DESIGN FOR SIX SIGMA &
ROBUST DESIGN OF PRODUCTS
AND PROCESSES FOR QUALITY
Gülser Köksal
EM507
METU, Ankara
2009
OUTLINE
•
DFSS
– DMAIC vs. DFSS
– Different DFSS roadmaps
– DMADV Roadmap
– How To implement DFSS
•
•
•
Robust design examples
A review of design of experiments and
orthogonal arrays
Taguchi’s robust design approach
– Loss Fuunctions
– Signal-to-Noise Ratios
•
Robust design case study: Cookie recipe
design
Slides 3-16 are selected from the following presentation:
DFSS – DMAIC
To design new products
or processes, or to
improve the designs of
existing ones in order to
satisfy customer
requirements
To improve the existing
processes in order to satisfy
customer requirements.
Six Sigma
Process Management
To achieve the business results,
managing the processes efficiently.
Optimization
Characterization
DMAIC
Define
Define the problem with outputs and potential
inputs
Measure
Analyze the existing process: Is the process
measured correctly? If so, what is the capability
of the process?
Analyze
Analyze and identify the important factors that
cause the variation of the process: Where and
when do the defects occur?
Improve
Optimize the output by optimizing the inputs: To
reach at the six sigma process, what should be
the levels of each factor?
Control
Which controls should be done in order to
continue process at six sigma?
Improvement Strategies
Customer
Requirements
Process
Capability
DMAIC
DFSS
NO
Is the gap
small?
YES
Fundamental
Redesign
Iterative
Improvement
• Design a new product /
process
• Broad approach
• Blank sheet of paper approach
• High risk
• Longer time span
• Addressing many CTQs
• Goal: Quantum Leap
•
•
•
•
•
•
•
Fix an existing process
Narrow Focus
Use current process model
Low risk
Shorter Time Span
Addressing few CTQs
Goal: Improvement
When to Go for DFSS
 Changing customer expectations: by the time the current
problems are solved, new problems will occur
 Technology development: new technologies allow to meet all
customer requirements at lower cost or gain a competitive
edge
 Next generation: the existing products remaining lifetime is
very short, a successor will be needed soon
 System limits: the performance gap is due to system / business
model configurations that cannot be changed or the available
technology does not allow to meet CTQs
 Process entirely broken: the existing process is unable to meet
many CTQs, too many successive DMAIC projects required
Influence on cost, cycle time and
quality
MANUFACTURING TRANSACTION
%20-30
DESIGN
MANU.-TRAN.
DESIGN
%70-80
Different DFSS Methodologies
 Several roadmaps have been proposed.
 They are very similar to each other. The underlying tools
are the same
DFSS Methodology: DMADV
Define the project goals and customer requirements.
Measure and determine customer needs and
specifications; benchmark competitors and industry.
Analyze the process options to meet the customer needs.
Design (detailed) the process to meet the customer
needs.
Verify the design performance and ability to meet
customer needs.
DFSS Methodology: DCCDI
Define the project goals.
Customer analysis.
Concept ideas are developed, reviewed and
selected.
Design is performed to meet the customer and
business specifications.
Implementation is completed to develop and
commercialize the product/service.
DFSS Methodology: IDOV
Identify the customer and specifications (CTQs).
Design translates the customer CTQs into
functional requirements and into solution
alternatives.
Optimize uses advanced statistical tools and
modeling to predict and optimize the design
and performance.
Validate makes sure that the design developed
will meet the customer CTQs.
DFSS Methodology: DMADV
Define the project goals, customer requirements, and
opportunities
Measure in detail customer needs and priorities, market
conditions, and benchmark competitors
Analyze the data collected, prioritize CTQs, determine
relations between CTQs and parts/processes
Develop concept, innovative solutions, and optimal
solutions to product and process design
