Sampling constant

The sampling constant for the radioisotope " Na in a sample ( homogenized human liver has been reported as approximate 35 g. (a) What is the expected relative standard deviation fo sampling if f.O-g samples are analyzed (b) How many f.O-g samples need to be analyzed to obtain a maximum sampling error of 5% at the 95% confidence level ... 

FIGURE 25.5 Sample constant amplitude signal (a) and variable amplitude signal (b). 

IAEA/AL/095 1996). Both methods were suitable, but needed to be repeated several times to produce the small particle size that was required. The particle size reduction, e.g. of IAEA-395 from a median size of 30 pm to 3.5 pm, improved the homogeneity of elements. Sampling constants (the minimum mass that can be used to achieve a random error of i % at the 65 % confidence level) improved from a factor of 1.2 for Sc, up to a factor of 800 for Au. The average improvement was about a factor of 2-10. (Ni Bangfa et al. 1996). From these initial experiences, it is dear that preparation of reference materials is critical with respect to the final particle size distribution, which should exhibit a low maximum (<50 pm) and a narrow range in particle sizes. Milling techniques to meet such criteria are available today, and materials that show intrinsic uniformity are particularly suitable to achieve the desired properties. 

The sampling variance of the material determined at a certain mass and the number of repetitive analyses can be used for the calculation of a sampling constant, K, a homogeneity factor, Hg or a statistical tolerance interval (m A) which will cover at least a 95 % probability at a probability level of r - a = 0.95 to obtain the expected result in the certified range (Pauwels et al. 1994). The value of A is computed as A = k 2R-s, a multiple of Rj, where is the standard deviation of the homogeneity determination,. The value of fe 2 depends on the number of measurements, n, the proportion, P, of the total population to be covered (95 %) and the probability level i - a (0.95). These factors for two-sided tolerance limits for normal distribution fe 2 can be found in various statistical textbooks (Owen 1962). The overall standard deviation S = (s/s/n) as determined from a series of replicate samples of approximately equal masses is composed of the analytical error, R , and an error due to sample inhomogeneity, Rj. As the variances are additive, one can write (Equation 4.2) ... 

In order to determine the sampling variance accurately, it is necessary to minimize the individual components of analytical variance as much as possible. Once the sampling constant(s) are determined, one can predict what the magnitude of the sampling variance should be for a given analyte and for various masses of the sample of a given material. 

If a different amount is taken, other than which is specified in the certificate, then this has a significant impact on the confidence interval for the certified value in that particular sample. Extrapolation of uncertainty to different sample sizes, in particular uncertainties due to inhomogeneity at smaller sample size, is not possible without extensive sampling studies. Even so, RM producers should support analysis procedures that require different sample sizes by supplying sampling information such as sampling constants see also Section 4.3. 

Ingamells CO (1976) Derivation of the sampling constant equation. Talanta 23 263... 

Ingamells CO, Switzer P (1973) A proposed sampling constant for use in geochemical analysis. Talanta 20 547... 

An indication of the minimum size of a subsample can be obtained by using the concept of a sampling constant. For example, in the laboratory, the sampling constant can be used to estimate the minimum size of the test portion. However, the suitability of the chosen test portion size must be confirmed as part of method validation. The sampling constant Ks has units of mass. This is the mass of the test portion necessary to ensure a relative subsampling error of 1% (at the 68% confidence level) in a single determination. The value of /Ks is numerically equal to the coefficient of variation, CV (see Chapter 6, Section 6.1.3) for results obtained on 1 g subsamples in a procedure with insignificant analytical error. 

If the laboratory sample has been prepared in a particular way to pass a specific mesh size, the coefficient of variation of the result for one component varies inversely with m, where m is the mass of the test portion. A sampling constant (Ks) can be defined by the following ... 

Let us consider a catalytic cycle with random rate constants. For a given sample constants k, ...,k the ith order statistics is equal its ith smallest value. We are interested in the first order (the minimal) and the second order statistics. 

Ingamells related Gy s sampling constant to Ingamells constant by K, = fgcl(d X 10 )... 

Once the data are available, certification of sampling systems as unbiased, without qualification, is insufficient, and certification should also be accompanied by a statement of (1) the mean levels of each variable constituent that prevailed during conduct of the test, (2) the nominal sizing of the coal, and (3) some indication of the preparation (washing) to which the coal has been subjected, since these influence the sampling constants and may affect the magnitude of bias observed. 

The diagrams in Fig. llc-f can be measured by the force probe method, when the amplitude and phase are measured as the tip approaches and retracts the surface vertically. In the non-contact range, both the amplitude and the phase retain their constant values (Fig. llc,e). When the tip enters the intermittent contact range (Zphase reduces almost linearly on approaching the surface. The deviation of the amplitude signal from a certain set-point value As is used by a feedback loop to maintain the separation Zc between the tip and sample constant, and hereby visualise the surface structure. When the surface composition is uniform, the amplitude variation is mainly caused by the surface topography. However, if the surface is heterogeneous, the variation in the amplitude can be affected by local differences in viscoelasticity [108-110 ] and adhesion [111] of the sample (Sect. 2.2.2). 

Procedures. Batch equilibrations of interbed solids (Mabton Interbed, Rattlesnake Ridge sandstone, or tuff), tracers, and groundwaters were used to measure radionuclide distributions between solid and liquid phases. Triplicate measurements were made for each combination of temperature, redox condition, tracer concentration, tracer type, groundwater composition, and interbed sample. Constant temperatures were maintained by placing the... 

A quite similar consideration was published by INGAMELLS and SWITZER [1973] and by INGAMELLS [1974b 1976]. A sampling constant Cs is proposed which enables estimation of error of subsampling, i.e. the withdrawal of a small portion from a well mixed material. The relationship to GY s equation (Eq. 4-7) is given by ... 

It can be shown [35,41] that for a fictitious case of a two-component mixture in which the component of interest (trace element), A, is present only in grains containing 100 % of this component, the sampling constant is given by ... 

Ingamells, C.O. A further note on the sampling constant equation. Talanta 25,731-732 (1978)... 

Small deformation rheometry refers to testing procedures that do not cause structural damage to the sample. Constant stress rheometers, such as dynamic mechanical analyzers or oscillatory constant stress rheometers, are often used. 

Figure 3.41. The schematic of goniometer optics during data collection employing variable divergence and scatter slits apertures, which enables one to maintain the irradiated area of the sample constant at any Bragg angle. DS - divergence slit, ScS - scatter slit, RS - receiving slit.

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