Copy of L18 Small Taguchi 1

Title of the problem Polysi Deposition for VLSI

Write an Introduction to the problem Decrease the defects

Team members

Duration start date 27-Sep-06

Date today 08-Apr-23

Last Modified on 2-Mar-2007

password info for P. R. Apte L18**** L18 :- 1 Control factor with 2-Levels and upto 7 control factors with 3 levels each

This Excel Sheet is created by Dr. P. R. Apte, IIT Bombay, Powai, Mumbai-400 076, India e-mail: apte@ee.iitb.ac.in , web-page : http://www.ee.iitb.ac.in/~apte

Polysi Deposition for VLSI

Decrease the defects

L18 :- 1 Control factor with 2-Levels and upto 7 control factors with 3 levels each

This Excel Sheet is created by Dr. P. R. Apte, IIT Bombay, Powai, Mumbai-400 076, India e-mail: apte@ee.iitb.ac.in , web-page : http://www.ee.iitb.ac.in/~apte

YOU MAY OVER-WRITE ON THE 'orange' TEXT

IN ALL THE SHEETS

This Excel Sheet is created by Dr. P. R. Apte, TIFR, Mumbai, India e-mail: apte@tifr.res.in , web-page : http://www.ee.iitb.ac.in/~apte

USERNAMESTART DATE

STEP 1: Identify Main Function, failure mode and side effects

STEP 3: Identify Quality Characteristics and Objective Function

STEP 4: Identify Control Factors and their Levels

STEP 5: Identify Orthogonal Array (degrees of freedom for error)

Last Modified on 15-Feb-2007

26-Sep-06 TYPE THE DATE HERE

PolySilicon is deposited by "Low-Pressure Chemical Vapor Deposition" Technique. However, there are 3 problems : (1) Thickness Non uniformity, (2) defects (pin holes and/or particulates) and (3) Deposition Rate

STEP 2: Identify Noise factors, testing conditions (to capture the effects of noise)

Internal NoIsE parameters: All process parameters may have 'variations' External NoIsE parameters: power supply, gas pressures, ambient temperature, humidity etc may also have 'variations'

However, there are 3 quality characteristics of interest: (1) Defects (pin holes and/or particulates) : smaller-the-better,(2) Deposition rate : Larger-the-better and(3) Thickness non-uniformity : Nominal-the-Best, ideal value 1000 Ang.,

Assumptions are : All 6 control factors are ORTHOGONAL to each other and hence there would not be any need to study their interactions with each other

L18 array is chosen

1 control factor with 2 levels and upto 7 control factors with 3 levels are allowed.

Interaction AXB can be studied,

Reference : "Quality Engineering using Robust Design" by M.S. Phadke, Prentice Hall 1989, Chapter 4

This Excel Sheet is created by Dr. P. R. Apte, TIFR, Mumbai, India e-mail: apte@tifr.res.in , web-page : http://www.ee.iitb.ac.in/~apte

TODAY08-Apr-23

PolySilicon is deposited by "Low-Pressure Chemical Vapor Deposition" Technique. However, there are 3 problems : (1) Thickness Non uniformity, (2) defects (pin holes and/or particulates) and (3) Deposition Rate

Internal NoIsE parameters: All process parameters may have 'variations' External NoIsE parameters: power supply, gas pressures, ambient temperature, humidity etc may also have 'variations'

However, there are 3 quality characteristics of interest:

Defects (pin holes and/or particulates) : smaller-the-better,(2) Deposition rate : Larger-the-better and(3) Thickness non-uniformity : Nominal-the-Best, ideal value 1000 Ang.,

Assumptions are : All 6 control factors are ORTHOGONAL to each other and hence there would not be any need to study their interactions with each other

L18 array is chosen

1 control factor with 2 levels and upto 7 control factors with 3 levels are

Interaction AXB can be studied,

TESTS Smaller-the-better Nominal-the-Best Larger-the-Better Mean

Defects YES

Type YES or NOType Quality

Characteristic name/identifier

Repetitions in each row of expt (due to NoIsE Factor

combinations)Repetitions of confirmation expt

(using the 'best' settings)

You may overtype the number of measurements

for each experiment.(due to NoIsE Factor

combinations)

Type the number of times the 'BEST" experiment (with 'best'

CF levels) is repeated

LEVELSColumn # CONTROL FACTORS \ LEVELS 1 2

1 empty empty empty2 Temperature T1 T23 Pressure P1 P24 Nitrogen N1 N25 Silane S1 S26 Initial Settling time I1 I27 - - -8 Cleaning Method C1 C2

