Robust Design

New Product Development

1. MITSloan
Robust Design: Experiments for Better Products
Taguchi Techniques

2. MITSloan
Robust Design and Quality in the Product Development Process
Planning
Planning
Concept
De
ve
l
opme
n
t
Concept
De
ve
l
opme
n
t
Sy
stem-Level
Design
Sy
stem-Level
Design
Detail
DesignDetail
Design
Testing and Re
f
i
ne
m
e
nt
Testing and Re
f
i
ne
m
e
nt
Production
Ramp-Up
Production
Ramp-Up
Robus
t
Parameter &
Tolerance
Design
Quality efforts are
typically made here,
when it is too late.
Robus
t Conc
ept
and System
Design

3. MITSloan
Goalpost vs
Taguchi View
COST $
COST $
Nominal
Value
Nominal
Value

4. MITSloan
General Loss Function
Nominal Value
Variance
Cost Factor
Manufacturing (daily)
Product & Process Engineer (a priori)
Average Value
(
)
[
]
2
2
m
k
−
+
⋅
µ
σ

5. MITSloan
Who is the better target shooter?
Pat
D
rew
Adapted fro
m
: C
laus
ing, Don,
and
Gen
ich
i
T
aquch
i. “R
obust
Qua
lity.”

Bos
t
on, MA:
Har
v
ar
d B
u
si
n
e
s
s
R
e
vi
ew
, 1990. Rep
r
int No
.
9011
4.

6. MITSloan
Exploiting Non-Linearities
Y
A
Y
B
X
A
X
B
S
o
urce: Ross, P
h
illip J. “
T
aguchi Te
chniques f
o
r

Quality Engineer
ing (2
nd
Ed
it
ion
)
.
”

N
e
w
Yo
rk
,
NY: McG
r
a
w
Hil
l, 1996.

7. MITSloan
Goals for Designed Experiments „
Understanding relationships between design parameters and product performance
„
Understanding effects of noise factors
„
Reducing product or process variations

8. MITSloan
Robust Designs
A
Robust Product or Process
performs correctly,
even in the presence of noise factors.
„
Outer Noise
Environmental changes, Operating conditions, People
„
Inner Noise
„
Function & Time related (Wear, Deterioration)
„
Product Noise
„
Part-to-Part Variations

9. MITSloan
Parameter Design
Procedure

10. MITSloan
Step 1: P-Diagram
Step 1: Select appropriate controls,
response, and noise factors to explore experimentally.
„
controllable input
parameters
„
measurable performance
response
„
uncontrollable noise
factors

11. MITSloan
The “P” Diagram
Uncontrollable Noise Factors
Product or
Process
Product or
Process
Measurable
Performance
Response
Controllable Input
Parameters

12. MITSloan
Example: Brownie Mix
„
Controllable Input Parameters
„
Recipe Ingredients (quantity of eggs, flour, chocolate)
„
Recipe Direct
ions (mixing, baking, cooling)
„
Equipment (bowls, pans, oven)
„
Uncontrollable Noise Factors
„
Quality of Ingredients (size of eggs, type of oil)
„
Following Directions (stirring time, measuring)
„
Equipment Variations (
p
an shape, oven temp)
„
Measurable Performance Response
„
Taste Testing by Customers
„
Sweetness, Moisture, Density

13. MITSloan
Step 2: Objective Function Step 2: Define an objective function (of
the response) to optimize.
„
maximize
desired performance
„
minimize
variations
„
quadratic
loss
„
signal-to-noise
ratio

14. MITSloan
Types of Objective Functions
Larger-the-Better e.g. performance
ƒ(y) = y
2
Smaller-the-Better
e.g. variance
ƒ(y) = 1/y
2
Nominal-the-Best
e.g. target
ƒ(y) = 1/(y–t)
2
Signal-to-Noise
e.g. trade-off
ƒ(y) = 10log[
µ
2
/
σ
2
]

15. MITSloan
Step 3: Plan the Experiment Elicit desired effects: „
Use full or fractional factorial
designs to
identify interactions.
„
Use an orthogonal array
to identify main
effects with minimum of trials.
„
Use inner and outer arrays
to see the effects
of noise factors.

16. MITSloan
Experiment Design: Full Factorial
„
Consider
k
factors,
n
levels each.
„
Test all combinations of the factors.
„
The number of experiments is
n
k
.
„
Generally this is too many experiments, but we are able to reveal all of the interactions.

