Robust Design
ME 470
Systems Design
Fall 2011
What are the benefits of increasing the quality of a
product?
Customers will pay for
increased quality!
Customers will be loyal
for increased quality!
In 1980s, Ford discovered that the warranty claims on US
built products were far greater than Japanese built
product.
All products met the design specifications.
There was less variation in the
Japanese products
There are measurable results from less variation.
• Better performance
• Lower costs due to less scrap, less rework and less
inventory!
• Lower warranty costs
Taguichi developed a loss function to describe the
effects of variation.
Target
Traditional Approach
Target
Taguichi Definition
Why We Need to Reduce Variation
LSL
Nom
USL
Cost
Low Variation;
Minimum Cost
Cost
LSL
Nom
USL
High Variation;
High Cost
Why We Need to Shift Means
LSL
Nom
USL
Cost
Off target;
minimum
variability
Cost
LSL
Nom
USL
Off target;
barely
acceptable
variability
Definition of Robust Design
Robustness is defined as a condition in which the product or
process will be minimally affected by sources of variation.
A product can be robust:
Against variation in raw materials
Against variation in manufacturing conditions
Against variation in manufacturing personnel
Against variation in the end use environment
` Against variation in end-users
Against wear-out or deterioration
If your predicted design capability looks like this, you do not have a functional performance
need to apply Robust Parameter Design methods. Cost, however, may still be an issue if the
input (materials or process) requirements are tight!
If your predicted capability looks like this, you have a need to both reduce the variation
and shift the mean of this characteristic - a prime candidate for the application of Robust
Parameter Design methods.
Noise Factors are variables or parameters that affect system
performance and are difficult and or expensive to control.
Examples include climate, part tolerances, corrosion, or wear
over the life of a component.
Noise factors can be classified in many ways – customer
noise, manufacturing noise, and life cycle noise can be
useful classifications.
Customer usage noise



Maintenance practice
Geographic, climactic, cultural, and other issues
Duty cycle
Manufacturing noise



Processes
Equipment
Materials and part tolerances
Aging or life cycle noise



Component wear
Corrosion or chemical degradation
Calibration drift
Pressure Variation
Operator Variation
1008
1
Pressure (psia)
UCL=1007
1004
Mean=1000
1000
996
LCL=993.6
992
0
10
20
30
40
50
Observation Number
Operating Temperature
Fluid Viscosity
124
UCL=123.1
82
122
UCL=81.15
81
121
80
Mean=120.1
120
119
%A
Temperature (deg C)
123
118
LCL=117.0
117
116
79
Mean=78.18
78
77
76
0
10
20
30
40
50
LCL=75.22
75
Observation Number
0
10
20
30
40
Observation Number
50
There are several countermeasures for dealing with noise.




Ignore them!
– Will probably cause problems later on
Turn a Noise factor into a Control factor
– Maintain constant temperature in the plant
– Restrict operating temperature range with addition of
cooling system
 ISSUE : Almost always adds cost & complexity!
Compensate for effects through feedback
– Adds design or process complexity
Discover and exploit opportunities to shift sensitivity
– Interactions
– Nonlinear relationships
The Parameter Diagram is another way to describe an
Engineering System.
The Parameter Diagram
Control
Factors
Inputs
X1
X2
.
.
.
Xn
System
Noise
Factors
Z1
Z2
.
.
.
Zn
Outputs Y1
Y2
.
.
.
Yn
The traditional approach to variation reduction is to reduce
variation in X’s
USL
LSL
Y
Y
=f(
=f(
X1
X1
X2
X2
Xn
Xn
)
)
What are the advantages and disadvantages of this
approach?
Robust Design identifies factors that cause variation in Y.

Variation in Y can be described using the
mathematical model:
Sy 
s s
2
2
x1
x2
 ...  s x  s z  s z  ...  s z
2
n
where Xn are Control Factors
Zn are Noise Factors
2
1
2
2
2
n
Factors That Have No Effects
• A factor that has little or no
effect on either the mean or
the variance can be termed
an Economic Factor
• Economic factors should be
set at a level at which costs
are minimized, reliability is
improved, or logistics are
improved
Main Effects Plot
Y
SY2
A
Another Source of Variance Effects: Nonlinearities
High sensitivity
region
Expected
Distribution
of Y
Low sensitivity
region
Factor A has an effect
on both mean and
variance
Two Possible Control
Conditions of A
Summary of Variance Effects
Mean Shift
Variance Shift
A+
A+
A-
A-
Noise
Mean and Variance Shift
A+
A-
Noise
Noise
Non-linearity
Robust Design Approach, 2 Steps
Variance Shift
Step 1
Reduce the variability by exploiting the
active control*noise factor interactions
and using a variance adjustment factor
Step 2
Shift the mean to the target using a mean
adjustment factor
Factorial and RSM experimental designs are
used to identify the relationships required to
perform these activities
A+
A-
Noise
Mean Shift
B+
BNoise
Design Resolution
• Full factorial vs. fractional factorial
• In our DOE Frisbee thrower experiment, we used a full
factorial. This can become costly as the number of variables
or levels increases.
• As a result, statisticians use fractional factorials. As you might
suspect, you do not get as much information from a fractional
factorial.
• For the screening run in lab last week, we started with a halffractional factorial. (Say that fast 5 times!)
Fractional Factorials
A Fractional Factorial Design is a factorial design
in which all possible treatment combinations
of the factors are NOT run. The runs are just a
FRACTION of the full factorial matrix. The
resulting design matrix will not be able to
estimate some of the effects, often the
interaction effects. Minitab and your statistics
textbook will tell you the form necessary for
fractional factorials.
-1, +1, +1
+1, +1, +1
-1, +1, -1
+1, +1, -1
-1, -1, +1
+1, -1, +1
-1, -1, -1
+1, -1, -1
Design Resolution
• Resolution V (Best)
– Main effects are confounded with 4-way interactions
– 2-way interactions are confounded with 3-way interactions
• Resolution IV
– Main effects are confounded with 3-way interactions
– 2-way interactions are confounded with other 2-way interactions
• Resolution III (many Taguchi arrays)
– Main effects are confounded with 2-way interactions
– 2-way interactions may be confounded with other 2-ways
Minitab Explanation for Screening Run in Lab
Factors: 4
Base Design:
Runs: 16
Replicates:
Blocks: 1 Center pts (total):
4, 8 Resolution: IV
2
Fraction: 1/2
0
Design Generators: D = ABC
Alias Structure
I + ABCD
A + BCD
B + ACD
C + ABD
D + ABC
AB + CD
AC + BD
AD + BC
A = Ball Type
B = Rubber Bands
C = Angle
D = Cup Position
Means main effects can not be
distinguished from 3-ways.
Means certain 2-way interactions
can not be distinguished.
Hubcap Example of Propagation of
Errors
The example is taken from a paper presented at the
Conference on Uncertainty in Engineering Design
held in Gaithersburg, Maryland May10-11, 1988.
WHEELCOVER REMOVAL
WHEELCOVER RETENTION
COMPETING GOALS
OPERATIONAL GOAL
Retention Force, (N)
Retention Force, (N)
Retention Force, (N)
Retention Force, (N)