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. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.     

Coulter particle analysis used for studying the effect of sample treatment in slurry sampling electrothermal atomic absorption spectrometry

This work focuses on the potential of using a Coulter particle analyzer for method development in slurry sampling ETAAS. Plant materials were used as an example; the particle size distributions obtained after grinding in a mixer mill were measured for ground material and slurries prepared from flowers, leaves, stem and roots of the same plant material. Normally the particle size distribution is reported either as number of particles versus size or volume of particles versus size. The advantage of using the latter mode of reporting is demonstrated. It is shown that detailed information about the larger particles is lost when the distribution is reported in terms of the number-percentage. In the present case, 60 min of grinding gave similar size distribution for all the plant materials. All particles had diameters less than 50 μm and the calculated number of particles per mg was 6–8 × 10⁷. It is shown that the ultrasonic agitation used to homogenize the slurries, prior to injection of the sample, also had an effect on the particle size distribution.     

Monitoring the precision of routine analyses by using duplicate determinations

To ensure the reliability of results, analytical laboratories require a continuous qualitycontrol program which must take account of both systematic and random errors. Analyses of reference materials can be used to estimate systematic errors but estimates of random errors (precision) tend to be optimistic, mainly because reference materials cannot be put through the whole analytical process (e.g., primary sampling is often a major source of error). Estimates of precision must be based on routine samples. If duplicate determinations are done on routine samples, the precision can be estimated reliably. Within the optimum concentration range of analytical method (usually starting from 5-10 times the detection limit), the relative standard deviation (s_r can be regarded as being almost constant or independent of concentration. The precision can then be estimated by first calculating the s_r value of each pair of results. Individually, these are not reliable estimates of the true s_r, but they can be regarded as independent measurements of the same s_r and so can be pooled to obtain a more reliable estimate of precision with the number of duplicates as the degrees of freedom. The applicabiilty of the method is tested on soil, rock and ore samples.     

Estimation of the minimum uncertainty of DNA concentration in a genetically modified maize sample candidate certified reference material

Homogeneity testing and the determination of minimum sample mass are an important part of the certification of reference materials. The smallest theoretically achievable uncertainty of certified concentration values is limited by the concentration distribution of analyte in the different particle size fractions of powdered biological samples. This might be of special importance if the reference material is prepared by dry mixing, a dilution technique which is used for the production of the new and third generation of genetically modified (GMO) plant certified reference materials. For the production of dry mixed PMON 810 maize reference material a computer program was developed to calculate the theoretically smallest uncertainty for a selected sample intake. This model was used to compare three differently milled maize samples, and the effect of dilution on the uncertainty of the DNA content of GMO maize was estimated as well. In the case of a 50-mg sample mass the lowest achievable standard deviation was 2% for the sample containing 0.1% GMO and the minimum deviation was less than 0.5% for the sample containing 5% GMO. Received: 5 December 2000 / Revised: 14 March 2001 / Accepted: 19 March 2001     

Coulter particle analysis used for studying the effect of sample treatment in slurry sampling electrothermal atomic absorption spectrometry

This work focuses on the potential of using a Coulter particle analyzer for method development in slurry sampling ETAAS. Plant materials were used as an example; the particle size distributions obtained after grinding in a mixer mill were measured for ground material and slurries prepared from flowers, leaves, stem and roots of the same plant material. Normally the particle size distribution is reported either as number of particles versus size or volume of particles versus size. The advantage of using the latter mode of reporting is demonstrated. It is shown that detailed information about the larger particles is lost when the distribution is reported in terms of the number-percentage. In the present case, 60 min of grinding gave similar size distribution for all the plant materials. All particles had diameters less than 50 μm and the calculated number of particles per mg was 6–8 × 10⁷. It is shown that the ultrasonic agitation used to homogenize the slurries, prior to injection of the sample, also had an effect on the particle size distribution. Received: 16 February 1998 / Revised: 20 July 1998 / Accepted: 26 July 1998     

Sampling constants for niacin content in standard reference material 1846 Infant Formula

Modern measurement systems for food components often require use of ever smaller sample sizes, down to mg for some new microtechniques, which puts a stronger demand on development of reference materials with defined homogeneity for subsampling. One approach to evaluate the homogeneity of materials is the characterization of sampling constants, defined as that amount of material that gives a 1% error for subsampling. This approach was developed for geological sampling and has been applied in a limited way for inorganic components in food/biological materials. We have extended this approach to the determination of the sampling constants for an organic component, niacin, in the SRM 1846 Infant Formula material. This material was produced by blending of a dry vitamin mix (5% weight) into the bulk spray dried powder, for long term stability purposes. By analyzing similar aliquots of a reconstituted homogeneous fluid solution of a large sample size, in comparison to smaller portions of dry powder, an estimate of the variation due to sampling can be separated from estimates of variation due to analysis. Using either the AOAC microbiological method or a newly developed HPLC method, sampling constants for the niacin content of SRM 1846 are in the range of 1–3 g; use of smaller sub-samples can introduce significant variation into determinations using this SRM.     

