Representative process sampling for reliable data analysis a tutorial

Process sampling of moving streams of particulate matter, fluids and slurries (over time or space) or stationary one-dimensional (1-D) lots is often carried out according to existing tradition or protocol not taking the theory of sampling (TOS) into account. In many situations, sampling errors (sampling variances) can be reduced greatly however, and sampling biases can be eliminated completely, by respecting a simple set of rules and guidelines provided by TOS. A systematic approach for description of process heterogeneity furnishes in-depth knowledge about the specific variability of any 1-D lot. The variogram and its derived auxiliary functions together with a set of error generating functions provide critical information on:-process variation over time or space,-the number of extracted increments to composite into a final, optimal sample,-the frequency with which to extract increments-and which sampling scheme will be optimal (random, stratified random or systematic selection). In addition variography will delineate cyclic behaviors as well as long-term trends thereby ensuring that future sampling will not accidentally be performed with a sampling rate coincident with the frequency of any hidden cycle, eliminating the risk of underestimating process variation. A brief description of selected hardware for extraction of samples from 1-D lots is provided in order to illustrate the key issues to consider when installing new, or optimizing existing sampling devices and procedures. A number of practical examples illustrate the use of TOS and variography to design optimal sampling protocols for a variety of typical process situations

Revisiting the Replication Experiment

The Replication Experiment (RE) was introduced and applied to different sampling contexts in an earlier column. Here we want to show its features and usefulness in the context of evaluating a possible new sampling + analytical approach for raw material characterisation in a demanding industrial context: “Representative sampling and use of handheld X-ray fluorescence (HHXRF) to characterise lot and sample quality of quartzite in a pyro-metallurgical ferrosilicon plant”. The issue has a very sharp focus: Is the HHXRF approach applied to field samples able to quantify very troublesome, minute amounts of pollutant trace compounds in quartzite for the ferrosilicon process with the necessary accuracy and precision? We here focus on the application of the RE only in the context of the full evaluation, a much broader study

Representative sampling and use of HHXRF to characterize lot and sample quality of quartzite at a pyrometallurgical ferrosilicon plant

Material sampling is a critical component in mining and mineral processing industries. Nonetheless, sampling is often considered to be a simple matter and, as such, non-rigorous sampling protocols are often applied. The use of inappropriate methods produces inferior, non-representative estimates of sampling target composition. To address weaknesses in sampling protocols and evaluate the representativeness of collected samples, we performed a feasibility study of the ability of handheld X-ray fluorescence (HHXRF) to achieve a satisfactory characterization of a raw material lot at a pyrometallurgical ferrosilicon plant. Using composite and grab samples, we determined the various sampling error manifestations stemming from the fundamental sampling error, grouping and segregation error, as well as increment delimitation, increment extraction, and increment preparation errors), and performed a first foray determination of optimal sample mass, and estimated the heterogeneity within the sampling target. HHXRF results were compared with the results obtained using laboratory XRF. A first estimate of optimized sample mass for HHXRF was 10 kg, given the large size of crushed quartz blocks used in ferrosilicon plants—roughly cubic, 10 cm per side; accuracy improved with increased sample mass (18% error with a 10 kg sample versus 35% error when using a 1 kg sample). A 10 kg sample is also the mass a technician can realistically transport from the sampling site to the preparation facilities. The main contribution to the global estimation error is from primary sampling. Variographic analysis illustrated a sill equal to the nugget effect, indicating that two adjacent samples are no more similar than two samples separated by larger distance; this suggests equal spatial heterogeneity at all scales larger than the increment mass in the sampling target. Analytically, the HHXRF and desktop XRF results compared very well. Overall, the error associated with our first attempt at field composite sampling was half of that obtained via grab sampling for both the HHXRF and desktop XRF protocols. Relative to conventional analysis based on grab sampling and analysis via desktop XRF, the use of handheld XRF coupled with composite sampling would appear to be a feasible approach for an improved sampling protocol for obtaining fit-for-purpose characterizations of industrial quartzite

Measurement of E2 Transitions in the Coulomb Dissociation of 8B

In an effort to understand the implications of Coulomb dissociation experiments for the determination of the 7Be(p,gamma)8B reaction rate, longitudinal momentum distributions of 7Be fragments produced in the Coulomb dissociation of 44 and 81 MeV/nucleon 8B beams on a Pb target were measured. These distributions are characterized by asymmetries interpreted as the result of interference between E1 and E2 transition amplitudes in the Coulomb breakup. At the lower beam energy, both the asymmetries and the measured cross sections are well reproduced by perturbation theory calculations, allowing a determination of the E2 strength.Comment: 8 pages, 3 figure

Coulomb and nuclear breakup of 8^8B

The cross sections for the ($^8$B,$^7$Be-$p$) breakup reaction on $^{58}$Ni and $^{208}$Pb targets at the beam energies of 25.8 MeV and 415 MeV have been calculated within a one-step prior-form distorted-wave Born approximation. The relative contributions of Coulomb and nuclear breakup of dipole and quadrupole multipolarities as well as their interference have been determined. The nuclear breakup contributions are found to be substantial in the angular distributions of the $^7$Be fragment for angles in the range of 30$^\circ$ - 80$^\circ$ at 25.8 MeV beam energy. The Coulomb-nuclear interference terms make the dipole cross section larger than that of quadrupole even at this low beam energy. However, at the incident energy of 415 MeV, these effects are almost negligible in the angular distributions of the ($^7$Be-p) coincidence cross sections at angles below 4$^\circ$.Comment: Revised version, accepted for publication in Phys. Rev.

Calculations of three-body observables in ^8B breakup

We discuss calculations of three-body observables for the breakup of ^8B on a ^{58}Ni target at low energy using the coupled discretised continuum channels approach. Calculations of both the angular distribution of the ^7Be fragments and their energy distributions are compared with those measured at several laboratory angles. In these observables there is interference between the breakup amplitudes from different spin-parity excitations of the projectile. The resulting angle and the energy distributions reveal the importance of the higher-order continuum state couplings for an understanding of the measurements.Comment: 22 pages (postscript), accepted in Phys. Rev.

Nuclear and Coulomb Interaction in the 8B to 7Be + p Breakup Reaction at sub-Coulomb Energies

The angular distribution for the breakup of 8B into 7Be+p on a 58Ni target has been measured at an incident energy of 25.75 MeV. The data are inconsistent with first-order theories but are remarkably well described by calculations including higher-order effects. The comparison with theory illustrates the importance of the exotic proton halo structure of 8B in accounting for the observed breakup angular distribution.Comment: 4 pages, 3 figures, Phys. Rev. Letters (accepted). This is the version that will appear in the journal article. It contains minor changes and a new referenc