What is Robust Design or
Taguchi’s method?
• An experimental method to achieve product
and process quality through designing in an
insensitivity to noise based on statistical
principles.
History of the method
• Dr. Taguchi in Japan: 1949-NTT
– develops “Quality Engineering”
– 4 time winner of Demming Award
• Ford Supplier Institute, early 1980s
• American Supplier Institute, ASI
– Engineering Hall of Fame
• Statistics Community
– DOE
– S/N Ratio
Who uses Taguchi’s Methods
•
•
•
•
•
•
•
Lucent
Ford
Kodak
Xerox
Whirlpool
JPL
ITT
•
•
•
•
•
•
•
Toyota
TRW
Chrysler
GTE
John Deere
Honeywell
Black & Decker
Documented Results from Use
• 96% improvement of NiCAD
battery on satellites (JPL/ NASA)
• 10% size reduction, 80%
development time reduction and
20% cost reduction in design of a
choke for a microwave oven (L.G.
Electronics)
• $50,000 annual cost savings in
design of heat staking process
(Ann Arbor Assembly Corp)
• 60% reduction in mean response
time for computer system (Lucent)
• $900,000 annual savings in the
production of sheet-molded
compound parts (Chrysler)
• $1.2M annual savings due to
reduction in vacuum line
connector failures (Flex
Technologies)
• 66% reduction in variability in
arrival time and paper
orientation (Xerox)
• 90% reduction in encapsulation
variation (LSI Corp)
Insensitivity to Noise
• Noise = Factors which the engineer can not or
chooses not to control
– Unit-to-unit
• Manufacturing variations
– Aging
• Corrosion
• UV degradation
• wear
– Environmental
• human interface
• temperature
• humidity
How Noise Affects a System
Noise
Useful Energy
Energy
Signal Factor, M
Ideal Function of
Product or Process
Quality Characteristic, y
Harmful Energy
Caused by Noise
Control
Factors
Step 1: Define the Project Scope 1/2
• A gyrocopter design is to be published in a Sunday Comics
section as a do-it-yourself project for 6-12 year old kids
• The customers (kids) want a product they can easily build
and have a long flight time.
| WW |
--WL
----1/4”
---
BL
----
Step 1: Define the Project Scope 2/2
• This is a difficult problem from an engineering standpoint
because:
– hard to get intuitive feel for effect of control variables
– cant control materials, manufacturing or assembly
– noise factors are numerous and have strong effect on
flight.
Step 2: Identify Ideal Function
Time of Flight
• Ideally want the most flight time (the quality characteristic
or useful energy) for any input height (signal or input
energy)
• Minimize Noise Effect
• Maximize Slope
Drop Height
Step 3: Develop Noise Strategy 1/2
• Goal is to excite worst possible noise conditions
• Noise factors
– unit-to-unit
– aging
– environment
Step 3: Develop Noise Strategy 2/2
• Noise factors
– unit-to-unit
Construction accuracy
Paper weight and type
angle of wings
– aging
damage from handling
– environment
angle of release
humidity content of air
wind
+ many, many others
Step 4: Establish Control Factors and Levels
1/4
• Want them independent to minimize interactions
– Dimensionless variable methods help
– Design of experiments help
– Confirm effect of interactions in Step 7
• Want to cover design space
– may have to guess initially and perform more
than one set of experiments. Method will help
determine where to go next.
