Three level factorial design optimization

T. J. Mitchell and C. K. Bayne, D-optimal fractions of three-level factorial designs. Technometrics, 20, 369-383 (1978). 

Let us now consider the situation in which we optimize the solvent composition of the mobile phase and let us first suppose there are three solvents A, B and C involved. The aim is to know how much of each of them should be pre.sent. The methods of Section 6.3 are now no longer applicable since they can be applied only when there is a single variable. At first sight we could conclude that there are three variables, the contents of respectively A, B and C and that we could therefore apply in a first step the two- or more-level factorial designs of Section 6.4. If we suppose that the experimental domain goes from 0% to 100% for each of these variables, this would yield for a two-level design Table 6.13. 

In the final phase of the optimization study for earplug production (Sato, 2002) a 3 factorial design was carried out to study the dependencies of the three responses, apparent density (AD), equilibrium force (EF) and retention time (RT), on the fiow rate of the reticulate solution (A) and the quantity of water in the polyol solution (B). Only these two factors were found to be important, after the execution of a 2 " fractional factorial and a blocked 2 factorial design (see case studies in Sections 3A.9 and 4A.8). The other factors were fixed at levels chosen to provide the most desirable apparent densities, EFs and RTs, as well as convenient operational conditions. Table 6A.7 contains the results of the three responses for the three-level factorial experiments, which were performed in duplicate. 

For the final optimization, a modified factorial design involving three concentration levels of triethylamine and three pH levels was used. From these results, it was clear that the optimum conditions for the analysis of the carboxylic acid were so different from those required for the other compounds studied that it was not sensible to attempt to analyse all fonr together and indeed that carboxylic acids were better analysed by using conventional reversed-phase HPLC than by using ion-pairing. 

ED (BGE optimization). Three-level fnll factorial design. Factors SDS concentration, pH, phosphate concentration. Response resolntion and migration time. 

Some investigaoHs (16) recently proposed an experimemal design for optimizing the solubility and the release of a new retinoid from a gel formulation. In this case a 2 X 3 factorial experiment was designed to investigate the effect of three formulation components. If one factor is to be tested at two levels and two others at three levels, we have a 2 X 3 in 18 units (17,18). The experiment... 

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