「Status of Scientific Methods for ProductDevelopment Outside of Japan」

Robust Optimization using Taguchi Methods

Epoch Making Case Studies・・
TRIZ Symposium
Friday 09-12-2014

Shin Taguchi (田口伸）

CTO, ASI Consulting Group LLC
President, American Supplier Institute, Inc.
Bingham Farm, Michigan USA

shin.taguchi@asiusa.com

2

DFSS Process – IDDOV Project
I
Identify
Opportunities

DDO

V

DefineRequirement

DevelopConcept

Optimize
Concept

Verify &Launch

Pugh’s Concept
Generation & Selection
CCO
R Total N
Leak
I Chang% C
Test
TeCourte
FluidsTime# E
syMeetJury
ECheckePotentiPDisposal
R ald T
I Guidelin
injuryesAopport.

Project
Charter

Project
Charter

VOCW
H
A
T

CONFLICTS
HOW

RELATION
SHIPS
HOW
MUCH

House ofQuality© 2010 ASI Consulting Group, LLC

1TO
DA
Y

2RA
M
P

DATUM

Project
Selection

3
JA
CK

4
PI
T

5
SU
C
K
O
UT

6
M
IC
R
O
B
S

TRIZ
Axiomatic Design&Creativity
Tools
Strategic
TargetWinning
DesignConcept

Optimized
DesignRobust Optimization
 Ideal Function
 P-diagram Noise Strategy
 Signal-to-Noise Ratio Two-step Optimization
Tolerance Optimization
RobustEngineering

Design
ReviewVerify&Launch

Validated
ProductDesign
Review

Implementation

3

History of Taguchi Method
10’s

Robust Design Shelf

T Methods

Standardized S/N for Non-linear Ideal Function
Automotive
Mahalanobis
Taguchi
System00’s Robust Engineering
Hall of Fame
Dynamic S/N Application to other Systems
1993
Robust Technology
JQES
90’s
Noise Compounding
Robust Design
Operating Window
Energy Thinking
Imported to
80’s Dynamic S/N Application to Mechanical SystemUSA
Non-dynamic S/N Tolerance Design
70’s On-line Quality Engineering
Quality Loss Function
Dynamic S/N for Measurement
Inner Array
60’s Parameter Design
50’sDesign
Of
Experiment© 2010 ASI Consulting Group, LLC

Focus on “Work”
Linear Graph
ANOVA
OA

Outer Array

2-Step Optimization
Robustness
By Control x Noise

Deming Prize1948 Morinaga Company - Caramel Candy Hardness

y = Caramel Hardness

Function

Take advantage ofInteractions between Control & Noise , AxN, BxN, ..
to achieve “Robustness”

BeforeAfter0 deg.
© 2010 ASI Consulting Group, LLC

10 deg. 20 deg. 30 deg. 40 deg.
Temperature (C)Noise Factor

44 types of Countermeasures for Noises

I.

IgnoreII.

Control / Eliminate Noise

III.

Compensate Effect of Noise(s)IV.

5

Example: Standardization, Control Charting, Poka-Yoke
Traditional Quality Assurance Activities, Tolerance Design

Example: Feedback Control, Adaptive Control(Feed forward Control), Engine Control,
Matching Assembly, Anti-lock Brake, Etc.

Minimize Effect of Noises

If you decide to add acompensation system,
you like to optimize thecompensation function
for “Robustness”

Example: Generation & Selection of Robust Design Concept
Optimization for Robustness (Parameter Design)
The better you can achieve IV, theless $ needed to do II & III© 2010 ASI Consulting Group, LLC

1950 ~ 56: NT&T Cross Bar Switching System

6

Winning competition by optimizing “Robustness”

Budget # People # Years
Result5057
Not finished
AT&T Bell Labs
NT&T ECL

11Lease
SellContractors
Mfg. companies

ECLDesign© 2010 ASI Consulting Group, LLC

Users
Tel Co.
End users

6Superior

Leasing by ECL has
100% Warranty- 40 Years for Exchanger- 15 Years for Tel. sets

During six years ofdevelopment, ECL has optimized
over 3000 Design Control Factors
for “Robustness”, i.e. looking forrobustness by studying
interactions between
Control and Noise.

