70 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS ing on the evolution of the parameter domains. Moreover, a specific program was written in order to evaluate the real number of possible combinations with the constraint conditions already mentioned. These last values show that, even with bigger steps for the first three parameters (x•, x 2, x3), the initial number of trials to be taken into account for a hypothetical systematic screening is very high (233,016). This number clearly shows that an experimental design approach (1,6) would be inappropriate for this study. The six first columns of Table I summarize the number of allowed values, with the corresponding step in parentheses for each parameter for each series. ESTIMATING CRITERION To be launched on the market, a formulation has to be stable for at least a three-year period. Therefore, accelerated aging tests enable us to predict this duration. A prelim- inary study established that a ten-day period led to a significant response. Thus the total evaluation of one series needed at least ten days. Therefore, the serial procedure of the ANTICOMPLEX was a major advantage. In spite of its typical binary response (yes or no), this property was quantified to segregate the different formulations. Finally, the stability at the high level of 50øC was considered more significant than that at room temperature (maximum values 65 and 35, respectively). The scale of stability is defined in Table II, and the real contribution of this property to the global estimating criterion is the sum of the two values (at room temperature and 50øC). Table II also describes the scales of transparency and oily phase concentration used in this study. Thus this second property resulted from the product of these two values. Finally, the measurement of fluidity was directly converted in an integer value for the global estimating criterion as described in Table II. The four measurements y• to Y4 were converted to absolute values for the global estimating criterion according to their own conversion scale. EFFICIENCY OF THE ANTICOMPLEX With the above-mentioned step values and calculations of the estimating criterion, Table I Permitted Values and Steps Parameters Number of trials Series x 1 x2 x3 x4 x5 x 6 Theoretical Real 1 10 (5.0) 7 (5.0) 11 (5.0) 91 (0.5) 39 (0.5) 41 (0.5) 112,001,930 233,016 2 6 (5.0) 5 (5.0) 6 (5.0) 67 (0.5) 28 (0.5) 14 (0.5) 4,727,520 44,139 3 7 (5.0) 3 (5.0) 5 (5.0) 58 (0.5) 27 (0.5) 13 (0.5) 2,137,590 24,565 4 6 (5.0) 2 (5.0) 7 (5.0) 11 (0.5) 21 (0.5) 11 (0.5) 213,444 2,475 5 11 (2.5) 3 (2.5) 14 (2.5) 2 (0.5) 16 (0.5) 6 (0.5) 88,704 1,354 6 48 (0.5) 1 (0.5) 68 (0.5) 1 (0.5) 15 (0.5) 1 (0.5) 48,960 714 7 33 (0.5) 1 (0.5) 44 (0.5) 1 (0.5) 11 (0.5) 1 (0.5) 15,972 362 8 15 (0.5) 1 (0.5) 11 (0.5) 1 (0.5) 9 (0.5) 1 (0.5) 1,485 92 The first values indicate the permitted number of solutions for each parameter. The step values are mentioned in parentheses. The eighth series was simply calculated. The last two columns show the theoretical and real number of trials (depending on the explicit constraints).

FORMULA OPTIMIZATION 71 Table II Scales of Properties Properties Quotations Stability Transparency Y3 = L * Oily phase Fluidity y• = Room temperature [0-1 day] 0 [1-5 days] 3 [5-10 days] 7 • 10 days 35 Measure of L (%)a [0-70] 1 [70-80] 2 [80-85] 5 [85-90] 8 [90-100] 10 Y4 = Measure of fluidity (cps) b [0-25] [25-50] [50-75] •75 Y2 = 50ø C [0-1 day] 0 [1-5 days] 6 [5-10 days] 13 • 10 days 65 Oily phase (%) [5-10] [10-20] [20-3O] [30-4O] [40-5O] 100 105--fluidity value 95--fluidity value 0 1 2 5 8 10 This table explains the transcription between the experimental measurements the algorithm. • Minolta CT 210•Lab scale. b Brookfield Viscometer LVT--Speed 60 rpm--Spindle n ø 1. and the quotations used by seven series of 20 trials were performed. The number of trials (140) must be compared to the initial number of possible combinations (233,016). The ratio between these two numbers clearly demonstrates the efficiency of this methodology and the rapidity toward the estimated optimum region for this formulation study. The last two columns of Table I correspond to the maximum and the restricted number of trials according to the fluctuation of the parameter domains. These values show perfectly the drastic and progressive reduction of combinations at every series of 20 trials. More explicitly, Figure 1 illustrates the massive decrease of the restricted number of trials to be explored at each step according to the constraints. GRAPHICAL INTERPRETATION In spite of the number of parameters and the "block box" strategy, which prevents any mathematical modeling, we can expect a graphical analysis of the process as well, which we obtained by methods based on a mathematical modeling as surface response tech- niques (7). Figure 2 is a typical illustration of the fluctuations of parameter limits. As can be seen, the general tendency is a significant reduction at each series, with rare and isolated enlargements of these limits. This figure also depicts the evolution of the barycenter values. As indicated previously, the barycenter corresponds to the predicted optimum at each step of the iterative procedure. This evolution is consistent with the limit fluctu- ations and is rather progressive without drastic changes between series. It is remarkable that after the fourth series, before the modification of the step values for