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Unformatted text preview: Taguchi Methods and ‘ Response Surface ' Alternatives Once in control,
goal is to produce
uniformly near a
target. I ° Mean on target ° Reduce variation Three possible
situations:
 Smaller is better 0 Larger is better ° On target is best On target is best.
Taguchi considered
deviation from target to be loss to
society. Taguohi
models this as: 120’) =K(Y—T)2
Y 2 Quality Control ' T 2 Target value On average, loss is
proportional to: ‘ E(Y — T)2
= Varﬂ’)
+ (Bier?)2
where
B iaS : difference of mean and Target 5 For smaller is better,
Taguehi has less as: L(Y) = Y2
_ i.e. on average
E(Y 2).
So Target is 0. For larger is better,
Taguchi considers
loss as: MY) =1/y2
0f E(1/y2). First step in Taguchi
' Method is parameter % I design. Parameters
are inputs known or
suspected to affect the
quality characteristic. Goal: Design in
quality, don’t sample
to catch poor output. 8 Parameters are divided
into two groups: ° Control variables
parameters which can be
controlled in the process. ° Noise variables—
parameters which vary and
are usually not controlled (sometimes hard or
expensive to control). Levels are chosen
for each of the
control variables. Levels are chosen 1 and temporarily
ﬁxed for each of the  noise variables. Control variables are placed into inner array.
Example: [\JNHMNNHh—d :Nl—tNr—tNr—twv—‘l Eight design points, each
row one design point 11 Noise variables are
' placed in outer array Example: '
2 l
2 2 Generally the levels span
What is experienced in
production conditions. 12 The structure of each
array is typically ° Factorial design ° Fractional factorial design
(sometimes referred to as
 “orthogonal array”.) The arrays are then
crossed and observa—
tions collected. 13 Goal of analysis:
Minimize
_ E(Y — N by choice of best control
variable settings. Taguohi suggests look at
“signal to noise” ratio. % Bigger is better. Then
adjust mean. 14 Criticisms: ° Crossing inner and
outer arrays can lead to
unwieldy designs. ° Use of signal to noise
ratios very adhoc and
hard to generalize
(various versions). '15 Alternatives proposed
include ReSponse
Surface Methodology
' (RSM). * Goals:  Model the response Y as a
function of control and noise
variables.  Use information on distribution
of noise variables to model
mean and variance. l6 Simple example: I Y = Lamina thickness
X I : Viscosity (control variable) _ X 2 :— Ambient humidity (noise variable) . Fitted model:
Y = 60+B‘1X1+B\12X1X2 Select X to minimize loss. 17' E(f)=6O+BIXI ‘
+6 X E(X2) 12 1 Var()7) 2(612X1r Var(X2) 2 +6 (Conditional mean and
variance, conditional 0n
~ parameter estimates). 18 More complex example: XPX2 —C0ntr01 X3 —N0ise 17:50 +61X1+BA2X2 + B23X2 'X3 E®Zﬁo+61X1+62X2+323X2+623X2 '(EX3)
Vam=(ﬁ23X2)Vaz(X3)+o Can set X2 set X1 to control mean. to minimizevariance 19' ...
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 Spring '11
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