Here are the key results from the response table: - For WL, the highest level of 2.0/ww had the steepest slope and highest S/N ratio, indicating it is the most robust setting - For WW, the middle level of 0.75 had the steepest slope and highest S/N ratio, indicating it is the most robust setting This step identifies the most robust settings for each control factor based on the experiment results.

1. 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.

2. 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

3. Who uses Taguchi’s Methods
• Lucent • Toyota
• Ford • TRW
• Kodak • Chrysler
• Xerox • GTE
• Whirlpool • John Deere
• JPL • Honeywell
• ITT • Black & Decker

4. Documented Results from Use
• 96% improvement of NiCAD • $900,000 annual savings in the
battery on satellites (JPL/ NASA) production of sheet-molded
• 10% size reduction, 80% compound parts (Chrysler)
development time reduction and • $1.2M annual savings due to
20% cost reduction in design of a reduction in vacuum line
choke for a microwave oven (L.G. connector failures (Flex
Electronics) Technologies)
• $50,000 annual cost savings in • 66% reduction in variability in
design of heat staking process arrival time and paper
(Ann Arbor Assembly Corp) orientation (Xerox)
• 60% reduction in mean response • 90% reduction in encapsulation
time for computer system (Lucent) variation (LSI Corp)

5. 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

6. How Noise Affects a System
Noise
Useful Energy
Energy Ideal Function of Quality Characteristic, y
Signal Factor, M Product or Process
Harmful Energy
Caused by Noise
Control
Factors

7. 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
----

8. 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.

9. Step 2: Identify Ideal Function
• 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
Time of Flight
Drop Height

10. Step 3: Develop Noise Strategy 1/2
• Goal is to excite worst possible noise conditions
• Noise factors
– unit-to-unit
– aging
– environment

11. Step 3: Develop Noise Strategy 2/2
• Noise factors
– unit-to-unit
Construction accuracy
Paper weight and type
angle of wings + many, many others
– aging
damage from handling
– environment
angle of release
humidity content of air
wind

12. 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.

13. 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)

14. Step 4: Establish Control Factors and Levels
3/4
Control factor array for the paper gyrocopter parameter optimization
experiment
1 2 3 4 5 6 7 8
Run WL WW BL Size B_Fold Gussets
1 1 1.0/ww 0.50 1.33 x WL 100% 1 0 None
2 1 1.0/ww 0.75 1.67 x WL 75% 2 15% 45deg
3 1 1.0/ww 1.00 2.00 x WL 50% 3 30% 45deg
4 1 1 .5/ww 0.50 1.33 x WL 75% 2 30% 45deg
5 1 1.5/ww 0.75 1.67 x WL 50% 3 0 None
6 1 1.5/ww 1.00 2.00 x WL 100% 1 15% 45deg
7 1 2.0/ww 0.50 1.67 x WL 100% 3 1 5% 45deg
8 1 2.0/ww 0.75 2.00 x WL 75% 1 30% None
9 1 2.0/ww 1.00 1.33 x WL 50% 2 0 45deg
10 2 1.0/ww 0.50 2.00 x WL 50% 2 15% None
11 2 1.0/ww 0.75 1.33 x WL 100% 3 30% 45deg
12 2 1.0/ww 1.00 1.67 x WL 75% 1 0 45deg
13 2 1.5/ww 0.50 1.67 x WL 50% 1 30% 45 deg
14 2 1.5/ww 0.75 2.00 x WL 100% 2 0 45deg
15 2 1.5/ww 1.00 1.33 x WL 75% 3 15% None
16 2 2.0/ww 0.50 2.00 x WL 75% 3 0 45deg
17 2 2.0/ww 0.75 1.33 x WL 50% 1 15% 45deg
18 2 2.0/ww 1.00 1.67 x WL 100% 2 30% None

15. Step 4: Establish Control Factors and Levels
4/4

16. Step 5: Conduct Experiment and Collect
Data
3 feet 6 feet 9 feet
20# paper 24# paper 20# paper 24# paper 20# paper 24# paper
1 0.68 s 0.55 s 1.48 s 1.48 s 2.31s 2.38 s
2 0.74 0.58 1.19 1.58 2.25 2.44
3 0.68 0.45 1.35 1.03 1.48 1.96
4 0.58 0.71 1.25 1.22 2.34 1.75
5 0.71 0.68 1.58 1.41 2.28 2.41
6 0.67 0.55 1.64 1 .51 2.44 2.08
7 0.65 0.7 1.16 1.21 2.68 2.7
8 0.71 0.6 1.93 1.75 2.61 2.73
9 0.84 0.63 1.83 1.64 2.09 2.5
10 0.74 0.61 1.7 1.22 2.09 2.31
11 0.61 0.45 1.22 1.03 1.48 1.96
12 0.61 0.58 1.38 1.22 2.28 2.3
13 0.87 0.68 1.64 1.19 2.02 2.41
14 0.81 0.65 2.09 1.51 2.27 2.67
15 0.84 0.63 1.7 1.22 1.51 2.5
16 0.68 0.68 1.54 1.64 2.44 2.5
17 0.71 0.68 1.54 1.51 2.6 2.6
18 0.61 0.84 1.96 1.64 2.73 3.05