17. MITSloan
Experiment Design: Full Factorial
Expt #
Param A
Param B
1A
1
B
1
2A
1
B
2
3A
1
B
3
4A
2
B
1
5A
2
B
2
6A
2
B
3
7A
3
B
1
8A
3
B
2
9A
3
B
3
2 factors, 3 levels each:
n
k
= 3
2
= 9 trials
4 factors, 3 levels each:
n
k
= 3
4
= 81 trials

18. MITSloan
Experiment Design: One Factor at a Time
„
Consider
k
factors,
n
levels each.
„
Test all levels of each factor while freezing the others at nominal level.
„
The number of experiments is
1+
k
(
n
-1)
.
„
BUT this is an unbalanced
experiment
design.

19. MITSloan
Experiment Design: One Factor at a Time
E
x
p
t
#
P
ar
am
A
P
ar
am
B
P
ar
am
C
P
ar
am
D
1A
2
B
2C
2D
2
2A
1
B
2C
2D
2
3A
3
B
2C
2D
2
4A
2
B
1C
2D
2
5A
2
B
3C
2D
2
6A
2
B
2C
1D
2
7A
2
B
2C
3D
2
8A
2
B
2C
2D
1
9A
2
B
2C
2D
3
4 factors, 3 levels each:
1+
k
(
n
-1) = 1+4(3-1) = 9 trials

20. MITSloan
Experiment Design: Orthogonal Array
„
Consider
k
factors,
n
levels each.
„
Test all levels of each factor in a balanced way.
„
The number of experiments is
n(k-1).
„
This is the smallest balanced experiment design.
„
BUT main effects and interactions are confounded.

21. MITSloan
Experiment Design: Orthogonal Array
Expt #
Param A
Param B
Param C
Param D
1A
1
B
1
C
1
D
1
2A
1
B
2
C
2
D
2
3A
1
B
3
C
3
D
3
4A
2
B
1
C
2
D
3
5A
2
B
2
C
3
D
1
6A
2
B
3
C
1
D
2
7A
3
B
1
C
3
D
2
8A
3
B
2
C
1
D
3
9A
3
B
3
C
2
D
1
4 factors, 3 levels each:
n(k-1)
= 3(4-1) = 9 trials

22. MITSloan
Using Inner and Outer Arrays
„
Induce the same noise factor levels for each combination of controls in a balanced manner
E1
E1
E2
E2
F1
F2
F1
F2
G2
G1
G2
G1
A
1
B1
C1
D1
A
1
B2
C2
D2
A
1
B3
C3
D3
A
2
B1
C2
D3
A
2
B2
C3
D1
A
2
B3
C1
D2
A
3
B1
C3
D2
A
3
B2
C1
D3
A
3
B3
C2
D1
inner x outer =
L9 x L4 =
36 trials
4 factors, 3 levels each:
L9 inner array for controls
3 factors, 2 levels each: L4 outer array for noise

23. MITSloan
Step 4: Run the Experiment Step 4: Conduct the experiment. „
Vary the input and noise parameters
„
Record the output response
„
Compute the objective function

24. MITSloan
Paper Airplane Experiment
Expt #
Weight
Winglet
Nose
Wing
Trials
Mean
Std Dev
S/N
1A
1
B
1
C
1
D
1
2A
1
B
2
C
2
D
2
3A
1
B
3
C
3
D
3
4A
2
B
1
C
2
D
3
5A
2
B
2
C
3
D
1
6A
2
B
3
C
1
D
2
7A
3
B
1
C
3
D
2
8A
3
B
2
C
1
D
3
9A
3
B
3
C
2
D
1

25. MITSloan
Step 5: Conduct Analysis Step 5: Perform analysis of means. „
Compute the mean value of the objective function for each parameter setting.
„
Identify which parameters reduce the effects of noise and which ones can be used to scale the response. (2-Step Optimization)

26. MITSloan
Parameter Design Procedure Step 6: Select Setpoints
„
Parameters can effect
„
Average and Variation (tune S/N)
„
Variation only (tune noise)
„
Average only (tune performance)
„
Neither (reduce costs)

27. MITSloan
Parameter Design Procedure Step 6: Advanced Use
„
Conduct confirming experiments.
„
Set scaling parameters to tune response.
„
Iterate to find optimal point.
„
Use higher fractions to find interaction effects.
„
Test additional control and noise factors.

28. MITSloan
Confounding Interactions
„
Generally the main effects dominate the response. BUT sometimes interactions
are
important. This is generally the case when the confirming trial fails.
„
To explore interactions, use a fractional factorial experiment design.

29. MITSloan
Confounding Interactions
S/N
B1
B2
B3
A1 A2 A3

30. MITSloan
Key Concepts of Robust Design
„
Variation causes quality loss
„
Parameter Design to reduce Variation
„
Matrix experiments (orthogonal arrays)
„
Two-step optimization
„
Inducing noise (outer array or repetition)
„
Data analysis and prediction
„
Interactions and confirmation