Alternative Calibration Procedures

If the basic conditions for the use of least squares fitting are not fulfilled (Fig. 6.6), especially if strongly deviating calibration points appear ( outliers or, more exactly, leverage points), the OLS method fails, i.e., the estimated calibration are biased and, therefore, are not representative for the relation between x and y. Whereas normality of the measured values can be frequently obtained by a suitable transformation, especially in the case of outlying calibration points, robust calibration has to be applied (Rousseeuw and Leroy [1987] Danzer [1989] Danzer and Currie [1998]). 

Robust calibration. The GAussian OLS criterion according to Eq. (6.16) is strongly sensitive against outliers. Therefore, robust methods of fitting have been developed following two strategies (Rousseeuw and Leroy [1987])  

It has been known for a long time (Edgeworth [1887]) that minimizing of the linear sums of deviations 

On the other hand, least trimmed squares (LTS) can be used to estimate the calibration parameters that points which produce the (n — h) largest deviation squares are rejected and the remaining h points are used for the LTS fitting  

Another way is the robust parameter estimation on the basis of median statistics (see Sect. 4.1.2 Danzer [1989] Danzer and Currie [1998]). For this, all possible slopes between all the calibration points bij = (yj — yi)/(xj — X ) for j i are calculated. After arranging the b j according to increasing values, the average slope can be estimated as the median by 

With the various problems associated with the conventional calibration procedures, it is an obvious solution to attempt to combine SEC with an absolute molecular mass technique. Light scattering, in the form of low-angle laser-light scattering, is the only readily available absolute technique for such 

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The SEC columns were calibrated using narrow molecular weight distribution water soluble polymer standards sodium polystyrene sulfonate, NaPSS (Pressure Chemical Company, Pittsburgh, PA) and dextrans (Pharmacia Fine Chemicals, Piscataway, NJ). The universal calibration curve proposed by Grubisic et al. (13) was found not to be applicable for these polymer standards. The alternative calibration procedure of Coll and Prusinowski (J ) which incorporates excluded volume effects in the numerical value of the Flory parameter was found to be applicable for this system ( ). The calibration curve for the two-column network system described above is shown in Figure 3. The Kyyy parameter used on the abscissa of Figure 3 is a normalized elution volume parameter defined by Equation 1,... 

For CE and CEC, the methods used for quantitative chromatography (Topic D2) are suitable, and alternative calibration procedures are described in Topic A5. Peak areas are more reliable than peak heights, as they are directly proportional to the quantity of a solute injected when working within the linear range of the detector. 

Note S—The instrument manufacturer provides an alternative calibration procedure using two reference points, zero pressure (<0.1 kPa) and the ambient barometric pressure. However, since this procure was not included in the interlaboratory program, the precision and bias can be affected by its use. 

Alternatively, either the Elamielec or the integral broad standard calibration procedure can be used. For this approach, the broad standard would be initially analyzed using a calibration based on some convenient standard that may be quite dissimilar in chemistry from the standard. From that point forward, the system is calibrated with the secondary standard. Thus, changes that affect the sample will be compensated for in the calibration procedure. 

Proper calibration of the DSC instruments is crucial. The basis of the enthalpy calibration is generally the enthalpy of fusion of a standard material [21,22], but electrical calibration is an alternative. A resistor is placed in or attached to the calorimeter cell and heat peaks are produced by electrical means just before and after a comparable effect caused by the sample. The different heat transfer conditions during calibration and measurement put limits on the improvement. DSCs are usually limited to temperatures from liquid nitrogen to 873 K, but recent instrumentation with maximum temperatures close to 1800 K is now commercially available. The accuracy of these instruments depends heavily on the instrumentation, on the calibration procedures, on the type of measurements to be performed, on the temperature regime and on the... 

These two conditions are crucial for a correct outcome of the experiment. If the experiment is not successful by using acetate or glucose, a more broad-spectral, however, well-defined type of substrate can be selected, e.g., a yeast extract. If the experiment is still not successful, a calibration procedure, i.e., an extended procedure number 4, is still an alternative. 

Two procedures for improving precision in calibration curve-based-analysis are described. A multiple curve procedure is used to compensate for poor mathematical models. A weighted least squares procedure is used to compensate for non-constant variance. Confidence band statistics are used to choose between alternative calibration strategies and to measure precision and dynamic range. 

Implications For B ethod Development. The effects of the calibration process on precision suggest the need for an additional step in the development of an analytical method. A suggested flow chart is shown in Figure 9. The analyst should first develop a method of adequate accuracy and precision without using calibration curves. The calibration step is then added, and the precision is rechecked. If precision has been excessively degraded, the analyst can choose among alternative calibration strategies, such as use of more standard measurements and use of the multiple-curve procedure. 

