11 taguchi technique ii

8/3/2019 11 Taguchi Technique II

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Materials Engineering 14Taguchi Technique II


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defined as mean divided by the standard deviation

a response variable that takes both the mean and the variation into consideration

Signal-to-Noise Ratio (S/N ratio)


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Signal-to-Noise Ratio (S/N ratio) made up of the mean level and the variation

around this mean

helps find a setting of the control factors thatgive the best mean level while keeping variationunder control


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Larger the Better

S/N Formulas

)1

(1

log10 / 2i yn

N S


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Nominal is Best

S/N Formulas

e

em

V V Sn N S )(

1

log10 /

)(1

1

)(1

2

2

mie

im

S yn

V

yn

S where:


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A manufacturer of resistors wants to improve yield on substrate chips, many of which have been rejected for thickness problems (tolerance204). They decided to run an experimentaldesign on the following factors:

Example

Factor Level 1 Level 2 Level 3

A Ceramic Material Paraffin Paste Mixture

B Machine Pressure 300 375 450

C Mixing Time 60 90 120

D Temperature 275 350 425


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ResultL9 (3 4 ) A B C D Thickness Totals

1 1 1 1 1 27 31 28 862 1 2 2 2 16 18 20 54

3 1 3 3 3 19 14 21 54

4 2 1 2 3 23 20 25 68

5 2 2 3 1 25 24 26 75

6 2 3 1 2 19 18 20 57 7 3 1 3 2 29 25 27 81

8 3 2 1 3 15 19 18 52

9 3 3 2 1 16 17 18 51

Response Table (Totals)Factor A B C D

Level 1 194 235 195 212

Level 2 200 181 173 192

Level 3 184 162 210 174

Total 578 578 578 578


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Solution

CF n

A

n

A

n

ASS

SS

CF

factor

total

23

22

21

222

2

)()()(5.5685.373,12)18...1627(

5.373,1227

)18...1627(

1.78

5.149184

9200

9194 222

DC B Atotalerror

A

SSSSSSSSSSSS

CF SS


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Source of variation dof SS MS f SS P(%)

A 2 14.5 7.25 1.67 5.82 1

B 2 318.72 159.36 36.72 310.04 55

C 2 76.94 38.47 8.86 68.26 12

D 2 80.28 40.14 9.25 71.16 13error 18 78.06 4.34 112.86 20

Total 26 568.5

Solution

Reponse Table, Averages

Factor A B C D

Level 1 21.6 26.1 21.7 23.6

Level 2 22.2 20.1 19.2 21.3

Level 3 20.4 18 23.3 19.3

OptimumSettings A 3 B2 C2 D3

target thickness valuesnearest 20


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Compute for the corresponding S/N Ratios Nominal is Best (as required by the problem)

Solution

e

em

V

V Sn N S

)(1

log10 /

)(1

1

)(1

2

2

mie

im

S yn

V

yn

S

76.2234.4

)34.433.465,2(31

log10 / N S

34.4]33.465,2)283127[(2

1

33.465,2)283127(31

222

2

e

m

V

S


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Solution

Response Table (S/N Totals)

Factor A B C D

Level 1 55.8 64.5 66.8 75.4Level 2 72.7 65.5 62.8 67.3

Level 3 65.6 64.1 64.5 51.4

Total 194.1 194.1 194.1 194.1

Original Settings A 3 B2 C2 D3

Revised Settings A 2 B2 C1 D1

choose highest S/N ratio

L9 (3 4 ) A B C D S/N Ratio

1 1 1 1 1 22.82 1 2 2 2 19.1

3 1 3 3 3 13.9

4 2 1 2 3 19.1

5 2 2 3 1 28.0

6 2 3 1 2 25.6

7 3 1 3 2 22.68 3 2 1 3 18.4

9 3 3 2 1 24.6


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Source of Variation SS dof MS f

SS P(%)

A 48.0 2 24.0 30.0 46.4 30.9

B 0.3 (2)

C 2.7 (2)D 99.4 2 49.7 62.1 97.8 65

error 3.0 4 0.8 6.2 4.1

Total 150.4 8 100

Solution

Therefore, choosing the correct settings for the ceramic material and the heat treat temperature will reduce the variation in the thickness of the substrate chips. Machine pressure and mixing time will be adjusted tomove the process mean to the target value.


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Identify control factors

Determine optimum levels for control factors

Identify signal factors using raw data ANOVA

Determine optimum levels for signal factors

Perform confirmation run

Control critical control and signal factors

Summary of Steps for Analysis


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Additional Notes The first ANOVA table is used to determine the

signal factors while the second ANOVA table isused to identify the control factors.

Factor settings that will be considered in theprocess line would depend on the revised

setting, and the signal factors may be adjusted toproduce results close to the desired value.


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Exercise A manufacturer of rubber hosing wants toincrease the strength of his product. Hedetermines four factors that could influence hisprocess. He sets them at the following levels:

Factor Level 1 Level 2 Level 3

A Machine Temperature 300 350 400

B Reaction Time 5 10 15

C Agitation Speed 100 150 200

D Silicon Excess Rate 10 20 30


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11 taguchi technique ii

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