Page 384 - Six Sigma Demystified

364 Six SigMa DemystifieD

goal using a desirability function d. A composite response D is generated as the
simple geometric mean of each response desirability function as follows:

D = (d × d × d × ↑ × d ) 1/m
3
m
2
1
The composite desirability function D is maximized in each case so that
values of desirability near 1 (the maximum) indicate that all responses are in
the desirable range simultaneously.

Minimizing the Response

The desirability function, when the goal is to minimize the response (i.e.,
smaller is better), requires a specified target value, which is the desired mini-
mum (where smaller values provide little improvement) and an upper bound
(a point of undesirable response).

 response − upper bound  s
d =  
 target − upper bound 

Maximizing the Response
The desirability function, when the goal is to maximize the response (i.e., larger is
better), requires a specified target value (the desired maximum, where larger values
provide little improvement) and a lower bound (a point of undesirable response).

 response − lower bound  s
d =   target − lower bound  

Target the Response
The desirability function, when the goal is to achieve a target value, requires a
specified target value and specified lower and upper bounds. When the re-
sponse is between the lower bound and the target, the desirability function is
as calculated for the maximize-the-response case. When the response is be-
tween the upper bound and the target, the desirability function is as calculated
for the minimize-the-response case.

Calculating the Weights
The weights s and t are determined as follows:

<1 (min = 0.1): Less emphasis on target; response far from target is very
desirable.