Desirability Function I

Concept and name introduced by Edwin C. Harrington Jr. in 1965 (Industrial Quality Control, Vol 21, No 10, p.494-498).
Harrington's desirability function:

$d^{H}(Y) := e^{-\vert Y'\vert^n}, \; \text{where} \, Y' \, \text{is an appropriate transformation of} \; Y.$

Appropriate in the sense of Harrington is to choose Y' in a way, so that d^H(LSL) = d^H(USL) = 1/e.
As a possible transformation he gives $Y' = \frac{\textstyle 2 Y - (USL + LSL)}{\textstyle USL - LSL}.$

Symmetric around the centre between LSL and USL. n serves as "deviation importance" parameter. The geometric mean is used as index.

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

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