are given in Table 3. It is worth of note that the calculated
responses, y1 and y2 are expressed in terms of the percentages of
the pseudocomponents Xi.
For the comparison of the two response surfaces reported in
Table 3, the corresponding contour plots are shown in Fig. 2.
In order to attain a robust optimization for the drug release, it
was required to be very close to a desired value – the target value
– in this case 35% for the release after 1 h and 75% for the release
after 8 h (Fig. 3). A desirability function approach was therefore
used. For this desirability study, the objectives were expressed by
the following limits for the two responses here considered:
30% 6 Y1 6 40%
70% 6 Y2 6 80%
ð14Þ
The best solution identified for the formulation is given in
Table 4 along with desirability functions for the optimization, di
(Ycal,i) the partial desirability and the D the overall desirability.
The optimal experimental conditions are expressed both in terms
of pseudocomponents Xi and as original components. In Fig. 4
(top) the variation of the global desirability as function of the
two response variables under study is graphically represented by
contour plots.
For a robust optimization the desirability function was further
assessed and optimized in terms of reliability. The purpose was
to identify the zone where the estimation of all responses can be
calculated with a probability 6 a% of not respecting the fixed constraints
for every response. For the two responses under study it
was imposed that:
Prob½30% < Y1 < 40% P 0:80
Prob½70% < Y2 < 80% P 0:80:
ð15Þ
Thanks to the respect of the constraints with a probabilityP(
1 a), the optimal zone was reduced and two more limited
areas were identified (Fig. 4, bottom). Here, the global desirability
is lower given the experimental error. These two areas were further
analyzed in order to define the composition space that ensures
confidence in the attainment of the requir