Robust calibration

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]) ... 

Robust calibration corresponds in most cases to the problem of outlying calibration points (leverage points). In consideration of that, attention must be directed to the linearity of the relationship in general and the randomness of the residuals. 

Sharma et al. (2005) developed robust calibrations for some of the key parameters from the spectra or fresh phase I and II composts and found by the laboratory measurement that for phase I samples were greater than those of the phase II samples except for ash, due to a higher degree of heterogeneity in the substrate. 

C.R. Mittermayr, H.W. Tan and S.D. Brown, Robust calibration with respect to background variation, Appl. 

Step 7 On-line analyzer calibration Calibrating an analyzer entirely on-line is a last resort, for reasons discussed in Section 15.2.6. It is preferable to do at least the initial work to calibrate the analyzer off-line, or to transfer to the on-line analyzer a method developed on an off-line analyzer or on another on-line analyzer. However, sometimes this is not possible. On-line analyzer calibration is similar to standard analytical chemistry method development, except that getting sufficient variation in sample composition to build a robust calibration model may be difficult or may take a long time. (Ways to address the challenges involved in on-line calibration are discussed in Section 15.2.6 and in Chapter 14.)... 

An interesting additional feature of using potentiometric sensors in array mode has been pointed out, which is to profit from the extra information to gain confidence in measurements, that is to perform redundant analysis. This strategy can be the basis for automated fault detection of the sensory elements [48] and also be an aid for more robust calibrations [49]. 

In order to achieve the demanded combination of temporal resolution and accurate yields, FTIR spectroscopy appears a suitable method for collecting data in combination with robust calibrations for quantitative results. Cigarette smoke is known to contain thousands of compounds and the amounts of the vapor phase components in the sidestream smoke are emitted at levels 2-10 times the mainstream amounts [66,67]. In order to utilize vibrational-rotational lines as reported in previous studies [63,64], FT-IR spectra would have to be collected at a spectral resolution of 1 cm 1 or better. Improved temporal resolution of the sidestream concentration profile could only be attained at an equivalent signal-to-noise level by collecting spectra at lower resolution. However, at lower resolution (below 1 cm x) the vibrational-rotational lines would no longer be spectroscopically resolved and accessible to quantification. 

The time required to complete the above described calibration procedure varies depending on the application. A critical factor in developing a robust calibration model is to incorporate all sources of spectral variance expected for future samples. The calibration procedure creates a model where the analyte-dependent signal is orthogonal to all nonanalyte-dependent sources of spectral variance. Significant time... 

Motion Artifacts and Skin Heterogeneity A key component to obtaining accurate and robust calibrations is the sample interface. The sample interface should ideally limit motion while maintaining a constant pressure and temperature. One approach to combat inadvertent motion artifacts is to intentionally build motion into the calibration model. This can be achieved by scanning the laser spot within a larger area. 

Engelen, S. and Hubert, M., Fast model selection for robust calibration methods, Analytica Chimica Acta, 544, 219-228, 2005. 

To illustrate the use of experimental designs in an analytical chemistry application, we will examine a problem taken from the agrochemical industry. The problem under investigation was to develop a robust calibration model for several commercial products based on UV spectral measurements. By the term robust model, we assume that the model will be able to give acceptable predictions even if there is some moderate variation in the controlled and uncontrolled variables. 

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