292 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS different, differing in many cases by only a small quantity of an ingredient, or a very small change in a process variable. Translating such a design into physical units, or, in fact, selecting the variables to study and measure, requires some expertise and there is no substitute for experience. Experienced formulators have been selecting factors for study as a routine matter, and it should be pointed out that, anything which can be quantitated and controlled may be selected. PHYSICAL SYSTEMS The majority of the products to which these techniques have been applied are in the pharmaceutical category rather than cosmetic science, and to solid dosage forms, in particular. But the techniques are applicable to any multivariate system, and one example involving a suspension may be of interest (7). The independent variables selected are shown in Table III. Four of these are formulation variables and one is a process variable. Table III Independent Variables (Suspension) x•--Veegum K Level (colloidal aluminum magnesium silicate) x2--Keltrol Level (xanthan gum) x3--Water Level (above a minimum 20% level) x4--Citric Acid Level xs--Time of Mixing (to wet active component) The most difficult thing about most products, pharmaceutical or cosmetic, is to select and determine those dependent variables (properties) upon which to base one's decision. In general, categories for the dependent variables can include any physical, chemical or biological property of the system, but the exact choice is more difficult. Any property which can be quantitated may be included as a dependent variable. Several of those selected for the suspension under study are listed in Table IV and several other possibilities are shown in Table V. Table IV Dependent Variables (Suspension) y•--Sedimentation Volume at Time, t y2--Viscosity y3--pH y4--Resuspendability ys--Specific Gravity y6--Zeta Potential y7--Flocculation/Monodispersion (agglomerates/particles) Once the variables are selected, the experimental design must be translated into physical units as shown in Table VI. As mentioned previously, there is no substitute for experience in this task. (It should also be noted that the value of alpha changes with the number of independent variables and that in this system with five independent variables, alpha equals 1.547). At this point, the experimental trials can be performed and the dependent variables (properties) can be measured.

OPTIMIZATION TECHNIQUES 293 Table V Other Possible Dependent Variables Chemical Stability Sedimentation Rate, dv/dt Viscosity: One Point (Slope) -• Shear Rate vs. Shear Stress Yield Value Area of Hysteresis Loop Coacervation Dissolution Cost Penetrometer Reading (Creams, Ointments) Grittiness Synuresis Table VI Oral Suspension Experimental Design--Translation to Physical Units Formulation Factors 0 - 1.547 -- 1.0 EU + 1.0 + 1.547 EU EU (Base) EU EU x• = Veegum K (1 EU = 2.586 mg) 0 1.414 4.O 6.586 8.O x2 = Keltrol (1 EU = 0.323 mg) 0 0.177 0.5 0.823 1.0 x• = Water • (! EU = 0.09 g/Liter) 0 0.049 0.139 0.229 0.238 x4 = Citric Acid (1 EU = 0.646 mg) 0 0.354 1.0 1.646 2.0 x 5 = Mixing/Wetting Time (! EU = 60 Min.) 27.18 60.0 120.0 180.0 212.82 •Greater than 20%. Any change in water content from the base will be corrected with an adjustment in the sorbitol solution content. The next step requires analysis of the data to generate predictor equations. The technique applied is regression analysis and the predictions will only be as good as the fit of the data to the equations generated i.e. the index of determination (R-square value) should be greater than 90%. The type of equation used with the design shown previously is a second order polynomial of the form, Y = a o + a•xp.. + as x 5 -•- a•X•2... q-a55X52 -• a12XlX2... -• a45X4X5, where: ¾ = level of given response, ai = coefficients for second degree polynomial, x i = level of the independent variable.