robust design
DESCRIPTION
New vision about robust designTRANSCRIPT
![Page 1: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/1.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
1
Robust Design
A New Definition of Quality.The Signal-to-Noise Ratio.Orthogonal Arrays.
![Page 2: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/2.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
2
The Taguchi Philosophy
Quality is related to the total loss to society due to functional and environmental variance of a given productQuality is related to the total loss to society due to functional and environmental variance of a given product
Taguchi's method focuses on Robust Design through use of:• S/N Ratio to quantify quality• Orthogonal Arrays to investigate quality
Taguchi starts with a new definition of Quality:
![Page 3: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/3.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
3
Meeting the specs vs. hitting the target
better quality worse quality
mm-5 m+5
![Page 4: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/4.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
4
Quadratic Loss Function:
L(y) = k (y - m)2
Fig 2.3 pp 18 fromQuality Engineering Using Robust Design
by Madhav S. PhadkePrentice Hall 1989
![Page 5: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/5.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
5
Quadratic Loss Function on Normal Distribution
Average quality loss due to µ and σ:
Fig 2.5 pp 26
E(Q) = k [(µ-m) + σ ] 2 2
![Page 6: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/6.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
6
Exploiting non-linearity:
Fig 2.6 pp 28
![Page 7: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/7.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
7
Parameters are classified according to function:
Fig 2.7 pp 30
![Page 8: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/8.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
8
Orthogonal Arrays
b = (XTX)-1XTy V(b) = (XTX)-1σ2
During Regression Analysis, an orthogonal arrangement of the experiment gave us independent model parameter estimates:
Orthogonal arrays have the same objective:For every two columns all possible factor combinations occur equal times.
L4(23) L9(34) L12(211) L18(21 x 37)
![Page 9: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/9.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
9
Simple CVD experiment for defect reductionmax n = -10 log (MSQ def)
10
![Page 10: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/10.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
10
Simple CVD experiment for defect reduction (cont)
Using the L9 orthogonal array:
![Page 11: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/11.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
11
Estimation of Factor Effects (ANOM)
m = 19 η1+η2+η3+...+η9
mA1 = 13 η1+η2+η3
mA2 = 13 η4+η5+η6
mA3 = 13 η7+η8+η9...
mB2 = 13 η2+η5+η8...
mD3 = 13 η3+η4+η8
η Ai,Bj,Ck,Dl = μ+αi+βj+γk+δl+eαi = 0Σ βi = 0Σ γi = 0Σ δi = 0Σ
![Page 12: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/12.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
12
Analysis of CVD defect reduction experiment
Fig 3.1 pp 46Tab 3.4 pp 55
![Page 13: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/13.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
13
ANOVA for CVD defect reduction experiment
Grand total sum of squares: ηi2 = 19,425 (dB)2Σi=1
9
Total sum of squares: ηi-m 2 = 3,800 (dB)2Σi=1
9
Sum of squares due to mean: m2 = 15,625 (dB)2Σi=1
9
Sum of squares due to error: ei2 = ??? (dB)2Σi=1
9
Sum of squares due to A: 3 mAi-m 2 = 2,450 (dB)2Σi=1
3
![Page 14: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/14.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
14
ANOVA for CVD defect reduction experiment (cont)
![Page 15: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/15.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
15
Estimation of Error Variance
The experimental error is estimated from the ANOVA residuals.
It is then used to estimate the error of the effects and to determine their significance at the 5% level.
![Page 16: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/16.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
16
Confirmation ExperimentOnce the optimum choice has been made, it is tested by performing a confirmation run.This run is used to "validate" the model as well as confirm the improvements in the process.
Variance of prediction (for the model)
σpred2 = σe2n0
+ σe2nr
This gives us +/-2σ limits on the confirmation experiment.
1n0
σe2 = 1n + 1
nA 1 - 1n + 1
nB1 - 1n σe2
![Page 17: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/17.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
17
The additive model
Fig 3.3 pp 63, enlarged 120%
Since we assumed additive model, we must make sure that there are no interactions:
![Page 18: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/18.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
18
Example: Large CVD experiment.
Objectives:
a) reduce defects n = -10 log (MSQ Def)
b) maximize S/N of rate n'= 10 log (µ / σ )
c) adjust poly thickness to a 3600 Å target.
10
102 2
![Page 19: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/19.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
19
Choosing the Control Factors
Tab 4.6-7 pp 88-90
![Page 20: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/20.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
20
Using the L18 orthogonal array...
Tab 4.3 pp 78, enlarged 120%
![Page 21: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/21.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
21
Data summary for large CVD experiment:
Tab 4.5 pp 85, enlarged 120%
![Page 22: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/22.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
22
Data analysis for large CVD experiment (cont)
Fig 4.5 pp 86, enlarged 120%
![Page 23: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/23.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
23
ANOVA table for large CVD experiment: η
![Page 24: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/24.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
24
ANOVA table for large CVD experiment : η’
![Page 25: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/25.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
25
ANOVA tables for large CVD experiment: η’’
![Page 26: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/26.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
26
Combined Prediction Using the Additive Model
Tab 4.6-7 pp 88-90
![Page 27: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/27.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
27
Verification for large CVD experiment
Tab 4.10-11 pp 92
for further reading: Quality Engineering Using Robust Design by Madhav S. PhadkePrentice Hall 1989
![Page 28: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/28.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
28
“Inner” and “Outer” Arrays
• Often one want to improve performance based on some “control”factors, in the presence of some “noise” factors.
• Two arrays are involved: the inner array explores the “control”factors, and the entire experiment is repeated across an array of the noise factors.
• Inner arrays are typically orthogonal designs• Outer arrays are typically small, 2-level fractional factorial designs.
![Page 29: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/29.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
29
Why use S/N Ratios?
• They lead to an optimum through a monotonic function.
• They help improve additivity of the effects.
⎟⎠
⎞⎜⎝
⎛−=
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
∑
∑
ii
STB
i iLTB
YnN
S
YnNS
sY
NS
2
2
2
2
1log10
11log10
log10Nominal is best:
Larger is better:
Smaller is better:
![Page 30: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/30.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
30
Taguchi vs. RSM
Taguchi RSMSmall number of runs Explicit control of InteractionsEngineering Intuition Statistical Intuition“Complete” package Training IssuesAdditive Models More General ModelsOrthogonal Arrays Fractional FactorialsA “Philosophy” A Tool
![Page 31: Robust Design](https://reader033.vdocument.in/reader033/viewer/2022051622/55cf974e550346d03390e31a/html5/thumbnails/31.jpg)
Lecture 9: Robust Design
SpanosEE290H F05
31
Design of Experiments Comparison of Treatments Blocking and Randomization Reference Distributions ANOVA MANOVA Factorial Designs Two Level Factorials Blocking Fractional Factorials Regression Analysis Robust Design
Analysis
Modeling