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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