NoIsE FACTORS \ LEVELS NoIsE Level 1 NoIsE Level 2

U NoIsE FACTOR 1 U1 U2

V NoIsE FACTOR 2 V1 V2

W NoIsE FACTOR 3 W1 W2

X NoIsE FACTOR 4 X1 X2

"empty", "-" are reservedfor indicatiing 'blank' columns

Go to a cell, delete contents (using 'delete' key) and write the Control Factor names (necessary) & Level names (optional)

T3P3N3S3I3-C3

NoIsE Level 3 NUMBER OF LEVELS

U3 3 Type 2 or 3 V3 3

Go to a cell, delete contents (using 'delete' key) and write the

Control Factor names (necessary) & Level names (optional)

Go to a cell, delete contents (using 'delete' key) and write the Control Factor names (necessary) & Level names (optional)

WHICH OUTER-ARRAY IS

REQUIRED =

L18 ArrayControl Factors

Expt. No. A B C D E F G H1 1 1 1 1 1 1 1 12 1 1 2 2 2 2 2 23 1 1 3 3 3 3 3 34 1 2 1 1 2 2 3 35 1 2 2 2 3 3 1 16 1 2 3 3 1 1 2 27 1 3 1 2 1 3 2 38 1 3 2 3 2 1 3 19 1 3 3 1 3 2 1 210 2 1 1 3 3 2 2 111 2 1 2 1 1 3 3 212 2 1 3 2 2 1 1 313 2 2 1 2 3 1 3 214 2 2 2 3 1 2 1 315 2 2 3 1 2 3 2 116 2 3 1 3 2 3 1 217 2 3 2 1 3 1 2 318 2 3 3 2 1 2 3 1

9 6repetition number =

repetition number =

Total no. of expts =

L18 Array is always the same

and hence no need to

change this - EVER

Expt. No.Control Factors Assigned to columns

empty Pressure Nitrogen Silane

1 empty T1 P1 N1 S1 I12 empty T1 P2 N2 S2 I23 empty T1 P3 N3 S3 I34 empty T2 P1 N1 S2 I25 empty T2 P2 N2 S3 I36 empty T2 P3 N3 S1 I17 empty T3 P1 N2 S1 I38 empty T3 P2 N3 S2 I19 empty T3 P3 N1 S3 I2

10 empty T1 P1 N3 S3 I211 empty T1 P2 N1 S1 I312 empty T1 P3 N2 S2 I113 empty T2 P1 N2 S3 I114 empty T2 P2 N3 S1 I215 empty T2 P3 N1 S2 I316 empty T3 P1 N3 S2 I317 empty T3 P2 N1 S3 I118 empty T3 P3 N2 S1 I2