Estimation of the minimum uncertainty of DNA concentration in a genetically modified maize sample candidate certified reference material

Homogeneity testing and the determination of minimum sample mass are an important part of the certification of reference materials. The smallest theoretically achievable uncertainty of certified concentration values is limited by the concentration distribution of analyte in the different particle size fractions of powdered biological samples. This might be of special importance if the reference material is prepared by dry mixing, a dilution technique which is used for the production of the new and third generation of genetically modified (GMO) plant certified reference materials. For the production of dry mixed PMON 810 maize reference material a computer program was developed to calculate the theoretically smallest uncertainty for a selected sample intake. This model was used to compare three differently milled maize samples, and the effect of dilution on the uncertainty of the DNA content of GMO maize was estimated as well. In the case of a 50-mg sample mass the lowest achievable standard deviation was 2% for the sample containing 0.1% GMO and the minimum deviation was less than 0.5% for the sample containing 5% GMO.     

Theoretical study of incomplete sampling of the first dimension in comprehensive two-dimensional chromatography

The process of regularly transferring material from the primary column to the secondary column is critical in producing comprehensive two-dimensional separations. A series of calculations have been performed to determine how sampling period, duty cycle, and sampling phase affect (1) the fraction of material transferred from the primary column to the secondary column, (2) the accuracy of primary retention time determination, and (3) the effective peak width along the primary retention axis. The results demonstrate that comprehensive two-dimensional separations can be produced without a substantial loss in quantitative precision and with only a moderate loss in primary column resolution if the sampling period is less than 1.5 times the primary peak standard deviation. The quantitative precision of total peak areas (for duty cycles less than 1.0) and primary retention time determination are rapidly reduced as the sampling period is increased above 1.5 times the primary peak standard deviation.     

In vivo solid phase microextraction sampling of human saliva for non-invasive and on-site monitoring

On-site sample preparation is an analytical approach based on direct sampling from the system under investigation. It has the advantage of combining sampling and sample preparation into a single step, thus generally is fast, minimizes the potential sources of error and eliminates the risks for analytes instability. For such analysis solid phase microextraction in thin film geometry (TF-SPME) can provide robust and convenient in vivo sampling, offering in the same time faster analysis and higher extraction recovery (i.e., better sensitivity) due to large surface to volume ratio.     

A new multi-axial particle shape factor--application to particle sampling

Because for a given sample size the sampling uncertainty increases with increasing particle mass, the mass of a representative sample depends on the particle mass during chemical, physical and biological analysis. Sampling theory can be used to formulate the quantitative relationship between the particle mass and the corresponding mass or weight of a representative sample. But in practice, especially for small particles, it is often easier to evaluate the particle size in dimension of length (e.g. μm) rather than in dimension of mass (e.g. μg). In order to be able to apply sampling theory to predict the mass or weight of a representative sample, a well-defined methodology that relates the mass of a particle to its size is required. We here propose a new multi-axial shape factor which requires information of multiple sizes of the particle of interest, whereas a uniaxial shape factor only needs one. In view of the information loss that is implicit in the use of a one-dimensional shape factor like the Brunton shape factor, the here-proposed new multi-axial shape is expected to perform better. Experimental data confirm the better performance of the new shape factor. A multi-segment generalisation of the new multi-axial shape factor is proposed.     

