Calibration functions

Robustness of methods based on broad-on-nar row approach (one of narrow standar ds is used as broad standard for correction of calibration function) is higher but some disadvantages also are observed. 

The comparison of the results of very different methods has to be judged very precisely, as, e.g., the given thickness of a layer is a function of the limit of detection (EOD) of a method. Additionally, the detected areas vary from about 0.01 up to about 400 mm-. Therefore, the methods with a low level of detection and with a high sensitivity (high slope of the calibration function) give a higher value for the layer thickness. Furthermore, the layers are broadened with time by diffusion. 

Long-time reproducibility of elution profiles broad standard calibration with dextran T-500 transformation of a scb-type calibration function into nb/Icb-type via universal calibration dp of synthetic glucans in the presence of significant amounts of monomer mass and molar degree of polymerization of Triticale (hybride) starch... 

On-line changing of solvent from DMSO to H2O for a starch glucan establishing an absolute calibration function characteristics of mass and molar degree of polymerization distribution for a broad distributed starch sample... 

Establishing a calibration function with one single broad distributed sample is an alternative to traditional peak postion calibration of SEC systems with a set of narrow distributed standards. An obvious advantage of this technique is time for peak position calibration elution profiles for the set of standards need to be determined for broad standard calibration the elution profile of one sample needs to be determined only. Establishing a linear calibration function with a broad distributed standard includes startup information [M (true), Mn(true)] and an iterative (repeat.. . until) algorithm ... 

To improve interpretation of nb/lcb glucan profiles from the S-500/S-1000 system, the initially obtained broad standard calibration function was... 

Figure 4.36. Cross validation between two HPLCs A stock solution containing two compounds in a fixed ratio was diluted to three different concentrations (1 10 20) and injected using both the 10 and the 20 /xl loop on both instruments. The steps observed at Amount = 100 (gray ellipses) can be explained with effective loop volumes of 9.3 and 20 pi (model 1) and 14.3 and 20 pi (model 2) instead of nominally 10 and 20 pi. This is irrelevant as both a sample and the calibration solution will be run using the same equipment configuration. The curved portion of the model 2 calibration function was fitted using Y = A /x this demonstrates the nonlinearity of the response at these high concentrations. The angle between the full and the dotted line indicates the bias that would obtain if a one-point calibration scheme were used.

This example assumes that RIA was chosen. The principle behind RIA is the competition between the analyte A and a radioactively tagged control C (e.g., a /-marked ester of the species in question) for the binding site of an antibody specifically induced and harvested for this purpose. The calibration function takes on the shape of a logistic curve that extends over about three orders of magnitude. (Cf. Fig. 4.38a.) The limit of detection is near the B/Bo = 1 point (arrow ) in the upper left corner, where the antibody s binding sites are fully sequestered by C the nearly linear center portion is preferrably used for quantitation. 

Size exclusion chromatography (SEC) separates molecules of a polymer sample on the basis of hydrodynamic volume. When the chromatograph is equipped only with a concentration-sensitive detector, i.e. conventional SEC, a molecular weight distribution (MWD) can be obtained from the chromatogram only through use of a calibration function relating molecular weight and elution volume V (2). 

M. Forina,G. Drava,C. Armanino,etal, Transfer of calibration function in near-infrared spectroscopy. Chemom. Intell. Lab. Syst., 27 (1995) 189-203. 

The composition of steels or other metals is commonly analyzed by emission or X-ray spectrometry during and after the production process. Both methods have to be calibrated by solid samples. These are either exactly analyzed samples taken from the same process or synthetic melted mixtures of the matrix with added accompanying elements (RMs). Available CRMs are then used to control the slope of the calibration function. Today, available RMs and CRMs are increasingly and exclusively used in spectral laboratories as the chemical analysis became much restricted and typical control laboratories were totally closed (Slickers 1993). 

Suitable calibration of instruments used is a fundamental necessity, and it is rarely performed in an appropriate way. Most often, linear calibration functions are regarded... 

Finally, a comparison between real and calculated signal intensities can demonstrate the quality of calibration, even if a nonlinear calibration function correlates better with the observed response (Table 4). 

Consequently, the proof of calibration should never be limited to the presentation of a calibration graph and confirmed by the calculation of the correlation coefficient. When raw calibration data are not presented in such a situation, most often a validation study cannot be evaluated. Once again it should be noted that nonlinearity is not a problem. It is not necessary to work within the linear range only. Any other calibration function can be accepted if it is a continuous function. 

N Number of repeated measurements for the estimation of x by means of a calibration function ... 

Calibration function (in the stricter sense, i.e. of quantities characterizing quantitative properties, e.g., signal intensity vs analyte amount)... 

Calibration function of quantities characterizing qualitative properties, viz signal position as a function of the type of species... 

Both steps are characterized by the corresponding natural laws as well as empirical relations caused by measuring instruments and conditions. All such laws and rules are put together by the measuring function (calibration function). 

The evaluation function Q = / 1 (z) that transfers measured z-values into information on Q may be the reciprocal function of one of the following calibration functions (Danzer [1995a]) ... 

In general, the evaluation function for quantitative analysis is the inverse of the calibration function y = f(x) (Currie [1995, 1999], IUPAC Orange Book [1987, 1988]) ... 

On the other hand, indirect reference measurements are based on empirical calibration functions obtained experimentally and frequently based on Unear models... 

Calibration functions corresponding to Eq. (2.22) are not generally transferable over long times and not from one laboratory to another. However in the case of blank-free or blank-corrected relations... 

Calibration in analytical chemistry relates mostly to quantitative analysis of selected species and, therefore, to calibration functions of the kind y = f(x). 

On the other hand, indirect reference measurements which result in an empirical calibration function, frequently based on a linear model, y = a + b - x + ey see Sect. 2.4, Eq. (2.22), where the intercept a corresponds to... 

From the different character of xstandard and xsampie (Figs. 6.2 and 6.3) it can be seen that the relationship between the calibration function... 

Fig. 6.3. Three-dimensional model of calibration, analytical evaluation and recovery spatial model (A) the three relevant planes are given separately in (B) as the calibration function with confidence interval, in (C) as the recovery function with confidence interval, and in (C) as the evaluation function with prediction interval (D)... 

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