repetition number = 9 6

NUMBER OF MEASUREMENTS

Temperature

Initial Settling time

repetition number =

CHOSEN FACTORIAL OR ORTHOGONAL

1 2 3 4 5 6 7

U NoIsE FACTOR 1 U1 U1 U1 U2 U2 U2 U3V NoIsE FACTOR 2 V1 V2 V3 V1 V2 V3 V1W NoIsE FACTOR 3 W1 W2 W3 W2 W3 W1 W3

Control Factors Assigned to columns

- Cleaning Method

- C1 1.00E+00 0.00E+00 1.00E+00 2.00E+00 0.00E+00 0.00E+00 1.00E+00

- C2 1.00E+00 2.00E+00 8.00E+00 1.80E+02 5.00E+00 0.00E+00 1.26E+02

- C3 3.00E+00 3.50E+01 1.06E+02 3.60E+02 3.80E+01 1.35E+02 3.15E+02

- C3 6.00E+00 1.50E+01 6.00E+00 1.70E+01 2.00E+01 1.60E+01 1.50E+01

- C1 1.72E+03 1.98E+03 2.00E+03 4.87E+02 8.10E+02 4.00E+02 2.02E+03

- C2 1.35E+02 3.60E+02 1.62E+03 2.43E+03 2.07E+02 2.00E+00 2.50E+03

- C3 3.60E+02 8.10E+02 1.22E+03 1.62E+03 1.17E+02 3.00E+01 1.80E+03

- C1 2.70E+02 2.73E+03 5.00E+03 3.60E+02 1.00E+00 2.00E+00 1.00E+04

- C2 5.00E+03 1.00E+03 1.00E+03 3.00E+03 1.00E+03 1.00E+03 3.00E+03

- C1 3.00E+00 0.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00 1.00E+00

- C2 1.00E+00 0.00E+00 1.00E+00 5.00E+00 0.00E+00 0.00E+00 1.00E+00

- C3 3.00E+00 1.62E+03 9.00E+01 2.16E+02 5.00E+00 4.00E+00 2.70E+02

- C2 1.00E+00 2.50E+01 2.70E+02 8.10E+02 1.60E+01 1.00E+00 2.25E+02

- C3 3.00E+00 2.10E+01 1.62E+02 9.00E+01 6.00E+00 1.00E+00 6.30E+01

- C1 4.50E+02 1.20E+03 1.80E+03 2.53E+03 2.08E+03 2.08E+03 1.89E+03

- C2 5.00E+00 6.00E+00 4.00E+01 5.40E+01 0.00E+00 8.00E+00 1.50E+01

- C3 1.20E+03 3.50E+03 3.50E+03 1.00E+03 3.00E+00 1.00E+00 1.00E+04

- C1 8.00E+03 2.50E+03 3.50E+03 5.00E+03 1.00E+03 1.00E+03 5.00E+03

Total no. of expts = 18

CHOSEN FACTORIAL OR ORTHOGONAL

ARRAY==>L9

NoIsE Factor combinations used as repetitions for each (row of) experiment

L4 / F4 F6 F8 / L8 L9 L12

REPETITIONS

NoIsE FACTOR names

meas # 1

meas # 2

meas # 3

meas # 4

meas # 5

meas # 6

meas # 7

F2 EXPT NO. 1 2 3 4 5 6 7A 1 2BCD

F3 EXPT NO. 1 2 3 4 5 6 7A 1 2 3BCD

F4 EXPT NO. 1 2 3 4 5 6 7A 1 1 2 2B 1 2 1 2CD

F6 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 2 2 2B 1 2 3 1 2 3CD

F8 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 2 2 2B 1 1 2 2 1 1 2C 1 2 1 2 1 2 1D

F12 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 1 1 2B 1 1 1 2 2 2 1C 1 2 3 1 2 3 1D

F16 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 1 1 1

B 1 1 1 1 2 2 2C 1 1 2 2 1 1 2D 1 2 1 2 1 2 1

L4 EXPT NO. 1 2 3 4 5 6 7A 1 1 2 2B 1 2 1 2C 1 2 2 1D

L8 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 1 2 2 2B 1 1 2 2 1 1 2C 1 2 1 2 1 2 1D 1 2 1 2 2 1 2

L9 EXPT NO. 1 2 3 4 5 6 7A 1 1 1 2 2 2 3B 1 2 3 1 2 3 1C 1 2 3 2 3 1 3D 1 2 3 3 1 2 2

U3 U3V2 V3W1 W2

1.00E+00 0.00E+00

3.00E+00 1.00E+00

5.00E+01 1.80E+02

4.00E+01 1.80E+01

3.60E+02 1.20E+01

2.70E+02 3.50E+01

7.20E+02 3.15E+02

2.25E+02 1.00E+00

2.80E+03 2.00E+03

0.00E+00 1.00E+00

8.00E+00 3.00E+00

3.00E+00 0.00E+00

1.50E+01 3.90E+01

1.80E+02 2.50E+01

1.00E+00 1.00E+00

6.00E+02 8.00E+00

2.00E+03 2.00E+03

NoIsE Factor combinations used as repetitions for each (row of) experiment

L4 / F4 F6 F8 / L8 L9 L12

meas # 8

meas # 9

8 9 10 11 12 13 14 15 16

8 9 10 11 12 13 14 15 16222

8 9 10 11 12 13 14 15 162 2 2 2 21 1 2 2 22 3 1 2 3

8 9 10 11 12 13 14 15 161 2 2 2 2 2 2 2 2

2 1 1 1 1 2 2 2 22 1 1 2 2 1 1 2 22 1 2 1 2 1 2 1 2

8 9 10 11 12 13 14 15 16

8 9 10 11 12 13 14 15 162221

8 9 10 11 12 13 14 15 163 32 31 23 1

Expt. No. 1 2 3 4 5 6 7 8 9

1 ### ### ### ### ### ### ### ### 0.0E+002 ### ### ### ### ### ### ### ### 1.0E+003 ### ### ### ### ### ### ### ### 1.8E+024 ### ### ### ### ### ### ### ### 1.8E+015 ### ### ### ### ### ### ### ### 1.2E+016 ### ### ### ### ### ### ### ### 3.5E+017 ### ### ### ### ### ### ### ### 3.2E+028 ### ### ### ### ### ### ### ### 1.0E+009 ### ### ### ### ### ### ### ### 2.0E+03

