Achievement by desirability

The Desirability Index D can be formulated as a function of factors $X_{1}, \ldots, X_{F}$ and errors $\epsilon_i,\; i = 1, \ldots, Z$ .

$\begin{eqnarray*}D(P)& := & D( d_i(Y_i)_{i= 1,\ldots,Z})\\ & = & D(d_i(f_i(X_{... ...i2}, \ldots, X_{iF},\epsilon_i))_{i= 1,\ldots,Z})\\ & = & D(X) \end{eqnarray*}$

Perform optimisation by estimating models $\hat{f_i}$ and calculating
$\hat{D(P)} := D(d_i(\hat{f}_i(X_{i1},X_{i2}, \ldots, X_{iF}))_{i= 1,\ldots,Z})$ .
The ranking in $\mbox{$I \! \! R$ }$ induces a ranking in $\mbox{$I \! \! R$ }^Z$ and ${\bf X}_{opt}$ is easily identified.

Multi-Objective-Optimisation problem has been turned into a response surface problem.

Dipl.-Stat. Detlef Steuer
1999-10-04