Qualitative response, method optimization

In reference 88, response surfaces from optimization were used to obtain an initial idea about the method robustness and about the interval of the factors to be examined in a later robustness test. In the latter, regression analysis was applied and a full quadratic model was fitted to the data for each response. The method was considered robust concerning its quantitative aspect, since no statistically significant coefficients occurred. However, for qualitative responses, e.g., resolution, significant factors were found and the results were further used to calculate system suitability values. In reference 89, first a second-order polynomial model was fitted to the data and validated. Then response surfaces were drawn for... 

During method optimization, initially qualitative responses, related to the quality of the separation, are considered. On the other hand, during robustness testing, first quantitative responses are studied. Nevertheless, all types of responses can be evaluated during both method optimization and robustness testing. 

In this section, we look at methods of obtaining a mathematical model that can be used for qualitative predictions of a response over the whole of the experimental domain. If the model depends on two factors, the response may be considered a topographical surface, drawn as contours or in 3D (Fig. 4). For more factors, we can visualize the surface by taking slices at constant values of all but two factors. These methods allow both process and formulation optimization. 

A second approach uses the unimodal model-independent method, which begins with the assumption that the size distribution consists of a finite number of fixed size classes. The detector response expected for this distribution is simulated, and then the weight fractions in each size class are optimized through a minimization of the sum of squared deviations from the measured and simulated detector responses. The third system uses the multimodal model-independent method. For this, diffraction patterns for known size distributions are simulated, random noise is superimposed on the patterns, and then the expected element responses for the detector configuration are calculated. The patterns are inverted by the same minimization algorithm, and these inverted patterns are compared with known distributions to check for qualitative correctness. 

The responses considered from the circumscribed CCD (Table 2.14) applied during the optimization phase of the development of a chiral enantiosepara-tion method in Reference 28 were also all qualitative, that is, migration time of the first and the second enantiomer (tmi and t i), and resolution between the two enantiomers Rs (Table 2.18). 

---