Validate the solutions and implement
DFSS Methodology: DMADV
TOOLS
DEFINE
MEASURE
ANALYZE
DEVELOP
VALIDATE
Project management
QFD
Benchmarking
Value analysis
Financial analysis
SIPOC
IPDS
FMEA
TRIZ
Design scorecards
MSA
Basic statistical techniques
DOE
Optimization
Simulation
Robust design
Tolerance design
Reliability engineering
Design for manufacture and assembly
All methodologies are similar
Measure in
detail
customer
needs and
priorities,
market
conditions,
and
benchmark
competitors
Define the
project
goals,
customer
requirements
, and
opportunitie
s
Define
Measure
Identify
Analyze the
data collected,
prioritize
CTQs,
determine
relations
between CTQs
and
parts/processe
s
Develop
concept,
innovative
solutions, and
optimal
solutions to
product and
process
design
Validate
the
solutions
and
implement
Analyze
Develop
Validate
Design
Optimize
Verify
How is it implemented?
 2 weeks of DFSS training
 Six Sigma BB or GB knowledge required for participation
 2 project groups and 1 project per group
 In between training and after training there are a lot of MBB coachings (2-3
days/project-month)
Six Sigma Black Belt
BB Week 1
BB Week 2
BB Week 3
BB Week 4
Design For Six Sigma
Six Sigma Green Belt
GB Week 1
DFSS Week 1 DFSS Week 2
GB Week 2
Or combined Six Sigma / DFSS Black Belt training program
Totally 5 weeks of training
Black Belts work on the design project
Team members may participate on a common project
Robust Design Problem
To make system outputs insensitive to variation in inputs,
process and environmental factors.
X1
X2
X3
X4
X5
Y1
Product or
Process
Y2
Y3
X6
Inputs
(Control
Factors)
Outputs
W1
W2
W3
Noise Factors
(uncontrollable)
Robust Product Design Example
Making system output robust to environmental usage conditions
Sugar
Flour
Egg
Milk
Oil
Making a cake using
a cake mix
Taste
Texture
Baking
powder
Inputs
Oven type
Altitude from sea level
Customer
requirements
(controllable)
Noise factors (uncontrollable)
A robust cake mix recipe reduces variability in taste and texture.
Robust Product Design Example
Making system output robust to component variability
Period
Utilizing the second degree relationship between system output and inputs
What should be the
pendulum length to
minimize variation
in the period?
Pendulum length
Robust Process Design Example
W2
Making system robust to process variability
W1
What should be the
amount of steam
blown and amount of
water sprayed into
the closed system to
generate a level of
20% humidity?
%10
Water
%20
%30
Steam
S2
S1
Guidelines for Robust Design through
Statistical Experimentation
1. Choose control factors and their levels
2. Identify uncontrollable (noise) factors and decide
on how they will be simulated
3. Select the response variable(s) and determine
the performance measures (mean, standard
deviation, SNR, etc.)
4. Setup the experimental layout (choose
appropriate design array(s))
5. Conduct the experiments and collect data
6. Analyze the data (effects, ANOVA, regression)
7. Choose optimal control factor levels and predict
the performance measure at these levels
8. Confirm the optimal levels by experimentation
Orthogonal Arrays
Ortogonal
No. of
Max. no. of
Array
L4
L8
L9
L12
L16
L16
L18
L25
L27
L32
L32
L36
L36
L50
L54
L64
L64
L81
rows
4
8
9
12
16
16
18
25
27
32
32
36
36
50
54
64
64
81
factors
3
7
4
11
15
5
8
6
13
31
10
23
16
12
26
63
21
40
Max. no. of factors at these levels
2
3
7
11
15
1
31
1
11
3
1
1
63
-
3
4
7
13
12
13
25
40
4
5
9
21
-
5
6
11
-
Ortogonal Array Construction Example
One factor with 2 levels,
6 factors with 3 levels
Quality (Consumer) Loss
The quality of a product is measured by estimating “the total
loss to the customers due to variation in the product’s functions.
For ideal quality, loss is zero. Higher the loss, lower the quality.
(b)
(b)
LSL
µ=T
USL
(b)
Quality characteristic (X)
Quality Loss
= b (x-T)2
Average Quality Loss = b (2+(-T)2) (Taguchi,1989)
Loss coefficient
Smaller-the-Better Response
• Loss Function L(Y)
Examples:
A 2
L( y)  2 y

