Robustness assessment in computer-assisted liquid chromatography procedures based on desirability functions

A novel approach based on the use of desirability functions is presented for the robustness assessment of liquid chromatographic separations as derived from computer-assisted methods development processes. The approach is based on generally accepted hypothesis that a robust separation procedure will be inert to small random variations of the operational variables, typically encountered in the day-to-day routine analytical practice. This means that peak positions along the chromatograms must keep standstill or move insignificantly when operational variables are not intentionally changed. Thus, the degree of peak positions variation as evaluated from mathematical retention models can be used to assess the robustness of the developed procedures before testing the actual performance experimentally. In the approach proposed, this assessment is obtained by fixing a bilateral partial desirability window around each peak in the simulated chromatogram. The whole chromatogram robustness is characterized by an overall desirability value calculated as the geometric mean of the partial desirability windows evaluation. An added advantage of this approach is that the robustness value calculated is normalized between zero and one and thus, easy to interpret. Thus, when chromatograms are simulated and small random variations are introduced into the operational factors of the model, values for the overall desirability close to one means that the procedure performs robustly. On the contrary, low values for the overall desirability clearly indicated a serious lack of robustness. When used in conjunction with the Pareto optimality approach, as shown here, this robustness assessment strategy allows testing several Pareto front solutions before the final experimental testing which is always needed. In this way, a dramatical reduction of the experimental effort is obtained. Although the approach is theoretically applicable to any chromatographic separation, examples of reversed phase liquid chromatographic procedures are used to show the performance of the proposed methodology.