Microhomogeneity assessments using ultrasonic slurry sampling coupled with electrothermal vaporization isotope dilution inductively coupled plasma mass spectrometry

Ultrasonic slurry sampling electrothermal vaporization inductively coupled plasma mass spectrometry (USS-ETV-ICP-MS) is a very powerful technique for the direct analysis of solid materials prepared as slurries. The use of isotope dilution USS-ETV-ICP-MS (USS-ETV-ID-ICP-MS) for micro-homogeneity characterization studies of powdered reference materials based on elemental analyses, was investigated. Slurry analysis conditions were optimized taking into consideration density, particle size, analyte extraction, slurry mixing, analyte transport and sampling depth. Slurries were prepared using 1–20 mg of material and adding 1.0 ml of 5% nitric acid diluent containing 0.005% Triton X-100®. Three reference materials were analyzed (RM 8431a Mixed Diet, SRM 1548a Typical Diet and SRM 2709 San Joaquin Soil). Cu and Ni were determined in each material and Fe was also determined in RM 8431a Mixed Diet. ETV conditions were optimized and the benefit of using Pd as a carrier to enhance transport, combined with oxygen ashing was demonstrated. The accuracy of the method was verified by comparing analytical results with certified values. The precision of the method was demonstrated by comparing R.S.D.'s for slurry samples and aqueous standards and elemental ‘homogeneity’ was quantified based on the slurry sampling variability. The representative sample mass analyzed was calculated taking into consideration extraction of analyte into the liquid phase of the slurry. Representative sample masses of approximately 4 mg of RM 8431a provided slurry sampling variabilities of 10% or less for Cu, Fe and Ni. Representative sample masses of approximately 10 mg of SRM 1548a provided slurry sampling variabilities of approximately 10% for Cu and Ni. Representative sample masses of approximately 0.3 mg of SRM 2709 resulted in total analytical variabilities of less than 7%, highlighting the fact that the San Joaquin Soil is clearly the most homogeneous of the materials characterized.     

Comparative study on the precision of potentiometric techniques applied with ion-selective electrodes: Part 1. Direct techniques

The measurement techniques used with ion-selective electrodes, e.g. standard edition, double known addition, known subtraction, etc., are summarized. In each case, the error in the unknown concentration measured (c_x) can be characterized by the term [σ(C_x)/C_x]/σ(E) where σ(E) is the standard deviation of the potential measurement. The formulae developed make it possible to calculate the expected error for any strategy of standard addition or subtraction and to optimize precision by proper selection of the concentration and volumes of standard solutions.     

Development and validation of a new direct sampling method for coarse mono- and mixed waste fractions bound in bales

Sampling of coarse waste materials is considered to be a particularly challenging task and is at the same time the most crucial step in the overall data acquisition process. Despite this fact, research work on new sampling methods or new scientific approaches to sampling has been rather limited over the last decades. This paper focuses on a completely new sampling procedure for coarse two-dimensional materials similar to municipal solid waste or packaging plastics. The developed method is especially suitable for materials with particle sizes >100 mm and is based on the ‘press-and-drill method’ introduced by researchers from Fachhochschule Nordhausen. The basic idea is to sample the material in its compressed form (e.g. as bales) with a drilling tool in order to gain increments. The study presented in this paper shows the results of two extensive test series applying this new sampling technique to a middle-calorific fraction produced from packaging material (mainly plastics, textiles and paper). In parallel, the state-of-the-art approach was also applied on the same materials to gain valuable reference data. Results from both approaches are used for the extensive validation of the new sampling method. The verification of accuracy was realised by doping the material with defined pieces of foil containing molybdenum sulphide (MoS₂) which acted as a tracer in the bale. The results obtained by the new direct bale sampling showed not only good accordance with the actual tracer content in each bale but also with results derived from the state-of-the-art approach. In this study, homogeneously distributed parameters (e.g. loss of ignition) were included just as inhomogeneously distributed elements (i.e. Cu). It is shown that sufficient representativeness for coarse materials (d₉₅ > 300 mm) is obtained despite relatively small sample amounts and without previous comminution of the material.     

Computerized image processing for evaluation of sampling error in ion microprobe analysis

A method is described for the microscale evaluation of sample heterogeneity as applied to in-situ ion microprobe analysis. Computer feature analysis of digitized ion images is utilized to generate sampling constants, which can be related to the degree of heterogeneity present for a particular constituent in the sample. The expected precision for a series of analyses, or the number of analyses required for a desired precision can also be determined. This approach, which is experimentally verified for NBS SRM-664 low-alloy steel, can be used both to minimize sampling error and to assess the applicability of specific reference materials to microprobe analysis.     

