Importance

In the desirability objective function D(X), each response can be assigned an importance relative to the other responses. Importance (r_i) varies from the least important ( + ) a value of 1, to the most important ( +++++ ) a value of 5. If varying degrees of importance are assigned to the different responses, the objective function is:

$D = (d_1^{r_1} \cdot d_1^{r_2}\cdot...\cdot d_1^{r_n})^{\frac{1}{\sum r_i}} = \left(\displaystyle\prod_{i=1}^{n}d_i^{r_1} \right)^{\frac{1}{\sum r_i}}$

where n is the number of responses in the measure. If all the importance values are the same, the simultaneous objective function reduces to the normal form for desirability.