10 ### ### ### ### ### ### ### ### 1.0E+0011 ### ### ### ### ### ### ### ### 1.0E+0012 ### ### ### ### ### ### ### ### 3.0E+0013 ### ### ### ### ### ### ### ### 0.0E+0014 ### ### ### ### ### ### ### ### 3.9E+0115 ### ### ### ### ### ### ### ### 2.5E+0116 ### ### ### ### ### ### ### ### 1.0E+0017 ### ### ### ### ### ### ### ### 8.0E+0018 ### ### ### ### ### ### ### ### 2.0E+03

Repetitions or Measurements for each expt.

Feed the data in these rows and columns

You can have upto 16 measurements per expt

2 NF with 2-levels each =

How to use NoIsE Factors for generating

repetitions for each expt

3 NF with 2-levels each =

How to use NoIsE Factors for generating

repetitions for each expt

1 NF with 2-levels 1 NF with 3-levels=

2-4 NF with 3-levels each =

10 11 12 13 14 15 16

factorial

Blanks will not affect the results of mean, Variance and SN Ratio

L4 Orthogonal Array

factorial

L9 Orthogonal Array

Expt. No. 1 2 3 4 5 6 7

1 1.00E+00 0.00E+00 1.00E+00 2.00E+00 0.00E+00 0.00E+00 1.00E+00

2 1.00E+00 2.00E+00 8.00E+00 1.80E+02 5.00E+00 0.00E+00 1.26E+02

3 3.00E+00 3.50E+01 1.06E+02 3.60E+02 3.80E+01 1.35E+02 3.15E+02

4 6.00E+00 1.50E+01 6.00E+00 1.70E+01 2.00E+01 1.60E+01 1.50E+01

5 1.72E+03 1.98E+03 2.00E+03 4.87E+02 8.10E+02 4.00E+02 2.02E+03

6 1.35E+02 3.60E+02 1.62E+03 2.43E+03 2.07E+02 2.00E+00 2.50E+03

7 3.60E+02 8.10E+02 1.22E+03 1.62E+03 1.17E+02 3.00E+01 1.80E+03

8 2.70E+02 2.73E+03 5.00E+03 3.60E+02 1.00E+00 2.00E+00 1.00E+04

9 5.00E+03 1.00E+03 1.00E+03 3.00E+03 1.00E+03 1.00E+03 3.00E+03

10 3.00E+00 0.00E+00 0.00E+00 3.00E+00 0.00E+00 0.00E+00 1.00E+00

11 1.00E+00 0.00E+00 1.00E+00 5.00E+00 0.00E+00 0.00E+00 1.00E+00

12 3.00E+00 1.62E+03 9.00E+01 2.16E+02 5.00E+00 4.00E+00 2.70E+02

13 1.00E+00 2.50E+01 2.70E+02 8.10E+02 1.60E+01 1.00E+00 2.25E+02

14 3.00E+00 2.10E+01 1.62E+02 9.00E+01 6.00E+00 1.00E+00 6.30E+01

15 4.50E+02 1.20E+03 1.80E+03 2.53E+03 2.08E+03 2.08E+03 1.89E+03

16 5.00E+00 6.00E+00 4.00E+01 5.40E+01 0.00E+00 8.00E+00 1.50E+01

17 1.20E+03 3.50E+03 3.50E+03 1.00E+03 3.00E+00 1.00E+00 1.00E+04

18 8.00E+03 2.50E+03 3.50E+03 5.00E+03 1.00E+03 1.00E+03 5.00E+03

Repetitions or Measurements for each expt.

