Introduction to Robust Design
and Use of the Taguchi Method
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The Design Axiom & Taguchi Method
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What is Robust Design
Robust design: a design whose performance is insensitive to variations.
Simply doing a trade study to optimize the value of F
would lead the designer to pick this point
Example: We want to pick x to maximize F
F
x
This means that
values of F as
low as this can
be expected!
What if I pick this
point instead?
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What is Robust Design
• Robust has many definitions here are a few that we found.
• A process that does not change with changing noise.
• Designing products and processes that are minimally
impacted by external forces such as environment, customer
use, or manufacturing conditions
• The cost of failure in the Robust Design method helps
ensure customer satisfaction. Robust Design focuses on
improving the fundamental function of the product or
process. Robust Design facilitates flexible designs and
concurrent engineering. It is the most powerful method
available to reduce product cost, improve quality, and reduce
development interval
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What is Robust Design
• The robust design process is frequently formalized through
“six-sigma” approaches (or lean/kaizen approaches)
• Six Sigma is a business improvement methodology
developed at Motorola in 1986 aimed at defect reduction in
manufacturing.
• Numerous organizations that have implemented these
systems, including:
• Aerospace (NASA, Boeing, Nothrop Grumman)
• automobiles,
• xerography, telecommunications, electronics, software,
• etc
Problems Using Robust Design
• An example of a problem with Robust Design: A team of engineers was working on the design of a radio receiver for ground to aircraft communication. This receiver required high reliability, and low bit error rate for data transmission. Building series of prototypes to sequentially eliminate problems would be expensive. The other problem was that computer simulation effort for evaluating a single design was time consuming and expensive. So, how can you speed up development but assure reliability
• Another example: A manufacturer introduced a high speed copy machine only to find that the paper feeder jammed almost ten times more frequently than what was planned. The traditional method for evaluating the reliability of a single new design idea took several weeks. How can the company conduct the needed research in a short time and come up with a design that would not embarrass the company
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Example of Lean Activities at NASA
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QPMR_hq20070801ecm
Progress on Ares “Lean” Activities (cont’d)
• Some example results that are being incorporated into mainline efforts:
– Streamlining boards/panels approval process: reduced from 5 to 2 the
number of board approval steps within Ares
– Design reviews process: 39% reduction in time to conduct design reviews
– Time for risk approval: 66% reduction in the time to evaluate and approve
a candidate risk through the risk management system
– Trade studies: 50% reduction in the number of steps to conduct formal
trade studies - from idea to decision
– Task description sheet (TDS) development for ADAC cycles: from 3% to
80% automation
Back to Project Summary Quad Chart
Less Time on Waste……More Time for
Value Added Work
Taguchi Method for Robust Design
• Systemized statistical approach to product and process
improvement developed by Dr. G. Taguchi
• Approach emphasizes moving quality upstream to the
design phase
• Based on the notion that minimizing variation is the primary
means of improving quality
• Special attention is given to designing systems such that
their performance is insensitive to environmental changes
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The Basic Idea Behind Robust Design
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Reduce
Variability
Reduce
Cost
Increase
Quality
ROBUSTNESS ≡ QUALITY
Any Deviation is Bad: Loss Functions
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x xT xUSL xLSL
No
Loss Loss Loss
x xT xUSL xLSL
Loss = k(x-xT)2
The traditional view states that there is no
loss in quality (and therefore value) as
long as the product performance is within
some tolerance of the target value.
xLSL = Lower Specification Limit xUSL = Upper Specification Limit xT = Target Value
In Robust Design, any deviation from the
target performance is considered a loss in
quality the goal is to minimize this loss.
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Define C = The unit repair cost when the deviation from target equals the maximum tolerance level
= Tolerance interval (allowable parameter variation from target to SL)
T = Target value
Y = The actual metric value for a specific product
V = Deviation from target = Y-T
L(V) = Economic penalty incurred by the customer as a result of quality deviation from target (The quality loss)
Computing The Taguchi QLF
The Loss Function
L(V) = C(V/)2
Example: The repair cost for an engine shaft is $100. The shaft diameter is
required
to be 101 mm. On average the produced shafts deviates 0.5 mm from target.
Determine the mean quality loss per shaft using the Taguchi QLF.