1953 Ina Seito (INAX) Tile Manufacturing Tunnel Kiln 7
Optimization using small scale pilot
Reducing Variability  Speed up the process

R&D

Mass production

L27 was conductedusing
small pot mill.

L8 was conductedusing full mfg. scale toconfirm
y = Tile Thickness(mm)

After Optimization

USL

Speed up theprocess forhigher productivity

NominalLSL
Before Optimization© 2010 ASI Consulting Group, LLC- Tunnel Kiln -Inside
Tiles

OutsideTiles

Position
Within Kiln

1959 Japan National Railroad Train Body Welding
DoE with Multiple Response
L16123456789101112131415
16

AA Gxx x
A G G H H H B D E1111111112222222221111222211112222311112222222211114
1122
1122
1
122112251
1221122221
1221
161
12222
11112222
1
1

7
1
12222
1
122
1
1
1
122

8
12
12
12
12
12
12
12
12

Workability
Response Table
ANOVA (Optional)

FIeeAxC C

9 10 11 12 13 14 151 1 1 1 1 1 1
2 2 2 2 2 2 2
1 1 1 2 2 2 22 2 2 1 1 1 1
1 2 2 1 1 2 22 1 1 2 2 1 1
1 2 2 2 2 1 1
2 1 1 1 1 2 2
2 1 2 1 2 1 2
1 2 1 2 1 2 1
2 1 2 2 1 2 1
1 2 1 1 2 1 22 2 1 1 2 2 1
1 1 2 2 1 1 22 2 1 2 1 1 2
1 1 2 1 2 2 1

Workability
E000110100000
1000N1110000011110011D0000010100000100

Appearance
FaceReverse
G
1001001000101011F0110
10011
10
10000

Appearance
Response Table
ANOVA (Optional)

B
00
000
1
00
00
0
00
1
00

G
100
0
0
000
100
1000
1

F
00
1
100
100
1
1000
10B
0
1
00
1
10
1
0000
1
10
0

X-Ray
G
3
342242323
340
3
14F
1
10220211
1103030B
0000000010001100

1963 Bullet Train
TensileStrength
2
Kg/mm
43.7
40.2
42.4
44.7
42.4
45.9
42.2
40.6
42.4
45.5
43.6
40.6
44.0
40.2
42.5
46.5

X-Ray
Response Table
ANOVA (Optional)

Elongation
%
33.6
40.2
30.5
23.7
34.7
21.8
24.8
29.8
33.7
25.5
36.9
29.0
30.3
39.0
27.9
40.8

Tensile Strength
Response Table
ANOVA (Optional)

Elongation
Response Table
ANOVA (Optional)

Trade-off Decisions© 2010 ASI Consulting Group, LLC

Overall Optimization

Prediction & Confirmation

891960’s to Present: Metrological Institute of Japan
Government Research Institute for Metrology

Ideal Function for Measurement System
Two-step Optimization for Measurement Function

Control Factors
A, B, C, D. E, ….
Ideal Function
y=βMy

M = True Value

Measurement
Systemy = Measured ValueβM

Noise Factors
O, P, Q, R, S

© 2010 ASI Consulting Group, LLC

Apply 2-Step Optimization
Step-1: Maximize S/N
Step-2: Adjust β to 1.000

10Data Obtained During Development of Bathroom Scale
Input M is the True Value and Output Response is Measured Value.
N1 and N2 are Compounded Noise Conditions
Among three designs A1, A2 and A3, which design is the most robust, and why?