Step 4: Establish Control Factors and Levels
2/4
• Methods to explore the design space
–
–
–
–
shot-gun
one-factor-at-a-time
full factorial
orthogonal array (a type of fractional factorial)
Step 4: Establish Control Factors and Levels
3/4
Control factor array for the paper gyrocopter parameter optimization
experiment
1
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
WL
1.0/ww
1.0/ww
1.0/ww
1 .5/ww
1.5/ww
1.5/ww
2.0/ww
2.0/ww
2.0/ww
1.0/ww
1.0/ww
1.0/ww
1.5/ww
1.5/ww
1.5/ww
2.0/ww
2.0/ww
2.0/ww
3
WW
0.50
0.75
1.00
0.50
0.75
1.00
0.50
0.75
1.00
0.50
0.75
1.00
0.50
0.75
1.00
0.50
0.75
1.00
4
BL
1.33 x WL
1.67 x WL
2.00 x WL
1.33 x WL
1.67 x WL
2.00 x WL
1.67 x WL
2.00 x WL
1.33 x WL
2.00 x WL
1.33 x WL
1.67 x WL
1.67 x WL
2.00 x WL
1.33 x WL
2.00 x WL
1.33 x WL
1.67 x WL
5
Size
100%
75%
50%
75%
50%
100%
100%
75%
50%
50%
100%
75%
50%
100%
75%
75%
50%
100%
6
1
2
3
2
3
1
3
1
2
2
3
1
1
2
3
3
1
2
7
B_Fold
0
15%
30%
30%
0
15%
1 5%
30%
0
15%
30%
0
30%
0
15%
0
15%
30%
8
Gussets
None
45deg
45deg
45deg
None
45deg
45deg
None
45deg
None
45deg
45deg
45 deg
45deg
None
45deg
45deg
None
Step 4: Establish Control Factors and Levels
4/4
Step 5: Conduct Experiment and Collect
Data
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
3 feet
20# paper 24# paper
6 feet
20# paper
24# paper
9 feet
20# paper
24# paper
0.68 s
0.74
0.68
0.58
0.71
0.67
0.65
0.71
0.84
0.74
0.61
0.61
0.87
0.81
0.84
0.68
0.71
0.61
1.48 s
1.19
1.35
1.25
1.58
1.64
1.16
1.93
1.83
1.7
1.22
1.38
1.64
2.09
1.7
1.54
1.54
1.96
2.31s
2.25
1.48
2.34
2.28
2.44
2.68
2.61
2.09
2.09
1.48
2.28
2.02
2.27
1.51
2.44
2.6
2.73
0.55 s
0.58
0.45
0.71
0.68
0.55
0.7
0.6
0.63
0.61
0.45
0.58
0.68
0.65
0.63
0.68
0.68
0.84
1.48 s
1.58
1.03
1.22
1.41
1 .51
1.21
1.75
1.64
1.22
1.03
1.22
1.19
1.51
1.22
1.64
1.51
1.64
2.38 s
2.44
1.96
1.75
2.41
2.08
2.7
2.73
2.5
2.31
1.96
2.3
2.41
2.67
2.5
2.5
2.6
3.05
Data for Runs 5 and 15
2.5
Time (sec)
2
1.5
Run 5
Run 15
1
0.5
0
0
2
4
6
Height (ft)
8
10
Step 6: Conduct Data Analysis 1/7
• Calculate signal-to-noise-ratio (S/N) and Mean
• Complete and interpret response tables
• Perform two step optimization
– Reduce Variability (minimize the S/N ratio)
– Adjust the mean
• Make predictions about most robust configuration
Step 6: Conduct Data Analysis 2/7
• Calculate signal to noise ratio, S/N, a
variability
metric in decibels
S/N gain
reduction
S/N =
Useful output
Harmful output
3
6
12
27%
50%
75%
Effect of Mean
= Variability
around mean
2
y
= 10 log 2
s
Note: This is one of many
forms of S/N ratios.