17. Data for Runs 5 and 15
2.5
2
Time (sec)
1.5
Run 5
1 Run 15
0.5
0
0 2 4 6 8 10
Height (ft)

18. 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

19. Step 6: Conduct Data Analysis 2/7
• Calculate signal to noise ratio, S/N, a
metric in decibels variability
S/N gain reduction
Useful output 3 27%
S/N =
Harmful output 6 50%
12 75%
Effect of Mean
= Variability around mean
y2
= 10 log 2 Note: This is one of many
s
forms of S/N ratios.

20. Step 6: Conduct Data Analysis 3/7
Results of the parameter optimization experiment
1 2 3 4 5 6 7 8 slope S/N
Run WL WW BL Size B_Fold Gussets (sec/ft)
1 1 1.0/ww 0.50 1.33 X WL 100% 1 0 None 0.25 6.94 dB
2 1 1.0/ww 0.75 1.67 X WL 75% 2 15% 45deg 0.25 2.67 dB
3 1 1.0/ww 1.00 2.00 X WL 50% 3 30% 45deg 0.19 -0.24 dB
4 1 1.5/ww 0.50 1.33 X WL 75% 2 30% 45deg 0.22 0.69 dB
5 1 1.5/ww 0.75 1.67 X WL 50% 3 0 None 0.26 9.04 dB
6 1 1.5/ww 1.00 2.00 X WL 100% 1 15% 45deg 0.25 3.81 dB
7 1 2.0/ww 0.50 1.67 X WL 100% 3 15% 45deg 0.26 -1.95 dB
8 1 2.0/ww 0.75 2.00 X WL 75% 1 30% None 0.29 4.73 dB
9 1 2.0/ww 1.00 1.33 X WL 50% 2 0 45deg 0.26 2.64 dB
10 2 1.0/ww 0.50 2.00 X WL 50% 2 15% None 0.24 2.81 dB
11 2 1.0/ww 0.75 1.33 X WL 100% 3 30% 45deg 0.19 0.76 dB
12 2 1.0/ww 1.00 1.67 X WL 75% 1 0 45deg 0.24 3.87 dB
13 2 1.5/ww 0.50 1.67 X WL 50% 1 30% 45deg 0.24 1.62 dB
14 2 1.5/ww 0.75 2.00 X WL 100% 2 0 45deg 0.28 0.87 dB
15 2 1.5/ww 1.00 1.33 X WL 75% 3 15% None 0.23 -3.96 dB
16 2 2.0/ww 0.50 2.00 X WL 75% 3 0 45deg 0.27 9.04 dB
17 2 2.0/ww 0.75 1.33 X WL 50% 1 15% 45deg 0.28 4.88 dB
18 2 2.0/ww 1.00 1.67 X WL 100% 2 30% None 0.31 2.99 dB

21. Step 6: Conduct Data Analysis 4/7
Response Table
Factor response averages table for the
parameter optimization experiment
Factor Time Time
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

22. Step 6: Conduct Data Analysis 5/7
Response plot

23. 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

24. 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%
– no body folds Predicted Performance
– no gussets S/N = 9.44 dB
Slope = .31 sec/ft

25. 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 9.86
Slope .31sec/ft .32 sec/ft

26. How Taguchi’s Method Differs from an
Ad-hoc Design Process
• Organized Design Space • Concurrently Addresses
Search Manufacturing Variation
• Clear Critical Parameter • Concurrent Design-Test
Identification Not Design-Test-Fix
• Minimize Development
• Focus on Parameter
Time (Stops Fire Fighting)
Variation (Noise)
• Corporate Memory
• Clear Stopping Criteria Through Documentation
• Robustness centered not • Encourages Technology
Failure Centered Development Through
• Reusable Method System Understanding

27. How Taguchi’s Method Differs from
Traditional Design of Experiments
• Focused on reducing the • Tries to reduce interaction
impact of variability between control factors
rather than reducing rather than study them
variability Requires little skill in
• Focused on noise effects statistics
rather than control factor • Usually lower cost
effects
• Clearly focused cost
function - maximizing the
useful energy

28. How Taguchi’s Method Differs from
Shainin’s Method
• Focused on both Product • Widely Used
and Process Design rather Internationally
than Primarily on Process
• Fire prevention rather than
• Oriented to developing a
fire fighting
robust system not finding
a problem (Red X). • Accessible
Taguchi tells what • Many Case Studies
parameter values to set to Available
make system insensitive to
parameter Shainin
identifies as needing
control.

29. 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