A1A2A3

M1=10 Kg
N1
N2
9.9
10.1
9.8
10.2
19.9
20.1

M2=20Kg
N1
N2
19.8
20.2
19.6
20.4
39.8
40.2

M3=30Kg
N1
N2
29.7
30.3
29.4
30.6
59.7
60.3

Answer _____________© 2010 ASI Consulting Group, LLC

True/ False Questions
Answer by Brad
Correct
Answer

True

False

True

100%

0%

False

0%

100%

S / N = +∞ dB

Answer by Shin
Correct
Answer

True

False

True50%50%

False

50%50%

Answer by Mike
CorrectAnswer

TrueFalse

True0%

100%

False

100%0%© 2010 ASI Consulting Group, LLC

S / N = −∞ dB

S / N = +∞ dB

11131979 Toyota Van Body Structure
Optimize Function to Reduce Cost & WeightControl Factors & Levels
Level-1

Level-2

Level-3Component- A

Lighter

Base

Heavier

Component- B

Lighter

Base

Heavier

Component- C

Lighter

Base

Heavier: :: :: :: :Component- Z

Lighter

Base

Heavier

S/N of Ideal Function
32.0
30.0
28.0
26.0
24.0
22.0
20.0
18.0

A1 A2 A3

B1 B2 B3

C1 C2 C3:: ::Measure Ideal Function (Crash Performance)

Challenge to improve function and reduce weight simultaneously!

© 2010 ASI Consulting Group, LLC

Z1 Z2 Z3

Design Space in Inner Array
Measure Ideal Function under Noise Strategy
Use S/N to Assess Robustness!

Design Space
123
45678910111213
14
15
16
1718

A

B

CDEeee1
11
1
1111112222222222
1112223331112223333
123
123
12312312312341231232313122313125123231123312312231612323131223112331271233122312313121238123312312123231231

Inner Array

Explore DesignSpace© 2010 ASI Consulting Group, LLC

Function
Outer Array

Outer
Array

Ideal Function withNoise Strategy
N1N2P1P2P3P4P1P2P3P4V1 V2 V3 V4 V5y1 y2 y3 y4 y5y6 y7 y8 y9 y10y11 y12 y13 y14 y15
y16 y17 y18 y19 y20
y21 y22 y23 y24 y25
y26 y27 y28 y29 y30
y31 y32 y33 y34 y35
y36 y37 y38 y39 y40

1415The Taguchi Study Group has been meeting every month to discuss
practical applications, one group in Nagoya since 1953, and anothergroup in Tokyo since 1964. Through these successes and failures,the method has taken huge evolutions.

Genichi Taguchi
W. E. Deming
Yuin Wu
1979 Basement of Dr. Deming’s House© 2010 ASI Consulting Group, LLC

161980 Bell Labs 256k Chip Photolithography Window Size
Science vs. Engineering
Photolithography
Noise Factors
Chip to Chip
Within Chip

P1

Two-step Optimization
Apply
2-step Optimizationy = Window Size
(Nominal-the-Best)

Control Factors
Plasma Etching Time
Exposure Time
Spin Speed
Bake Time
Aperture, Etc.

Step-2

Baseline

Step-1

P2

Q1
Q4

Q2
Q3
Q5

Three 2-level factors
Six 3-level factors

L18(23 x 36)

yTarget( 3.0µm )Yield: 33%

87%

Bell Systems Technical Journal May 2003
© 2010 ASI Consulting Group, LLC

171985 Chrysler Sheet Mold Compound
Reduced Rework Cost by $900k/YearFire Fighting to Fire PreventionSheet Molded Compound Process Improvement
Chrysler, 1985

Response
y ＝ # of Porosity （STB）
Objective
Minimize:y and σ y Control Factors were assigned
to an L16 with selected two-factor
interactions.
 It was confirmed that theoptimum condition resulted in justabout no porosity.

Control Factors

Forming Pressure,
Temperature, Cycle Time,Pattern Design, Under
Coating, Weight,
Glass Type, etc.

 Direct Run Yield was improved
from 74% to 96%.
 Cost reduction due to reduced
rework was $900,000/Yr.

Not objective ofTaguchi Methods.