Solution: L(0.5) = C·(V/)2 = 100·(0.5/1)2 = 100·0.25 = $25 per unit
Overview of Taguchi Parameter Design Method
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1. Brainstorming
2. Identify Design Parameters
and Noise Factors
3. Construct Design of
Experiments (DOEs)
4. Perform Experiments
5. Analyze Results
Design Parameters: Variables under your control
Noise Factors: Variables you cannot control or
variables that are too expensive
to control
Ideally, you would like to investigate all
possible combinations of design parameters
and noise factors and then pick the best
design parameters. Unfortunately, cost and
schedule constraints frequently prevent us
from performing this many test cases – this is
where DOEs come in!
Taguchi Design Representatif
• The response is the output of the design, which is characterized by FRs.
• Signal factors (M) are parameter that can be set to achieve specific
response (i.e., FRs).
• Control factors (z) are DPs with which designer can control the output
response (i.e., FRs)
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• Scaling factors (R) are special cases
of control factors that can be altered to
achieve a desired relationship between
a signal factor and output response
• Noise factors (x) are those variables
in a design that are uncontrolable
or unpredictable, and represent an
uncertainty that desired output response
will be achieved.
Design of Experiments (DOE)
Exp.
Num
Variables
X1 X2 X3 X4
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1
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Exp.
Num
Variables
X1 X2 X3
1 1 1 1
2 1 2 2
3 2 1 2
4 2 2 1
Design of Experiments: An information gathering exercise. DOE is a
structured method for determining the relationship between process inputs
and process outputs.
L9(34) Orthogonal Array
L4(23) Orthogonal Array
L4(23)
Number of
Experiments
Number of
Variable Levels Number of
Variables
Here, our objective is to intelligently choose the
information we gather so that we can determine the
relationship between the inputs and outputs with the
least amount of effort
Num of Experiments must be ≥ system degrees-of-freedom:
DOF = 1 + (# variables)*(# of levels – 1)
N3 1 2 2 1
N2 1 2 1 2
N1 1 1 2 2
1 2 3 4
Inner & Outer Arrays
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Experim
ent N
um
ber
Design Parameters Noise E
xperim
ent N
um
Performance
Characteristic
evaluated at the
specified design
parameter and
noise factor values
Inner Array – design parameter matrix
Outer Array – noise factor matrix
X1 X2 X3 X4
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1
y11 = f {X1(1), X2(1),
X3(1), X4(1),
N1(1), N2(1), N3(1)}
y52 = f {X1(2), X2(2),
X3(3), X4(1),
N1(1), N2(2), N3(2)}
Processing the Results (1 of 2)
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Experim
ent N
um
ber
Design Parameters
Nois
e
Experiment Num
Performance
Characteristic
evaluated at the
specified design
parameter and
noise factor values
Compute signal-to-noise (S/N) for each row
n
j
iji yn
NS1
21log10/
Maximizing performance
characteristic
n
j ij
iyn
NS1
2
11log10/
Inner Array – design parameter matrix
Outer Array – noise factor matrix
Minimizing performance
characteristic
Processing the Results (2 of 2)
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Experim
ent N
um
ber
Design Parameters
Sig
nal-to
-Nois
e (
S/N
)
Isolate the instances of each design parameter at each
level and average the corresponding S/N values.
X1 X2 X3 X4
1 1 1 1 1 S/N1
2 1 2 2 2 S/N2
3 1 3 3 3 S/N3
4 2 1 2 3 S/N4
5 2 2 3 1 S/N5
6 2 3 1 2 S/N6
7 3 1 3 2 S/N7
8 3 2 1 3 S/N8
9 3 3 2 1 S/N9
X2 is at level 1 in
experiments 1, 4, & 7
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//// 741
)1(1
NSNSNSNSAvg T
Visualizing the Results
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Plot average S/N for each design parameter
ALWAYS aim to maximize S/N
In this example, these are the best cases.
Robust Design Example
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Compressed-air cooling system example
Example 12.6 from Engineering Design, 3rd Ed., by G.E. Dieter
(Robust-design_Dieter-chapter.pdf)
Pareto Plots and the 80/20 Rule
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20% of the variables in any given system control 80% of the variability in
the dependent variable (in this case, the performance characteristic).
0% 20% 40% 60% 80% 100%
X1
X2
X3
X4
X5
X6
X7
X8
X9
X10
Cumulative effect
Individual design parameter effects
20% of the variables
80% of the variability in
the dependent variable
Conclusions
• Decisions made early in the design process cost very little in
terms of the overall product cost but have a major effect on
the cost of the product
• Quality cannot be built into a product unless it is designed
into it in the beginning
• Robust design methodologies provide a way for the designer
to develop system that is (relatively) insensitive variations
• Improvement through quality, reliability, and durability.
• Manufacturing cost reduction & Design cycle time reduction.
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