Transcript
8/12/2019 Design for Robustness
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Black Belt Intermediate
Tools/Refresher Training
DOE for Variance Reduction
and Robust Design
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DoE Analys is Methods
Advantages
Gives you the m& smodel and the interactions
Provides built in sensitivity analysis
Can provide a good estimate of m& sover the selected rangeof independent variables
Disadvantages
Number of runs can be expensive if doing in hardware
Extrapolation outside model is a extremely risky
IVs DVs
y= b0+ b1A + b2B + b3AB+ b4A2 + . . .s= w0+ w1A + w2B + w3AB+ w4A2 + . . .^^
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Potent ial DoE app l icat ions
System Characterization
Flowdown of Requirements
System Optimization Robust Design
Simulation Efficiency
Algorithm Development
Transfer Function Definition
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Robust Design using DoE
A B C . . . . . G Y1 Y2 . . . . . Yn Y-bar s
Innerorthogonal
array
Variation due tonoise and IV
errors
y = b0
+ b1
A + b2
B
+ b3
AB
+ b4
A2 + . . .
s = w0+ w1A + w2B + w3AB+ w4A2 + . . .
^
^
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Sett ing up a Robus t DoE in Mini tab (3
factor example)Set up the DoE from the previous page the same as discussed in DoE training
The Inner Orthogonal Array looks exactly like
our previous DoEs
Gather multiple responses
with each run. Y1, Y2, and
Y3 These columns must be
entered manually.
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Analysis of the Data
Utilizing Row Statistics for the multiple responses, calculate the Mean and Standard Deviationfor each run
Analyze the DoE as you normally would, first using Mean_Y as the response and then
using SD_Y as the response.The DoE results will provide you with an Y-hat and S-hat equation
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g G Industrial SystemsEXERCISE: Robust Design
Your job is to design a catapult that will throw any of three balls (nerf, wiffle, or rubber) the same distance.Your goal is to select and fix the proper setting for Pull Back Angle and Stop Angle such that any of the threeballs will always fly the same distance +/- 6 inches. However, your design will also be judged by how far the
balls fly. The farther the balls fly the higher the price the customer will pay.
Using the Catapult, (or substitute data) build a y-hat and s-hat model using different ball types. Make thedesign robust to ball type using an outer array design. Specifications are +/- 6 accuracy. Confirm your results.
Use Pull Back Angle and Stop Angle as the two Independent Variables
Use a Wiffle, Nerf, and Rubber ball as the noise variables.
Fix the other setting for the Catapult as follows
Cup Height = 1 Hook position = 5
Pin Position = 4 Number of RBs = 1
Your Minitab table should look something like this
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g G Industrial SystemsHand l ing Random Noise as a Resu l t of
Noise Inputs
A B C . . . . . G Y1 Y2 . . . . . Yn Y-bar s
y = b0+ b1A + b2B + b3AB+ b4A2 + . . .
s = w0+ w1A + w2B + w3AB+ w4A2 + . . .
1
Innerorthogonal
array
Variation due to H,I, and J; random
variables
Monte CarloBased Sampling
strategy
^
^
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g G Industrial SystemsRandom Noise thru Sys temat ic Variat ion of
Noise Variables2
H
I
J
Outerorthogonal
array
A B C . . . . . G Y1 Y2 . . . . . Yn Y-bar s
Innerorthogonal
array
H
I
J
+ + + ........
- + + ..........
+ - + .........
- - + ..........
+
+
+
-
+
+
+
-
+
-
-
+
+
+
-
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+
-
+
-
-
-
-
-
A B C . . . . . G Y1 Y2 . . . . . Yn Y-bar s
Variation due to H,I, and J; random
variables
Variation due tosystematic sampling of
H,I, & J
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Varying the Independent Variables with
Mon te Carlo3
Variation due to Athrough Gtolerances
Monte Carlo BasedSampling strategy
y =
s =
^
^
- 1 A + 1
A B C . . . . . G Y1 Y2 . . . . . Yn Y-bar s
Innerorthogonal
array
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Hand l ing Variances in the Independen t
Variables w ith DoE4
Outer orthogonalarray
- 1 A + 1
y = s =^
A B C . . . . . G Y1 Y2 . . . . . Yn Y-bar s
Innerorthogonal
array
Variation due tosystematic sampling of
A - G
A
B...
G
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Hand l ing Variances in Simu lat ion DoEs
5
A B C . . . . . G Y
Innerorthogonal
array
y =^
Can have combinations of options 1 - 4
6
Estimates by considering component
variations in Y-hat Differentiate Y-hat and estimate variance
Using non-replicated designs
Test TolerancesDetermine Ymax and Ymin
S = (Ymax - Ymin) / 6
+ / - Settings aretolerances of A -
G
A B C . . . . . G Y
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DoE App l ications Using
Prototypes
Assessing robustness and building empirical models from
prototypes is possible.
Must be able to actually vary the Independent Variables and assess
the effect on the response.
Assess product reliability
A good way to build low fidelity models for predicting and optimizing
system performance.
Examples of Prototype opportunities
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22Full Factorial
3 Replicates
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Mult ip le Response
Optim izat ion Too l
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Checking for Variance Shifting Factors:
STAT>
ANOVA>
HOMOGENEITYof VARIANCE
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Evaluate eachterm
independently
for effects on
Std. Dev.
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