Best in ClassGood Company
Typical Company© 2010 ASI Consulting Group, LLC

Prevention
Prevention ofRe-occurrence
Fire Fighting

I have a big problem withmy son, Shin.
He helps his clients tofire fight.
I am not interested inFire-Fighting.
Please do not use
Taguchi Methods for FireFighting
G. Taguchi, 1988

1988 ASI Symposium’s Theme was:18

An 8 letter word

© 2010 ASI Consulting Group, LLC

Robust Assessment vs. Validation
It is most important is to recognize the difference between:“Robust Assessment” and “Validation”.
Conduct “Robust Assessment” first, then “Validate”
Short Time,~ One Day

To evaluate how robust
the function is against various
customers usage conditions

Longer Time,~ 12 Months.

1. To check if the productmeets all requirements.
2. Detect all “Buds” ofproblems.

Ideal Function + Noise Strategy

 Signal-to-Noise Ratio
Why is this so critical???
© 2010 ASI Consulting Group, LLC

19

20

VOC
Theme
Selection

Strategic
TargetProductPlanning
StartsDFSS Projects
Decoupled Development- New Technology- New Design Concept- Common Design- Standardized Design- Best Practice- Design Guideline- Manufacturing Technology- New Material Development© 2010 ASI Consulting Group, LLC

DFSS Projects

Validation
LaunchCPCP

Step- 2RobustDesign
Shelf

Scalable
Adjustable&Robust

Step- 1

Robust Assessment
Robust OptimizationNote: Ideally, “A” should be 30%
and 70% for “B”.
Only way to reduce Time-toMarket drastically say by 50%.
 Satisfy the VOC in 12
months is easier than 36
months1990 Hardness Tester Standard Sample by Asahi Giken
Achieved the Best in Industry
 Asahi Giken is a very small company with
XXX people.
 They were able to develop new hardness
standard samples that is the best inindustry in “price” and “accuracy”.

MHeat Energy© 2010 ASI Consulting Group, LLCSampleHardeningy∆ Hardness21

1980’s Paper Feeder by Xerox
1 Hr Robust Assessment Test

Operating Window Concept22

Noise Compounding

Control Factors

12345678910111213
1415
161718AB

CDEFGH

1
1
1
1
1
1
1
1
112222222222
1
1122233
3
1
1
12223
3
3

3
12
3
123
12
3
123
123
123

4
123
12323
13
1223
13
12

5
12323
11233
123
12231612323131223112331271233122312313121238123312312123231231For each run of L18, measure the operating window

Result-1
Result-2
Result-3
Result-4
Result-5
Result-6
Result-7
Result-8
Result-9
Result-10
Result-11
Result-12
Result-13
Result-14
Result-15
Result-16
Result-17
Result-18

Operating Window Response
N1
N20fx

0

f = Spring
Forcefz
fxfz

f = SpringForce

2 Step Optimization
Step-1: Maximize O.W.
Step-2: Adjust Forcefx = Force to start feeding one by one, say 4 sheets
fz = Force to start multi-feed/ paper jam
Noise Compounding
N1 = Noise Condition which tends to miss-feed = Slippery & Heavy Paper + Worn Roller + High Humidity
N2 = Noise Condition which tends to multi-feed = Coarse & Light Paper + New roller + Dry

Dynamic Response with Ideal Function
M = Roller Angular
Displacement© 2010 ASI Consulting Group, LLC

2 Step Optimization
PaperFeeder

y = Paper Linear
Displacement

Step-1: Maximize S/NStep-2: Adjust β23

1993 Oxygen Sensor by 3M
Main Function + Compensation
M = Actual Oxygen
Concentration
M* = Blood Temperature(Vary from 17C to 37C)

OxygenSensory = Io/I(Measured Oxygen
Concentration)

Three approaches(a) M* is a noise factor.
(b) M* is a signal factor if its effect is to be compensated(c) M* is an indicative factor if its effect is to becompensated by “Look-up Table” approach.
Ideal Function for (b)We need to know the values of β1, β2 andβ3.
y = β + β * ( M * − M S* ) MyM * = 37  CβM * = 28 C
M * = 18 C© 2010 ASI Consulting Group, LLC

