Sample preparation variance

In chromatography, we have on the one hand the instrumental variance , which is not dependent on the concentration, and which is related only to the noise of the detector or the oscillations of the pump. This variance is the same at high and at low concentrations and is described by WE = 0 (iv= 1 at all concentrations). On the other hand, we can postulate a sample preparation variance with the same percentage deviations at all concentrations (characterized by WE = 2). 

This experiment introduces random sampling. The experiment s overall variance is divided into that due to the instrument, that due to sample preparation, and that due to sampling. 

When executed improperly, sample preparation is the source of the second-largest component of the overall variance of sampling and analysis. Although it is not specified as a requirement, it is generally recognized that the variance of sample division and analysis is not more than 20% of the total variance of sampling, division, and analysis (ASTM D-2013). The particle size distribution (size consist) of the laboratory sample depends on its intended use in the laboratory and the nature of the test methods to be applied. The minimum allowable... 

Nd-Pt-Sb. NdPtSb crystallizes with the Caln2 type structure, a = 0.4544, c = 0.7878 (Rossi et al., 1981 powder X-ray diffraction data). For the experimental details, see the LaPtSb. At variance with these data, Wenski and Mewis (1986a) reported the LiGaGe type structure for the NdPtSb compound, a = 0.4535, c = 0.7866 from X-ray single crystal investigation. For the sample preparation, see PrPtSb. 

Uncertainty in a method can come from both the sample preparation and the analysis. The total variance is the sum of the two factors ... 

The subscript T stands for the total variance the subscripts s and a stand for the sample preparation and the analysis, respectively. The variance of the analytical procedure can be subtracted from the total variance to estimate the variance from the sample preparation. This could have contribution from the steps shown in Figure 1.2 ... 

Precision is measured by making replicate measurements. As mentioned before, it is known to be a function of concentration and should be determined at the concentration level of interest. The intrasample variance can be determined by splitting a sample into several subsamples and carrying out the sample preparation/analysis under identical conditions to obtain a measure of RSD. For example, several aliquots of homogenized fish liver can be processed through the same extraction and analytical procedure, and the RSD computed. The intersample variance can be measured by analyzing several samples from the same source. For example, different fish from the same pond can be analyzed to estimate the intersample RSD. 

Sample preparation involves physical and chemical treatments which are potential sources of bias, variance, contamination, and mechanical loss. Sample preparation should be planned carefully and documented in sufficient detail to provide a complete record of the sample history. Furthermore, samples taken specifically to test the quality assurance system should be subjected to the same preparation steps as the test sample. 

Only in one test (the fourth round-robin) were the identified chemicals quantified (4), and then only to facilitate the evaluation of sample preparation methods. The quantitative results varied widely. Weaknesses were revealed in the procedures because all the chemicals were polar and adsorptive. Comparison of the quantitative results as a means of deciding upon the best sample preparation procedures proved to be an unreasonable approach, however, as the total variance in the results was clearly the product of several factors the sample preparation procedure, the quantitative method, and the instrumental technique. Nevertheless, the exercise proved to have considerable educational value. The test revealed weaknesses in the existing ROPs (6) and the methods were subsequently improved to cover the gaps (7). 

In order to assess the precision of the chemical analysis relative to the variation due to sample preparation and sampling, duplicate samples and repeat measurements should be carried out. The duplicate samples, prepared independendy of each other and analyzed randomly along with all other samples, with each duplicate sample also analyzed in duplicate, allows estimation of sampling uncertainty by the analysis of variance (ANOVA) statistical interpretation method. 

In combining the total variance for a sample preparation and analysis each has their own list of uncertainties. The overall uncertainty (U0) at a specific confidence limit is selected and the value calculated using ... 

If the variance due to sample preparation is negligible (i.e. 82 = 0) and most of the uncertainty is due to the analytical stage only, then ... 

In the analytical procedure, an accurately measured aliquot of the product is diluted Avith a diluent (normally the mobile phase) and the resulting sample solution is injected into the HPLC. Because the majority of injectable pharmaceuticals are clear solutions, typically a simple dilution step is all that is needed for sample preparation. However, if the parenteral product is an emulsion or a suspension, appropriate steps must be taken to dissolve the product to achieve a clear solution (ultrasonication, filtration, etc.). For the assay procedure, the sample concentration chosen should be such that the peak areas obtained from multiple injections from the same sample are reproducible with minimum variance (<2% relative standard deviation). Peak shape and retention time also play important roles in the precision of the assay. A tailing factor less than 1.5 and a capacity factor less than 10 for the active peak are generally required for a good analytical method. A reference standard solution having the same concentration and using the same diluent as the sample solution is prepared. 

Other procedural details such as test lot preparation to aliquot all the samples needed for the validation experiments should also be described briefly in this section of the protocol.] Referring to SOP 123, the reportable value is defined as the average of the three replicates. For this validation, accuracy, precision, and linearity of the replicate values will be assessed consequently, the precision of the results reported is at the replicate level not the reportable value level. [Note this practice is done for two reasons first, to conserve resources, and second, when it is not possible to repeat an additional assay with exactly the same sample preparation. The repeatability component of the precision is defined as within-assay variance. Using the replicate values yields a within-assay variance.]... 

Intermediate precision components typically include day, operator, and assay. Day is a random effect that captures random environmental changes that are not controlled and may have an effect on the assay result. Operator, usually modeled as a random effect, captures the variation in assay results due to change in personnel running the assay. Assay captures the variation one would expect from one complete run of the method to the next complete run of the method. Thus, assay captures the random variation due to slight perturbations in the sample preparation from assay run to assay run (when run by the same operator on the same day). Often, it is not possible for each operator to run more than one assay on each day however, the validation experiments can be designed to estimate this variance component under a reasonable assumption. 

ICH Q2A defines repeatability as the variability of the assay results under the same operating conditions over a short interval of time. Repeatability is also termed intra-assay precision. A reportable value of an assay is often the average of a specified number of replicate values, where the replicates are processed using the same sample preparation. Thus, it is not possible to obtain a true repeat of the assay s reportable value. Repeatability can be modeled as the within-assay variability of the replicates however, it should be noted that this precision is at the level of the replicate and not at the level of the reportable value. If the reportable value is an average of K replicates the variance of the reportable values will be less than that of the replicates by a factor of l/K (the standard deviation will be less by a factor of (1/ k ). 

During this optimisation programme, samples of eel, fish oil, mussel and sewage sludge were prepared for intercomparison. Data from analysis of a crude eel extract and a refined (cleaned-up) sample were compared to test the variance associated with different methods of sample preparation. The clean-up methods included gel permeation chromatography, saponification, concentrated sulphuric acid treatment, alumina and silica-gel column chromatography. The differences in results of the within and between clean-up methods did not significantly influence the overall analytical variance after the appropriate optimisation. 

The Quantities a and U. Samples prepared by an unperturbed anionic polymerization process have a distribution function, which, as derived by Bohm (I), corresponds to a Gaussian error function. The same in general is the case for fractions produced by precipitation and/or solution. The distribution function then is characterized by two parameters, the variance a and the number average degree of polymerization Pn. On the other hand, a given distribution can be characterized by the nonuniformity (Uneinheitlichkeit in German) C7, defined by the equation... 

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