Uncertainties in sampling

Figure 1 shows the condition of materials submitted for analysis at various stages of becoming a product. Complications arise from uncertainties in sampling and of course in separating impurities. The availability of an instrument can effect the decision of which analysis to perform. 

These techniques are designed to minimize both the actual working time, required and the analytical uncertainties in sample analysis. Sample preparation and neutron activation procedures are based on proved analytical and microanalytical techniques. The unusually high sensitivity, reliability, and accuracy are achieved through a choice of optimum irradiation and counting times for the y-ray detection systems. 

To minimize extreme ambient temperature fluctuations. If the laboratory and dew-point instrument temperatures fluctuate by as much as 5°C daily, water activity readings may vary by 0.01 aw. Often, this much uncertainty in sample aw is unacceptable, so there is a need for a temperature-controlled model. 

In practice, measured isotope ratios are reported as mean and standard error. For analyses with stable ion-beam intensities, the within-run statistical errors are typically similar to those predicted by counting statistics. Uncertainties in sample weight, spike weight, spike concentration, chemical blanks, and filament blanks are typically small compared to the analytical uncertainty, but are also included in the error propagation through Eq. (1). 

W. Wegscheider, H. J. Zeiler, R. Heindl, J. Mosser, Quantifying Uncertainty in Sampling and Analytical Measurements. Ann. Chim. (Rome), 87 (1997), 273-283. 

Large, heavy crucibles will cause a greater uncertainty in sample temperature. 

Radiation detectors should have a low and stable radiation background to reduce interference and uncertainty in sample measurements (see Section 10.3). Contributors to the radiation background for a detector are the following ... 

Consider a typical procedure such as the spectrophotometrlc determination of an analyte in groundwater samples. Quite likely, a single calibration curve will be used to cover a concentration range that extends from below the regulatory limit (hopefully) to some elevated concentration far removed from the limit. In this situation, a DL can be based on confidence limits (CL) around the calibration curve (7-14). The DL estimate produced in this fashion can then reflect the combined uncertainties in sample analysis and calibration. 

The results of radionuclide measurements for substantial batches of foodstuffs should be compared immediately with generic or specific action levels, with account taken of uncertainties in sampling and measurement. 

The discussion on uncertainty in sampled systems concluded that the sampling interval should not exceed the open-loop response time of the process. For best results with easy processes, the sampling interval should be as short as practicable. But where dead time dominates, the sampling interval is best- keyed to the process response time. Unfortunately, practical considerations take precedence over performance for most applications. 

Table 1. Some sources of uncertainty in sampling and sample preparation (Gron, Hansen et al. 

The sampling and analytical variances must be determined from independent measurements. It is well established that once the analytical uncertainty (standard deviation) is reduced to a third or less of the sampling uncertainty, further reduction in analytical uncertainty is of little importance. Therefore, if the uncertainty in sampling is very large, it may be beneficial to opt for an analytical method that is rapid even though it might have lower precision. This will permit more samples to be analyzed, thereby resulting in a better estimate of the mean value. 

Almost invariably in these applications we can be satisfied if the analytical result obtained is within a range of 90-110% of the true result. This modest fitness-for-purpose requirement is an outcome of the high uncertainties in sampling of environmental materials. In these circumstances, the total uncertainty (sampling plus analytical) is not improved by the use of high-accuracy analytical methods. Overall, therefore, it is a more effective use of resources to analyse a larger number of samples with only moderate accuracy. 

Partial specific volumes and other volume quantities have been determined experimentally, predominantly by density measurements. However, sometimes experimental determinations of volumes of both macromolecules and nonmacromolecular components are not feasible, e.g., due to insufficient amounts of material, lack of purity of samples, uncertainties in sample concentration, and handling problems such as instability of samples or adsorption phenomena. In these cases estimates can be obtained by calculations or reliable approximations. Though first attempts to calculate volumetric properties of organic compounds reach back to 1839 [1839K1], only recently a universal approach has been elaborated which allows ab initio calculations of partial volumes of small molecules and polymers of different chemical composition and structure in aqueous solution [94D1]. 

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