COMPUTER-ASSISTED PRODUCT DEVELOPMENT 789 Both the old formula and the revised formula are then subjected to various types of tests and evaluations to determine whether a change in the product is warranted. In making such a change, it is important to know exactly how the final composition of the product is affected, since the change in the per- formance of the product may be reflected in a change in the percentage of a particular ingredient. Knowing the performance at several concentrations of the particular ingredient, the formulator can extrapolate the concentration yielding optimum performance. It is desirable to know the amount of each ingredient for the purpose of costing, and it is sometimes required that the ex- act composition of each product be available for legal and medical purposes. Determining the composition of a product that is prepared by mixing sev- eral raw materials is simple. For example, the composition of a lacquer thinner that is the combination of three organic solvents is simply given by the weight percentage formula. But in a case where any of the main components added to the product at the final batch stage is a previously processed component, its formula must be substituted in the final formula where the composition is calculated. The process of determining the final composition becomes very complex when many preprocessed components containing common ingre- dients are involved, for the contributions of each ingredient from each compo- nent must be considered. Often, preprocessed components consist of prepro- cessed subcomponents, making the calculation of the final composition of the product all the more cliffcult and time consuming. A program has been written that determines the composition of a lacquer containing several main components which break down into components, sub- components, and finally ingredients. The computer program is not needed if one is dealing with pure ingredients which cannot be broken down. Our pro- gram utilizes a system of matrices that describes each breakdown step and allows quick changes to be made in the composition of any item that might occur in the product as new formulas are suggested. The chemist selects the formula of the product, and in a matter of minutes the final composition is printed out. At the request of the user, various analyses about the formula are determined and printed. Thus, before a single resin or solvent is mixed, the chemist has a good idea what the product will be like. In addition, these pro- grams are adaptable to any kind of formulary work. A matrix is required for each breakdown step of the formula (•4). The matrix may be thought of as a table of the breakdown-along the left-hand column are the components and along the top row are the subcomponents contained in the components. The elements of the matrix are the coefficients or percentages of the subcomponents found in the components. The system requires first that the various breakdown steps be recognized, and that the components, subcomponents, and ingredients be recognized and assigned identification letter. For example, let us consider the breakdown of a lacq•er designated X. X is made from four main components: A• is a flow additive

790 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Aa, thinner Aa, paint base and A4, a color concentrate mix. A• is a pure in- gredient, purchased from the manufacturer as such and cannot be further broken down (except to chemical elements). A•, As, and A4, however, can be broken down further. The thinner is made from three solvents the base from four solvents, two vehicles, and two plasticizers. The color mix is pre- pared from three color pastes the pastes are each a combination of a dry pigment, a solvent, and a paint base As. As shown in Fig. 6, the lacquer X is broken down into four main components A's, six components B's, seven subcomponents C's, and finally 12 ingredient D's. Product (X) Moin Components (A's) Components (B's) Subcomponents (C's) Ingredients (D's) Flow odditive, A t --Flow odditive, B t • Flow odditive, C t • Flow odditive, D t •........•4DDD?.DSDI,I,II,III,II,SolventVehicle•Solvent./-•-//•..,/•Vehicle Thinner, A?. Thinner, B?. Thinner, C?. -•....._..•- 5 Point, X 6 Point Bose, AS •Point Bose, B$ Point Bose, / ••_•.Plasticizer I, D? • '• Pløsticizer II' De ß Solvent IV, C4 Solvent IV, D 9 B4•Pigment I, C 5. PigmentDiOI•II,Pigmenl • •Color Poste I, BS"•/"/-•Pigment II, C 6 Color Mix, A 4 •Color Poste II, •"Color Poste III, B6r Pigmen t III, C? Pigment III, Dig Figure 6. Breakdown of nafi lacquer for formulation program Notice that some of the main components are retained as components and subcomponents any item must be re-entered at each level until it is actually broken down. A•, the flow additive, cannot be broken down at all, hence it occurs as itself at each level. The paint base could have been broken down at matrix P however, since it is a subcomponent contained in each of the components, B4, Bs, and B6, it is not broken down until after those com- ponents are. The thinner is not contained in any item A, B, or C it is only contained in the lacquer X. Yet, it is not broken down untfi matrix S, simply to keep the number of components and subcomponents to a minimum. The matrix P describes the breakdown of the paint X, and has dimensions i x 4. P = (P•,• P•,2 P•,a P1,4) which may be interpreted as indicating: X = r•,, (A•) + r•,• (•) + r•,• (•) + r•,• (•)