to standard deviation (RPD) values of 5 and 5.

At-line determination of octanoic acid in cultivation broth--an electronic tongue (ET) feasibility study.

Production monitoring of "natural" 2-heptanone from octanoic acid in an industrial fed-batch cultivation based on Penicillium roqueforti requires development of a method for determination of octanoic acid dissolved in the water phase. An electronic tongue array using six non-specific potentiometric sensors with solid inner contact, and a pH electrode, has been introduced by spiking octanoic acid to a substrate obtained from four different cultivations, representing variations in the relevant industrial matrix. Multivariate calibration was performed on acid concentrations spanning 0.

On-line near infrared monitoring of glycerol-boosted anaerobic digestion processes: evaluation of process analytical technologies.

A study of NIR as a tool for process monitoring of thermophilic anaerobic digestion boosted by glycerol has been carried out, aiming at developing simple and robust Process Analytical Technology modalities for on-line surveillance in full scale biogas plants. Three 5 L laboratory fermenters equipped with on-line NIR sensor and special sampling stations were used as a basis for chemometric multivariate calibration. NIR characterisation using Transflexive Embedded Near Infra-Red Sensor (TENIRS) equipment integrated into an external recurrent loop on the fermentation reactors, allows for representative sampling, of the highly heterogeneous fermentation bio slurries.