Improving the Quality of Response Surface Analysis of an Experiment for Coffee-supplemented Milk Beverage: II. Heterogeneous Third-order Models and Multi-response Optimization

This research was motivated by our encounter with the situation where an optimization was done based on statistically non-significant models having poor fits. Such a situation took place in a research to optimize manufacturing conditions for improving storage stability of coffee-supplemented milk beverage by using response surface methodology, where two responses are Y(1)=particle size and Y(2)=zeta-potential, two factors are F(1)=speed of primary homogenization (rpm) and F(2)=concentration of emulsifier (%), and the optimization objective is to simultaneously minimize Y(1) and maximize Y(2). For response surface analysis, practically, the second-order polynomial model is almost solely used. But, there exists the cases in which the second-order model fails to provide a good fit, to which remedies are seldom known to researchers. Thus, as an alternative to a failed second-order model, we present the heterogeneous third-order model, which can be used when the experimental plan is a two-factor central composite design having -1, 0, and 1 as the coded levels of factors. And, for multi-response optimization, we suggest a modified desirability function technique. Using these two methods, we have obtained statistical models with improved fits and multi-response optimization results with the predictions better than those in the previous research. Our predicted optimum combination of conditions is (F(1), F(2))=(5,000, 0.295), which is different from the previous combination. This research is expected to help improve the quality of response surface analysis in experimental sciences including food science of animal resources.