M

Ideal Function for (c)As long as values ofβ1, β2, β3 are known,
the effect of temperature
can be compensate.

yβ1

M * = 37 C
M * = 28 C

β2β3M

M * = 18 C

24

1993 Ford Fuel Pump
Main Function + Compensation
SystemI = Current

Pump

Gas tank

EEC

V = DC Volts

Scope

ECT
RPM
Throttle
Position: :: :Back
Pressure

Injectory = Fuel FlowP’ = Back Pressure

Excess hot fuel back to tank(This is no longer allowed due to pollution standards)140120Baseline Design

Flow

100

N180

N260
4020000.05

0.1

0.15

0.2

0.25

0.3

IV/P

Flow

Optimum Design

160
14012010080
60

N1N240200© 2010 ASI Consulting Group, LLC

00.05

0.1

0.15
IV/P

0.2

0.25

0.3

Control Factors

Modulation Freq., Assembly Type
Motor Design, Valve Design
Mounting Angle, Etc.

SignalM = I V/P

Fuel Pump

Noise Factors

Responsey = Fuel Flow

Fuel Temperature, Fuel Type
Tank Pressure, Pump Wear
Driving Conditions, Mfg. Variation, Etc.

1988 ITT EW Receiver

SignalTime25ResponseProbability of Detection

EWReceiver

Ideal Function: P = e− β T
FORMULATION OF ROBUST OPTIMIZATION
M = Time

EWReceiver

Noise Factors
Noise Factors and Levels
123
G: # of LPI Threats
gg+5 g+10
H: LPI Starting Time
Low Med High
I: LPI Amplitude
Low Med High
J: # of PR Threats
m m+5 m+10
K: PR Starting Time -1 Low Med High
L: PR Starting Time -2 Low Med High© 2010 ASI Consulting Group, LLC

P = Prob{Not Detecting}Control Factors
Control Factors and Levels
123
A: LPI Scanning
Std +9 +19
B: # of Priority Scan
Std +4+9C: PR Scanning
Std +9 +39
D: Additional Dwell LPI Std +7 +15
E: Additional Dwell PR
Std +7 +15
F: Receiver Threshold Std +0.1 +0.2

Result & Benefit:
Achieved a remarkable 57%
reduction in detecting time undera dynamic EW environment.

1999 UTA Clutch Subsystem for Lift-gate Multiplexed Node
FACTORS & LEVELS

Dynamic response with:
M = Spring Forcey = Torque to Engage

Control Factors:
61 x 35  L18(61x36)
Convinced engineers toconduct this L18. After
hard work they came withthis result.
 No.1 to No.6 wereinfeasible!!
 Many data are missing
due to not being able tohave samples.

© 2010 ASI Consulting Group, LLC

Signal Factor
M: Spring ForceLevel-1-30%

Level-2
NominalLevel-3+30%

Noise Fcator
W: Aging

Level-1
InitialLevel-2
Ambient

Level-3
Cold

Level-4
Hot

Level-5
Final

y = Torque to Engage

L1 8 W1W2W3W4W5

M1 M2 M3 M1 M2 M3 M1 M2 M3 M1 M2 M3 M1 M2 M3

1No engagement

2 No engagement
3 No engagement
4 No engagement
5 No engagement
6 No engagement
7800----

841 40 34 420

42 47 0 40 41 0 31 44 00952 44 50 053000000000010--

102--60--51--

56-

1 1 57 61 46 00

55 000000000-

56--0--0--0

1 2 52 33 57 60 26 38 85 73 48 35 33 28 52 35 33
1 3 54 -51 0-00-00-

00-0

1 4 57 -40 0-00-

00-

00-

0

1 5 42 --0--0--0--0--

1 6 38 42 42 440

36 29 0 36 21 0

0 24 00

1 7 45 42 41 0000000000001 8 56 56 -0-00-00-00-0

Conducted data
analysis using
S/N, and it has
confirmed
successfully!!
This isa good set ofdata!!

