Robustness testing optimization

FIGURE 4 Factor level intervals examined during (a) method optimization and (b) robustness testing. 

Secondly, with the OVAT approach the importance of interactions is not taken into account. An interaction between two factors is present when the effect of one factor depends on the level of another factor. Since only one factor at a time is varied, the presence or absence of interactions cannot be verified. However, this is not dramatic, since in robustness testing the interaction effects are considered negligible. The evaluation of such interactions is more important in 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... 

In reference 20, a typical robustness test is not performed, but a study on the influence of peak measurement parameters is reported on the outcome. The study is special in the sense that no physicochemical parameter in the experimental runs is changed, but only data measurement and treatment-related parameters. These parameters can largely affect the reported results, as shown earlier, and in that sense they do influence the robusmess of the method. The different parameters (see above) were first screened in a two-level D-optimal design (9 factors in 10 experiments). The most important were then examined in a face-centered CCD, and conclusions were drawn from the response surfaces plots. 

MDOE embraces a number of tools which permit experiments to be conducted in the most efficient possible way, achieving several interesting results such as screening of the important factors, optimization of manufacturing and analytical procedures, minimization of costs and pollution, and robustness testing of products and processes. 

Most of these steps are similar to the screening at the beginning of method optimization (see Section 6.4.2). In the following we will highlight the main differences between both. The variables tested in a robustness test could be the same as those screened. However, occasionally additional factors of which it is thought that they could affect the content determination of a method but not the. separation are also examined. Examples are variables related to the sample pre-treatment or the detection. 

The levels selected in a robustness test are different from those at which factors are evaluated in method optimization. For optimization purposes the variables are examined in a broad interval. In robustness testing the levels are much less distant. They represent the (somewhat exaggerated) variations in the values of the variables that could occur when a method is transferred. For instance, in optimization the levels for pH would be several units apart, while in robustness testing the difference could be 0.2 pH units. The levels can for instance be defined based on the uncertainty with which a factor level can be set and re.set 36 and usually they are situated around the method (nominal) conditions if the method specifies pH 4.0, the levels would be 3.9 and 4.1. The experimental designs used are in both situations the same and comprise fractional factorial and Plackett-Burman designs. 

The responses of main interest are different during both applications. In optimization, responses related to the separation of peaks (Section 6.2) are modelled. In robustness testing the quantitative aspect (the content determination) of the method is of most interest, since it is the one that should remain unaffected by small variations in the variables. Responses related to the separation (resolution, relative retention) or describing the general quality of the chromatogram (capacity factors, analysis times, asymmetry factors, and column efficacy) are often also studied. As recommended by the ICH guidelines the results of a robustness test can be used to define system suitability test limits for some of the responses [82]. 

EXPERIMENTAL DESIGN IN METHOD OPTIMIZATION AND ROBUSTNESS TESTING... 

To determine the robustness of a method, several approaches exist. Basically, the situation for robustness testing is similar to that for screening during optimization, except for the range within which the factors are examined. The influence of small but deliberate changes in parameters on the response (s) is evaluated using either an OVAT or an experimental design approach (12). 

In this chapter, the use of multivariate approaches during method optimization and robustness testing is elaborated, discussed, and illustrated with examples. 

The responses of main interest also are different in method development and robustness testing. In development, the considered responses are related to the quality of the separation (l),such as, for electrophoretic methods, migration times, peak shapes, and the resolutions between neighboring peaks. When the separation is optimized and the method is validated, thus also in robustness testing, the responses of main interest are related to the quantitative aspects of the method, such as contents, concentrations, or recoveries. The responses considered during development occasionally are considered in a second instance, for example, as system suitability test (SST) parameters. 

Table 2.1 presents an overview of factors that can potentially be considered for optimization and robustness testing of CE methods. Lists of commonly used electrolytes/buffers (20-23) or additives (20) and characteristic properties of frequently applied solvents and surfactants (20) can be found in the literature. Sample concentration (see Table 2.1) is a factor occasionally included. However, the aim of the analytical method is to estimate this concentration through the measured signal, from a calibration procedure. In method optimization, responses related to the quality of the separation, for example, resolutions, are considered, and in this situation one can verify whether the sample... 

In the screening phase of method development and in robustness tests, the factors usually are examined at two levels (-1, +1). On the other hand, in the response surface designs, applied in method optimization, the factors are examined at three or more levels, depending on the applied design (see further). 

In method optimization, the range between the levels is much larger than in robustness tests. Often, the range selected for a factor in optimization represents the broadest interval in which the factor can be varied with the technique considered. In practice, the examined range is chosen based on earlier gathered knowledge and/or information from the literature. 

The factors and their levels examined during a screening phase in method development (27), an optimization phase in method development (28), and a robustness test (29) are presented in Tables 2.2,2.3, and 2.4, respectively. 

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. 

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