Error in calibration

Chemical parameters (e.g., partition coefficients, decay rates, temperature and moisture effects) are not usually considered as calibration parameters because they can be measured in a laboratory moreover, calibration is usually not possible due to lack of observed data. However, most scientists will agree that extrapolation of laboratory parameter measurements to field conditions is a risky assumption. If observed chemical data are available, refinement of initial chemical parameters through calibration should be considered. Errors in calibration-derived parameter values are often a function of how much calibration was performed or errors in system inputs and/or outputs. In many modeling efforts, conscientious model users will often overrun the calibration budget because of the natural tendency to continue to make calibration runs in an effort to minimize discrepancies between simulated and observed values. Parameter errors associated with calibration are more often a result of missing and/or erroneous data either as system inputs or outputs. 

Equation (4.20) was proposed by Hoskuldsson [65] many years ago and has been adopted by the American Society for Testing and Materials (ASTM) [59]. It generalises the univariate expression to the multivariate context and concisely describes the error propagated from three uncertainty sources to the standard error of the predicted concentration calibration concentration errors, errors in calibration instrumental signals and errors in test sample signals. Equations (4.19) and (4.20) assume that calibrations standards are representative of the test or future samples. However, if the test or future (real) sample presents uncalibrated components or spectral artefacts, the residuals will be abnormally large. In this case, the sample should be classified as an outlier and the analyte concentration cannot be predicted by the current model. This constitutes the basis of the excellent outlier detection capabilities of first-order multivariate methodologies. 

Despite the very different mechanism, the HSQC sequence (//eteronuclear Single Quantum Correlation) yields results equivalent to an HMQC sequence except that HSQC offers an additional benefit—the cross-peaks do not exhibit homonuclear JH—XH couplings along the FI axis. These splittings reduce sensitivity and resolution along this axis in HMQC spectra. On the other hand, the HSQC sequence contains more pulses and is more sensitive to errors in calibrations etc. The sequence is209 ... 

Errors in calibration and standardization result in poor accuracy, and are considered in Section 2.5. 

To avoid systematic errors in calibration, the standards must be accurately prepared and their chemical state must he identical to that of the analyte in the sample. The standards should be stable in concentration, at least during the calibration process. 

The goodness of a calibration can be summarized by two values, the percentage of variance explained by the model and the Root Mean Square Error in Calibration (RMSEC). The former, being a normalized value, gives an initial idea about how much of the variance of the data set is captured by the model the latter, being an absolute value to be interpreted in the same way as a standard deviation, gives information about the magnitude of the error. 

The calculation of the a -vector according to the procedure given above should result in values which are mainly influenced by numerical problems with respect to the inversion process. However, neither the measured absorbances in the course of kinetic analysis nor the absorption coefficients obtained by calibration procedures are faultless. On the contrary these errors have to be taken into consideration in eq. (4.4) by an additional vector e which takes into account noise in measurement and errors in calibration. It is a residual vector. In consequence, by use of the measured absorbances, in the following the concentration vector obtained is used to recalculate absorbances. The difference between calculated and measured absorbances correlates to the residual vector... 

Table 3. Results of PLS models for fresh Duke berry samples (r = coefficient of correlation RMSEC = root mean square of the standard error in calibration RMSEGV = root mean square of the standard error in cross-validation LV = latent variables). All data were preprocessed by second derivative of reduced and smoothed data.

Since the field data were gathered under actual operating conditions, there are many items that could not be as carefully controlled as in a laboratory testing. Some of these items consist of operating and maintenance procedures, brief periods of equipment downtime and errors in calibration that could account for the difference in heating value. 

Errors in calibration doses. A modified least squares method, taking into account that calibration doses also contain uncertainties, can be applied [37]. 

Systematic errors affect the accuracy but not the precision of the result. They are usually errors in calibration or observation where the same incorrect protocol is applied to all measurements. They displace all measurements from the true value by the same amount so they cannot be detected by a statistical analysis of only one data set. However, systematic error can be detected and reduced by comparing data sets from several different sources using meta-analysis and systematic review (Rimstidt et ah, 2012). 

These authors expand the basic relationship LOD = ks S to include 1) the use of population statistics (vs. sample set statistics) 2) the use of the pooled standard deviation (vs. the blank standard deviation) 3) a consideration of situations where the intercept of the calibration curve is non-zero and 4) a consideration of the errors in calibration parameters (slope and intercept). 

Thus far the discussion in this chapter has concentrated on the statistical treatment of random errors in calibration data and calibration equations, with only passing mention of the implications of the practicalities involved in the acquisition of these data. For example, no mention has been made of what kind of calibration data are (or can be) acquired in common analytical practice, under which circumstances one approach is used rather than another and (importantly) what are the theoretical equations to which the experimental calibration data should be fitted by least-squares regression for different circumstances. Moreover, it is important to address the question of analytical accuracy to complement the discussion of precision that we have been mainly concerned with thus far the meanings of accuracy and precision in the present context are discussed in Section 8.1. The present section represents an attempt to express in algebra the calibration functions that apply in different circumstances, while exposing the potential sources of systematic uncertainty in each case. 

These inadequacies could lead to an increase in systematic errors due to inadequate testing or errors in calibration and repair activities. 

Figure 31. Extinclion diagram in various combinations for detection of errors in calibration measurement a) Substance + scattering b) Substance+ nuoresecncc c) Pure substance d) Substance + impurity...

Finally, recall that while the above considerations are important, we are taking account only of random errors in calibration. These are not usually the major contributors to the combined uncertainty of a chemical measurement result. Errors caused by the chemical and physical pretreatment of the test material are likely to overwhelm calibration errors. Analysts should bear this in mind and avoid expending time on unrewarding changes to the calibration and measurement protocol. 

Bias error, , ias, corresponds to over or under estimation of the velocity vector. This may be due to error in calibration. The rms error, corresponds to the randomness of experimental parameter during measurements. One approach in the evaluation of rms error during PIV measurements is PIV recording of the static (quiescent) flow. This approach permits the study on experimental parameters such as particle image diameter and background noise. 

A 1.3.2 Reveal calculation and interpretation errors in calibration runs. 

Accept a data set (or conditionally accept, acknowledging that there may be significant error in calibration and prediction)... 

---