26

27

2000 ITT Switch Feel for Micro Switch
Double Nominal-the-BestNew Idea :Standardixed S/N

 L18 Optimization by Simulation
 Initially “Double Nominal-the-Best” wasused with 20dB gain. Dr. Taguchi thought too
much gain and something is wrong. He
developed the idea of “Standardized S/N.”© 2010 ASI Consulting Group, LLC

y = Force

Ideal Profileｍ３ｍ１ｍ２
M*=Displacement28

2002 Nissan Window Regulator Motor“To get Quality, Don’t Measure Quality”
Creative Noise Strategy for Robust Assessment

Input Signal

System or Sub-System

Automotive Direct Current

M: Electrical Power

Output Response

y: Mechanical Power(DC) Motor

Measurement for Ideal Function
120

4N•m
3N•m
2
N•m

100

PowerConsumption
(W)

8060
40

Figure6. Performance Comparison with Benchmark Product(dBA)(1) Audible Noise

6560258dBA reduction

55
0306090 120 150 180

Elapsed Time (sec)50

Noise Strategy45

comparableleft : CW
right : CCW
3Nm loaded
under the same
rev/min.
0 to 10kHz
Over All

Current Optimal Benchmark

N1
Motor-On Time
0 sec
© 2010 ASI Consulting Group, LLC

N2180 sec

4.3%
improved

2.7%
exceeded

23200(2) Energy Efficiency
(%)

2119
1715
Current Optimal Benchmark

2006 Position Sensor by Alps Electric
Make it measurable!!  Simulation Engine

Scope Big!!

Angle ofincidence

Magnetic Sensing System
M = True
Angle(0 to 360 Deg)

IC

Software108x108x360= 4,199,090
computations

Y = ComputedAngle

S/N
Improvement over iterations
049
NoiseFactors

Sensor

L108
L10848Control
Factors

29

Magnetism-10x 11iterations-20-30-40

38.7 dB Improvement
Baseline

Optimum

Number of Designs Explored
348 x 11 = 877,430,873,845,598,000,000,000= 0.88 Septillion© 2010 ASI Consulting Group, LLC

True Value Ｍ (deg)True Value Ｍ (deg)302008 Chrysler Frontal Crash
Deformable
Barrier
Front Sill +Cowl SideLower

Use of 10-min. Spring Mass Model Simulation
vs. 36 Hour Full CAE Simulation

Mid Sill

Rear Sill

Front Tire

Shot gun front

CrushCan

Crush CanExtension

Rail Tip

Shock Tower

RailKick down

CradleFront LegCradle Frt X-member LegCradleMiddle LegOM651
EngineDynamic Operating Window

B-Pillar +Aperture

A-pillar + Cowl
Side Upper

Rail Tip Extension
Engine to Front
X-memberMain Cradle

Frt Tunnel

Mid RailGooseneck+ Mount

Mid Tunnel

Rear Rail

Underbody
Stay Brkt Reinf

Rear Tunnel

Loading Zone Mass Legends

Dynamic Operating Window Ideal Function

β1Area2 you don’t
β2 want
to deform
Input:
M = Velocity

Area you want
1 to deform
200

β1

180
160

Area
2 you don’t
want to deform

β2140
120
1008060

Input:
M = Velocity

W/O Cradle Base
W/O Cradle OPT #1Cradle Baseline
Cradle OPT #1
Cradle OPT #2
Cradle OPT #3

Dash Intrusions (mm)Intrusion

Area you want
1 to deform

After Optimization
Output:
Y=Deformation

Output:
Y=Deformation

Before Optimization

4020

Cradle Concept  L54 iterated 5 times
K-member Concept  L54 iterated 5 times
Short Front Concept  L54 iterated 5 times

0D-Line Dash C-Line Dash A-Line Dash E-Line Dash
40 N1
40 N1
40 N140 N1

D-Line Dash C-Line Dash A-Line Dash E-Line Dash
40 N240 N240 N240 N2# of Designs Explored = 323 x 3 x 5 iterations > 1,400,000,000,000© 2010 ASI Consulting Group, LLC