The data has been brought from previous sheet and

this sheet is protected

You can have upto 16 measurements per

8 9 10 11 12 13 14 15 16

1.00E+00 0.00E+00 8.9E-01 0.51

3.00E+00 1.00E+00 5.4E+03 -37.30

5.00E+01 1.80E+02 3.3E+04 -45.17

4.00E+01 1.80E+01 3.8E+02 -25.76

3.60E+02 1.20E+01 1.8E+06 -62.54

2.70E+02 3.50E+01 1.7E+06 -62.23

7.20E+02 3.15E+02 9.7E+05 -59.88

2.25E+02 1.00E+00 1.5E+07 -71.69

2.80E+03 2.00E+03 6.5E+06 -68.15

0.00E+00 1.00E+00 2.2E+00 -3.47

0.00E+00 1.00E+00 3.2E+00 -5.08

8.00E+00 3.00E+00 3.1E+05 -54.85

3.00E+00 0.00E+00 8.7E+04 -49.38

1.50E+01 3.90E+01 4.5E+03 -36.54

1.80E+02 2.50E+01 2.6E+06 -64.18

1.00E+00 1.00E+00 5.4E+02 -27.33

6.00E+02 8.00E+00 1.4E+07 -71.51

2.00E+03 2.00E+03 1.6E+07 -72.00

S/N Ratio for smaller-the-better

Mean Sum of Squares

SN Ratio (smaller-the-Better)

You can have upto 16 measurements per

Blanks will not affect the results of mean, Variance

and SN Ratio

Main EffectsColumn #1 Column #2

Expt. No. SN Ratio (smaller-the-Better) empty Temperatureempty empty T1 T2 T3

1 0.51 0.51 0.512 -37.30 -37.30 -37.303 -45.17 -45.17 -45.174 -25.76 -25.76 -25.765 -62.54 -62.54 -62.546 -62.23 -62.23 -62.237 -59.88 -59.88 -59.888 -71.69 -71.69 -71.699 -68.15 -68.15 -68.1510 -3.47 -3.47 -3.4711 -5.08 -5.08 -5.0812 -54.85 -54.85 -54.8513 -49.38 -49.38 -49.3814 -36.54 -36.54 -36.5415 -64.18 -64.18 -64.1816 -27.33 -27.33 -27.3317 -71.51 -71.51 -71.5118 -72.00 -72.00 -72.00

Sum -432.2 -384.3 -145.4 -300.6 -370.6-48.02 -42.70 -24.23 -50.10 -61.76

-48.02 -42.70

-24.23 -50.10 -61.76

Ov Mean -45.36 ######-45.36 -45.36 ###-45.36 -45.36 -45.36

OV-Mean -45.36 -45.36 -45.36GrandTotal 47231

Total SSQ 10190

Factor-Effects Factor-Effects for Column #1Factor-Effects for Column #2-#8

Main EffectsInteraction between Column #1 and Column #2 Column #3 Column #4

E1 X T1 E1 X T2 E1 X T3 E2 X T1 E2 X T2 E2 X T3 Pressure NitrogenE1T1 E1T2 E1T3 E2T1 E2T2 E2T3 P1 P2 P3 N10.51 0.51 0.51

-37.30 -37.30-45.17 -45.17

-25.76 -25.76 -25.76-62.54 -62.54-62.23 -62.23

-59.88 -59.88-71.69 -71.69-68.15 -68.15 -68.15

-3.47 -3.47-5.08 -5.08 -5.08

-54.85 -54.85-49.38 -49.38-36.54 -36.54-64.18 -64.18 -64.18

-27.33 -27.33-71.51 -71.51 -71.51-72.00 -72.00

-82.0 -150.5 -199.7 -63.4 -150.1 -170.8 -165.3 -284.7 -366.6 -234.2-27.32 -50.18 -66.57 -21.13 -50.03 -56.94 -27.55 -47.44 -61.10 -39.03

-27.32 -50.18 -66.57 -21.13 -50.03 -56.94 -27.55 -47.44 -61.10 -39.03

###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36

-45.36 -45.36

Main EffectsColumn #4 Column #5 Column #6 Column #7Nitrogen Silane Initial Settling time -

N2 N3 S1 S2 S3 I1 I2 I3 - - -0.51 0.51 0.51

-37.30 -37.30 -37.30 -37.30-45.17 -45.17 -45.17 -45.17

-25.76 -25.76 -25.76-62.54 -62.54 -62.54 -62.54

-62.23 -62.23 -62.23 -62.23-59.88 -59.88 -59.88 -59.88

-71.69 -71.69 -71.69 -71.69-68.15 -68.15 -68.15

-3.47 -3.47 -3.47 -3.47-5.08 -5.08 -5.08

-54.85 -54.85 -54.85 -54.85-49.38 -49.38 -49.38 -49.38

-36.54 -36.54 -36.54 -36.54-64.18 -64.18 -64.18

-27.33 -27.33 -27.33 -27.33-71.51 -71.51 -71.51

-72.00 -72.00 -72.00 -72.00

-336.0 -246.4 -235.2 -281.1 -300.2 -309.1 -243.2 -264.2 -248.9 -298.6 -269.1-55.99 -41.07 -39.20 -46.85 -50.04 -51.52 -40.54 -44.03 -41.48 -49.76 -44.85