Step 6: Conduct Data Analysis 3/7
1
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
Results of the parameter optimization experiment
2
3
4
5
6
7
8
slope
S/N
WL
WW
BL
Size
B_Fold Gussets (sec/ft)
1.0/ww 0.50 1.33 X WL 100% 1
0
None
0.25
6.94 dB
1.0/ww 0.75 1.67 X WL
75%
2
15%
45deg
0.25
2.67 dB
1.0/ww 1.00 2.00 X WL
50%
3
30%
45deg
0.19 -0.24 dB
1.5/ww 0.50 1.33 X WL
75%
2
30%
45deg
0.22
0.69 dB
1.5/ww 0.75 1.67 X WL
50%
3
0
None
0.26
9.04 dB
1.5/ww 1.00 2.00 X WL 100% 1
15%
45deg
0.25
3.81 dB
2.0/ww 0.50 1.67 X WL 100% 3
15%
45deg
0.26 -1.95 dB
2.0/ww 0.75 2.00 X WL
75%
1
30%
None
0.29
4.73 dB
2.0/ww 1.00 1.33 X WL
50%
2
0
45deg
0.26
2.64 dB
1.0/ww 0.50 2.00 X WL
50%
2
15%
None
0.24
2.81 dB
1.0/ww 0.75 1.33 X WL 100% 3
30%
45deg
0.19
0.76 dB
1.0/ww 1.00 1.67 X WL
75%
1
0
45deg
0.24
3.87 dB
1.5/ww 0.50 1.67 X WL
50%
1
30%
45deg
0.24
1.62 dB
1.5/ww 0.75 2.00 X WL 100% 2
0
45deg
0.28
0.87 dB
1.5/ww 1.00 1.33 X WL
75%
3
15%
None
0.23 -3.96 dB
2.0/ww 0.50 2.00 X WL
75%
3
0
45deg
0.27
9.04 dB
2.0/ww 0.75 1.33 X WL
50%
1
15%
45deg
0.28
4.88 dB
2.0/ww 1.00 1.67 X WL 100% 2
30%
None
0.31
2.99 dB
Step 6: Conduct Data Analysis 4/7
Response Table
Factor response averages table for the
parameter optimization experiment
Time Time
Factor
Level
(slope) (S/N)
1.0/ww
0.23
2.80
WL
1.5/ww
0.25
2.01
2.0/ww
0.28
3.72
0.50
0.25
3.19
WW
0.75
0.26
3.82
1.00
0.25
1.52
1.33 X WL 0.24
1.99
BL
1.67 X WL 0.26
3.04
2.00 X WL 0.25
3.50
100%
0.26
2.23
Size
75%
0.25
2.84
50%
0.25
3.46
0%
0.26
5.40
B_Fold
15%
0.25
1.38
30%
0.24
1.76
Gussets None
0.26
3.76
45deg
0.25
2.39
Step 6: Conduct Data Analysis 5/7
Response plot
Step 6: Conduct Data Analysis 6/7
Two Step Optimization
• Reduce Variability (minimize the S/N ratio)
– look for control factor effects on S/N
– Don’t worry about mean
• Adjust the mean
– To get desired response
– Use “adjusting factors”, those control factors
which have minimal effect on S/N
Step 6: Conduct Data Analysis 7/7
• For gyrocopter
–
–
–
–
–
–
wing width = .75in
wing length = 2.00/0.75 = 2.67 in
body length = 2.00 x 2.67 = 5.33 in
size = 50%
Predicted Performance
no body folds
no gussets
S/N = 9.44 dB
Slope = .31 sec/ft
Step 7: Conduct Conformation Run
• To check validity of results
• To check for unforeseen interaction effects
between control factors
• To check for unaccounted for noise factors
• To check for experimental error
Predicted Confirmed
S/N
9.44 dB
Slope .31sec/ft
9.86
.32 sec/ft
How Taguchi’s Method Differs from an
Ad-hoc Design Process
• Organized Design Space
Search
• Clear Critical Parameter
Identification
• Focus on Parameter
Variation (Noise)
• Clear Stopping Criteria
• Robustness centered not
Failure Centered
• Reusable Method
• Concurrently Addresses
Manufacturing Variation
• Concurrent Design-Test
Not Design-Test-Fix
• Minimize Development
Time (Stops Fire Fighting)
• Corporate Memory
Through Documentation
• Encourages Technology
Development Through
System Understanding
How Taguchi’s Method Differs from
Traditional Design of Experiments
• Focused on reducing the
impact of variability rather
than reducing variability
• Focused on noise effects
rather than control factor
effects
• Clearly focused cost
function - maximizing the
useful energy
• Tries to reduce interaction
between control factors
rather than study them
Requires little skill in
statistics
• Usually lower cost
How Taguchi’s Method Differs from
Shainin’s Method
• Focused on both Product
and Process Design rather
than Primarily on Process
• Oriented to developing a
robust system not finding
a problem (Red X).
Taguchi tells what
parameter values to set to
make system insensitive to
parameter Shainin
identifies as needing
control.
• Widely Used
Internationally
• Fire prevention rather than
fire fighting
• Accessible
• Many Case Studies
Available
Plan for Application at Tektronix
•
•
•
•
•
•
Select a parameter design problem
Design the experiment
Perform the experiment
Reduce data
Report results to Company
Assuming success
– design more experiments
– train more engineers
– Plan for student-run experiments