Page 541 - Design for Six Sigma a Roadmap for Product Development

500 Chapter Fourteen

Controllable Factors

x …… x
x 1 2 n
• • •

Input (M) Output (y)
Product/Process
Response

• • •
z …… z
z 1 2 p
Uncontrollable Factors
Figure 14.1 A design P-diagram.

y f(x 1 ,…, x n ) (14.2)

Mathematically, z (z 1 ,…,z p ) is a random vector with unknown distri-
bution. The design parameter x (x 1 ,…,x n ) is also a random vector,
because in mass production, where we cannot guarantee production of
a massive number of identical products, there will be piece-to-piece
2 …
(piecewise) variation. We can assume x i N( x i , x i ) for i 1 n. We
i , which is the nominal value of the design
further assume that x i
parameter x i . The nominal value of the design parameter can be cho-
, which is the standard
sen by the designer, and we can define i x i
deviation of the design parameter, which can also be controlled (at a
cost) at tolerance design stage.
Because both x and z are random variables, the requirement Y will
of course be a random variable. In Taguchi’s parameter design, it is
assumed that there is a target value for Y specifically, T. For example,
the main basic function of a power supply circuit is to provide electri-
cal power to small appliances, and a key output performance is its out-
put voltage. If the needed voltage for a smaller appliance is 6 V, then
the target value T 6.

14.2 Loss Function and Parameter Design
14.2.1 Quality loss function
In the Taguchi method, quality loss function is a basic starting point:

L kE(Y T) 2 (14.3)