Análise da crista em experimentos de misturas com restrição na variância de predição

Abstract

Two articles are present in the composition of this work. In the first article the study presents the application of ridge analysis adapted to mixture planning considering the Scheffé (S-model) and Kronecker (K-model) quadratic models. The proposed methodology was performed with data from an experiment involving mixtures with three components, which objective was to maximize the predicted response. The results obtained using the Kronecker model were satisfactory in comparison to the solution provided by the Scheffé model, most known in literature. The second article presents a ridge analysis methodology for mixture experiments considering the modification suggested by Khuri and Myers in conjunction with the proposals from Draper and Pukelsheim, aiming at reaching the maximum or minimum value of the predicted response by means of the ridge trajectory under a prediction variance conditioned to a restriction. We used the data of mixtures of which components are not restricted and component mixtures with inferior and/or superior limit, aiming at maximizing the predicted response with the prediction variance under restriction. The suggested procedure was evaluated by a comparison between the results obtained from Draper and Pukelsheim’s proposals available in literature. We verified that the proposed methodology obtained success when allowing us to reach the predicted response with a value superior to the maximum considered by the already existing methods, accompanied by a smaller prediction variance. Predicted responses with values slightly lower than the maximum were also provided, however with a prediction variance smaller in size.