L(y)
y
A
L  2 (y2  s2 )

• Signal to Noise Ratio:
1 n 2
SNR  10 log(  yi )
n i 1
 10 log( y 2  s 2 )
• Gas, Energy etc.
consumption
• Noise
• Radiation
Larger-the-Better Response
• Loss Function L(Y)
Examples:
1
L( y )  A 2
y
2
L(y)
y
2
1
s
L  A2 2 (1  3 2 )
y
y
• Signal to Noise Ratio:
1 n 1
SNR  10log(  2 )
n i 1 y i
1
s2
 10log( 2 (1  3 2 ))
y
y
• Mechanical power
• Strength
• Wearout resistance
Nominal-the-Best Response
• Loss Function L(Y)
Examples:
L( y ) 
L(y)
L
y
A 2
2
(
s

(
y

T
)
)
2

• Signal to Noise Ratio:
1. Minimize variance
SNR  10logs 2
2. Bring the mean to the target
SNR  10log(ny 2 )
A
2
(
y

T
)
2
• Dimension (mm)
• Strength
• Voltage (V)
A Robust Design Experiment Layout
3
3
2
n 2 2 1
y 12
y 22
y 32
y 1n
y 2n
y 3n
……………
y 11
y 21
y 31
………....
………....
………....
………....
………....
……………
2 2 1 2
……………
1
2
3
……………
……………
m
1
2
3
……………
1
1
1
……………
i
1
2
3
………....
……………
1 1 1 1
1
2
3
Control Factors
………....
……………
j
Noise Factors
1 y m1
y m2
………....
y mn
Performance Measures
y1, s12 , SNR 1
y2 , s22 , SNR 2
ym , s2m , SNR m
Cookie Recipe Robust Design (A largerthe-better robust design problem)
Objective: To find the control factor levels that maximize cookie
chewiness under uncontrollable effects of the noise factors.
Control Factors:
A: Cooking temperature
B: Syrup content
C: cooking time
D: cooking pan
E: Shortening type
Levels:
Low, high
Low, high
Short, long
Solid, mesh
Corn, coconut
Noise Factors:
Z1: Cookie position
Z2: Temperature at test
Levels:
Side, middle
Low, high
(Source: W.J. Kolarik, 1995, Creating Quality, McGraw-Hill)
The experimental design layout, and data
collected
Chewiness
measurements
Z1: side side middle middle
Z2: low high low
high
y
1 4
s
( yi  y ) 2

3 i 1
loge s
1 4 1
SNR  10 log(  2 )
4 i 1 yi
Response Tables
Taguchi Analysis: y1; y2; y3; y4 versus A; B; C; D; E
Response Table for Signal to Noise Ratios
Larger is better
The following terms cannot be estimated,
and were removed.
A*B
Level
1
2
Delta
Rank
A
22,18
15,70
6,49
2
B
12,69
25,19
12,50
1
C
17,40
20,48
3,08
5
D
16,03
21,85
5,82
3
E
16,74
21,13
4,39
4
A*C
A*E
Response Table for Means
B*C
Level
1
2
Delta
Rank
B*D
B*E
C*D
A
20,250
14,000
6,250
4
B
8,750
25,500
16,750
1
C
12,750
21,500
8,750
2
D
13,750
20,500
6,750
3
E
16,250
18,000
1,750
5
C*E
D*E
Response Table for Standard Deviations
Level
1
2
Delta
Rank
A
4,774
7,781
3,007
1
B
5,437
7,117
1,680
2
C
5,756
6,798
1,042
3
D
6,132
6,422
0,289
5
E
6,665
5,889
0,776
4
Marginal Average (Main Effect) Plots
Main Effects Plot (data means) for SN ratios
A
B
C
24
21
Mean of SN ratios
18
15
12
1
2
1
D
2
1
2
E
24
21
18
15
12
1
2
1
2
Signal-to-noise: Larger is better
Variables A, B, D and E have significant effects on SNR. C does not
seem to be significant. But let us check this with ANOVA as well.
Interaction Plots
Interaction Plot (data means) for SN ratios
1
2
24
21
A
1
2
18
A
15
12
D
1
2
24
21
18
D
15
12
1
2
Signal-to-noise: Larger is better
Only AD interaction could be estimated and it seems to be
insignificant.
ANOVA for SNR
Analysis of Variance for SN ratios
Source
DF
Seq SS
Adj SS
Adj MS
F
P
A
1
84,126
84,126
84,126
28,18
0,034
B
1
312,689
312,689
312,689
104,74
0,009
C
1
18,981
18,981
18,981
6,36
0,128
D
1
67,643
67,643
67,643
22,66
0,041
E
1
38,553
38,553
38,553
12,91
0,069
Residual Error
2
5,970
5,970
2,985
Total
7
527,962
 Stat  DOE  Taguchi  Analyze Taguchi Design-Analysis
choose ‘fit linear model for Signal to Noise ratios’
Predict Results at the Optimal Levels
 Stat  DOE  Taguchi 
Predict Taguchi Results
Predict Results at the Optimal Levels
Taguchi Analysis: y1; y2; y3; y4 versus A; B; C; D; E
Predicted values
S/N Ratio
Mean
StDev
Log(StDev)
35,0761
37,25
5,89143
1,83763
Conduct confirmation
experiments at these
levels!
Factor levels for predictions
A
1
B
2
C
2
D
2
E
2
Eˆ (SNR)  T  (A1 T )  (B2 T )  (C2 T )  (D2 T )  (E2 T )