Design for Robustness

8/12/2019 Design for Robustness

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Proprietary to General Electric Company

g G Industrial Systems

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


9/22Proprietary to General Electric Company

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

^

^



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

+ + + ........

- + + ..........

+ - + .........

- - + ..........

+

+

+

-

+

+

+

-

+

-

-

+

+

+

-

-

+

-

+

-

-

-

-

-

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




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




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




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




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




Mult ip le Response

Optim izat ion Too l




Checking for Variance Shifting Factors:

STAT>

ANOVA>

HOMOGENEITYof VARIANCE




Evaluate eachterm

independently

for effects on

Std. Dev.


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Design for Robustness

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