Desirability Function II

Derringer and Suich 1980: Gaining flexibility (Journal of Quality Technology, Vol 12, No 4, p. 214-219)

$d^{DS}(Y):= \left\{ \begin{array}{rl} 0,& \mbox{for} \quad Y < LSL\\ (\frac{\... ...or} \quad T < Y \leq USL\\ 0,& \mbox{for} \quad USL < Y\\ \end{array}\right.$

The parameters $\beta_l$ and $\beta_r$ are weights for deviations to the left respectively to the right from the target.

Target value: $(LSL, T, USL, \beta_{l}, \beta{r})$
Minimisation: $(-\infty, T, USL, 0, \beta{r})$
Maximisation: $(LSL, T, \infty, \beta_l, 0)$

Advantages:

Consistent handling of all types of optimisation
Can model asymmetric importance of deviations from target
Can easily be extended to more than two segments
Easily communicated to the expert

Practical acceptance: used in STAVEX at Ciba-Geigy (Basel)
Recent project (Master Thesis): implemented as scheme for supplier evaluation in a big steel producing company

Disadvantage: piecewise definition

Interpretation: doubled value of $\beta$ gives doubled importance to deviations

$\scalebox{0.8}[0.75]{\rotatebox{-90}{\includegraphics{ds1.eps}}}$

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