An experiment with three factors and two responses

In RSM there is no restriction on the number of factors and responses studied. RSM can be applied to any number of factors, as well as model several responses at the same time. This is an important characteristic, because many times the product or process of interest must satisfy more than one criterion, such as, for example, present maximum yield with a minimum quantity of impurities, or have minimum production costs while keeping the quahty parameters within their specifications. To illustrate the flexibility of RSM, we present a real application in this section, whose objective was the simultaneous maximization of two distinct responses. 

at the Chemistry Institute of Campinas State University, performed a series of experiments on the S5mthesis of polypjrrrole in an EPDM rubber matrix, under the supervision of Professors M.A. de PaoH and M.I. Felisberti. The objective of the study was to obtain a product with electrical properties similar to those of polypyrrole and mechanical properties like those of EPDM rubber. Pol rpyrrole, a conducting polymer, is very brittle, which prevents its use in apphcations of practical interest. 

Valhm and V.F. Juhano analyzed the data of Table 6.9 as an assignment in a chemometrics course, and soon perceived that, since there are 27 different runs, it is possible to fit a fimction with up to 27 parameters to the data. The linear and quadratic functions for three variables are defined by only 4 and 10 parameters, respectively. Using them to model the data in the table, we will have many degrees of freedom left over to assess lack of fit. 

3 Factorial design to investigate the effects of reaction time (t), oxidant concentration (C) and particle size (P) on the yield (Y) and Young s modulus (M) of the product of polypyrrole synthesis in a matrix of EPDM rubber 

Analyses of variance for the fits of the linear and quadratic models to the Young s modulus data of Table 6.9. The values for the quadratic model are given in parentheses 

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