增量取样量接近分析试样量时的取样——理论修正与结果

化学分析取样几乎总是一个多步骤过程,所有的步骤都会导致分析结果的总体不确定性。样品采取之后,不论后续采样过程如何精细,前期采样阶段的误差都无法在后续采样过程中更正。第一次取样是最重要的,通常其方差远远超过实验室测量的方差。但这不意味着在最终实验室分析试样制备阶段可以忽略采样理论的原理。现代分析仪器旨在处理小样本(从毫克到几克)。在这种情况下,如果样品是包含少量分析物的混合颗粒,则物料的不均匀性可能会很大以至于破坏整个分析过程。不均匀性计算和样品制备过程中基本采样误差方差的估计对于开发适用的分析程序至关重要。在样本制备的最后步骤中,新的增量本是父增量本的重要组成部分,在估算样本方差时必须考虑到这种影响。TOS提供了用于处理这些情况的工具。通过两个案例阐明了不均匀性计算的应用。在第一个例子中,评估了鸡饲料中低含量添加剂的成分不均匀性,在第二个例子中,对样品制备进行了优化,以校正用于分析硅灰石精矿中矿物杂质含量的红外仪器。在处理颗粒混合物和评估混样效率时,不均匀性评估也很重要。     

Cost effective, robust estimation of measurement uncertainty from sampling using unbalanced ANOVA

There is an increasing appreciation that the uncertainty in environmental measurements is vitally important for their reliable interpretation. However, the adoption of methods to estimate this uncertainty has been limited by the extra cost of implementation. One method that can be used to estimate the random components of uncertainty in the sampling and analytical processes requires the collection of duplicate samples at 10% of the primary sampling locations and duplicating the analyses of these samples. A new program has been written and applied to a modified experimental design to enable a 33% reduction in the cost of analysing this 10% subset, whilst accommodating outlying values. This unbalanced robust analysis of variance (U-RANOVA) uses an unbalanced rather than the balanced experimental design usually employed. Simulation techniques have been used to validate the results of the program, by comparison of the results between the proposed unbalanced and the established balanced designs. Comparisons are also made against the seed parameters (mean and standard deviation) used to simulate the parent population, prior to the addition of a proportion (up to 10%) of outlying values. Application to a large number of different simulated populations shows that U-RANOVA produces results that are effectively indistinguishable from the results produced by the accepted balanced approach and are equally close to the true (seed) parameters of the parent normal population.     

Characterization of the mineral fraction in botanical reference materials and its influence on homogeneity and analytical results

Summary The NIST natural-product leaf Standard Reference Materials have been widely used in developing reliable methods of analysis. A small amount of mineral matter present in these materials was separated by flotation, and characterized qualitatively by microscopy and quantiatively by neutron activation analysis. Several elements are concentrated in the mineral fraction, which can lead to analytical error through incomplete dissolution or sampling statistics. Two new candidate materials prepared by the Office of Standard Reference Materials, SRM 1515 Apple Leaves and SRM 1547 Peach Leaves, have been processed with an air-jet mill, resulting in a very finely ground leaf material, with particle size less than 200 mesh. A cyclone classifier in the process discriminates against coarse grit, so that the content of minerals in the ground material is less than in the first-generation materials. Better homogeneity was in fact observed, even down to 100 mg sample size. One must use caution, however, to assure that any inhomogeneity found in real samples are appropriately considered and dealt with.     

Determination of sampling constants for selenium in biological reference materials by neutron activation

Summary A cyclic instrumental neutron activation analysis method has been used to calculate sampling constants and to evaluate homogeneity for Se in five biological reference and certified reference materials, namely NRC lobster hepatopancreas (RM TORT-1), IAEA horse kidney (RM-H8), and NIST bovine liver (SRM-1577a), oyster tissue (SRM-1566) and mixed diet (RM-8431). The between-weight-range heterogeneity has been observed to be no greater than the within-weight-range heterogeneity. The subsampling standard deviation (S _s) has been found to be less than the measurement standard deviation (S _m) for H-8 (>5 mg sample) and TORT-1 (>50 mg). For 1577a, S _s is almost equal to S _m; while S _s is 2–3 times higher than S _m for the other two materials. The sampling constants varied between 0.04 and 3.0 g for four materials while the mixed diet had a value of 31 g.     

Slurry sampling for graphite furnace atomic absorption spectrometry

Summary Slurry preparations are an effective way to introduce solids into the graphite furnace. Ultrasonic agitation keeps samples mixed prior to analysis. Several aspects of the ultrasonic slurry sampling approach are discussed including contamination concerns, analyte partitioning, and the effect of particle size. In addition, sample preparation strategies for slurry preparations of non-powdered materials are reviewed. The suitability of this method for assessing homogeneity is demonstrated.