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

  • Rheem, Sungsue (Graduate School of Public Administration, Korea University) ;
  • Rheem, Insoo (Department of Laboratory Medicine, Dankook University Hospital) ;
  • Oh, Sejong (Division of Animal Science, Chonnam National University)
  • Received : 2019.02.11
  • Accepted : 2019.02.22
  • Published : 2019.04.30


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.


response surface methodology;central composite design;heterogeneous third-order model;multi-response optimization;desirability


Supported by : National Research Foundation of Korea (NRF)


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