The measurement of aw (Basic Protocol) requires 1 hr of equilibration time and does not require internal calibration. The calibration procedure (see Alternate Protocol) is also simple and straightforward, and can be done in 2 to 3 hr. The equilibration time in this protocol usually takes 1 hr. 

It was found that the normal method of scanning the frequency doubling laser by rotating the tipping Brewster plate in the reference cavity was insufficiently smooth over the small ranges required a satisfactory alternative was found to be to shift electronically the reference point used for locking the reference cavity. Further refinements to the lasers were unnecessary, because their performance did not limit the accuracy of the measurements. The calibration procedure was responsible for most of the uncertainty, and was the least satisfactory aspect of the experiment as we now discuss. 

An alternative calibration technique was developed and successfully applied to techniques hyphenated to LA [43-48]. In addition, an increasing number of matrix-independent calibration procedures using external reference materials and/or internal standardization procedures is being developed [49-51]. 

Finally, a few words remain to be said about case (d) (S>l/2,I>l/2). At the present stage of knowledge, this case remains seemingly intractable for quantitative applications outside the non-selective excitation limit Vj/Vq l. The chief problem in applying pulse sequence at Fig. 8b) arises from the nuclear electric quadrupolar interactions affecting the S spins, which interfere with the ability of the 71-pulse trains to refocus the transverse magnetization. In contrast, pulse sequence at Fig. 8a) is able to produce experimental REDOR curves, which are, however, difficult to interpret quantitatively. As a best-effort solution, one may resort to sample-to-sample comparisons on a relative basis and the use of empirical calibration procedures with closely related model compounds [32]. Alternatively, the SEDOR approach, which does not suffer from these restrictions, would be preferable. 

Applications of NMR in process control, although not as popular as FT-IR and NIR, provide an alternative when the latter techniques fail. The advantages of low-field (10-60 MHz) low-resolution NMR in process control applications are its noninvasive nature and the lack of need for calibration procedures with feed or product, as it is tolerant to changes in process environment and feed quality. Process/quality control NMR applications are based on separation of the FID into separate responses from components with different T2S (Fig. 6). Longer in-stream analysis times, high... 

An alternate method exists to determine in situ bulk density usually only in very shallow water such as bays and estuaries, without the necessity of using radioactive isotopes. To accomplish the electrical resistivity of the soil and also of the pore water (to correct for variations in salinity) is measured using two probes (Rietsema and Viergever, 1979). This is a convenient measurement, although the equipment may be somewhat complicated to use because of having to use two separate probes to obtain one measurement in addition, the laboratory calibration procedure is not simple. What appears to be a more versatile device has been described by Bennett et al. (1983). 

The measurement of polymer molecular masses by dilute solution viscometry is not an absolute technique. However, the parameters used to relate solution viscosity to molecular mass are the same as those used in the universal calibration procedure (section 3.2.3). Earlier it was pointed out that one of the weaknesses associated with the universal calibration procedure was the use of literature values for these parameters. Alternatively, if some absolute molecular mass data is available, dilute solution viscometry can be used to determine these Mark-Houwink parameters. The choice is between extensive preliminary practical work and in making wide-ranging assumptions, often with quite old data on Mark-Houwink parameters. The use of a viscosity detector, whilst not removing the need for conventional calibration, does potentially widen the range of the applicability of the calibration, without the use of any assumptions. 

The universal calibration procedure outlined by Benoit [18] offers an alternative method of establishing a molecular mass calibration for HDPE chromatograms. The procedure assumes that, in the SEC analysis, the chain molecules separate and elute according to their hydrodynamic volumes, and this in turn is directly proportional to the product of [ /] M. (see Chapter 3, section 3.2.3). 

An alternative strategy is appropriate if determinations are to comply with a standard scheme of analysis, such as those developed by the British Standards Institution for the analysis of ceramic and refractory materials. In these schemes, samples are prepared as fused glass disks and calibration samples may then be prepared in the same way using specified proportions of high-purity element oxides. This calibration procedure can, therefore, be considered to be absolute in contrast to the relative measurements made against reference samples. 

Several other alternative calibration methods using aqueous standard solutions have been applied in the case that appropriate standard reference materials are not available. " Online solution-based calibration utilizes the introduction of mixed laser-ablated sample material together with nebulized standard solutions through desolvation units to the ICR Two setups are in use, based on adding the solutions either before (the so-called single gas flow system) or after (known as the dual gas flow system) the laser cell (see Figure 6.13). ° Using such a procedure, one can use either external standardization, analyte standard addition, or even isotope dilution techniques for small sample sizes. ... 

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