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.