-55.99 -41.07 -39.20 -46.85 -50.04 -51.52 -40.54 -44.03 -41.48 -49.76 -44.85

-45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###-45.36 -45.36 -45.36 ###

-45.36 -45.36 -45.36 -45.36

Main EffectsColumn #8

Cleaning Method C1 C2 C3 Ov-Mean0.51

#########

######

###-3.47

-5.08###

######

### ### ###### ### ### -45.36

### ### ###

### ### ### ###-45.36

YOU CAN MODIFIY THE CHART - PARTICULARLY THE Y-AXIS

T1 T2 T3

S3 I1 I2 I3 - - -

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

Factor Effect Plot for Quality Char Name

Column #1 Factor Effect Column #2-#8 Factor Effects

Control Factors and Their Levels

YOU CAN MODIFIY THE CHART - PARTICULARLY THE Y-AXIS

T1 T2 T3

S3 I1 I2 I3 - - -

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

Factor Effect Plot for Quality Char Name

T1 T2 T3

S3 I1 I2 I3 - - -

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

Ov-Mean

Factor Effect Plot

T1 T2 T3

S3 I1 I2 I3 - - -

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

Ov-Mean

Factor Effect Plot

LEVELSCONTROL FACTORS \ LEVELS 1 2 3

empty -48.02 -42.70 0 0Temperature -24.23 -50.10 -61.76 2 4428

empty (1) x Temperature (1,2,3) -0.43 2.59 -2.15 0 0empty (2) x Temperature (1,2,3) 0.43 -2.59 2.15

Pressure -27.55 -47.44 -61.10 2 3415Nitrogen -39.03 -55.99 -41.07 2 1029Silane -39.20 -46.85 -50.04 2 372

Initial Settling time -51.52 -40.54 -44.03 2 378- -41.48 -49.76 -44.85 0 0

Cleaning Method -45.56 -41.58 -48.95 2 163

Ov-Mean -45.36 -45.36 -45.36

Total sum of Squares due to Factor Effects 9786

Total sum of Squares = grand Total - 18*mean sq 10190

Error Variance (unpooled) 5 404

Error Variance (unpooled) per degree of freedom

(Error Variance pooled)) 11 1318

Error Variance per degree of freedom

Error Bar for each col #1 CF level = 2*SQRT(error var. per DF / repetition of each level) =

Error Bar for each #2-#8 CF level = 2*SQRT(error var. per DF / repetition of each level) =

95% confidence interval for pred. err = +-2*sqrt(pred err) =

Total Error

OV-MEAN -45.36 -45.36 -45.36 -45.36

Degrees of

Freedom

Sum of Squares

Prediction error variance (for 5 to 6 repititions) = sum of sq for error /neff =

0 - 0 yes yes - +- 7.29 dB2214 43 27 no no 18 +- 8.93 dB

0 - 0 yes yes - +- 8.93 dB +- 8.93 dB

1707 34 21 no no 14 +- 8.93 dB515 10 6 no no 4 +- 8.93 dB186 4 2 no pooled - +- 8.93 dB189 4 2 no pooled - +- 8.93 dB

0 - 0 yes yes - +- 8.93 dB82 2 1 no pooled - +- 8.93 dB

119.82

8.94 0.56

Mean Square

Factor Effect (percent)

F before pooling

empty or pooled F=<1.5

F After pooling

Error Bar on each CF Level

NO. OF unpooled 2-LEVEL CFs =

NO. OF unpooled 3-LEVEL CFs =

1/n = 1/(nexpts for mean) + (no of unpooled CF)/(nrepeat for each

level) =

nr = no of repeat expts =

1/neff = 1/n + 1/nrtherefore neff =

Main Effects

Level 1 Level 2 Level 3 SELECTLevelName

Column 1 empty empty empty - -

Column 2 Temperature T1 T2 T3 1 T1

Column 3 Pressure P1 P2 P3 1 P1

Column 4 Nitrogen N1 N2 N3 1 N1

Column 5 Silane S1 S2 S3 -

Column 6 Initial Settling time I1 I2 I3 -

Column 7 - - - - - -

Column 8 Cleaning Method C1 C2 C3 -

18.95 -19.11

See the 'RESULTS' here 1.13E-01 to 9.03E+00

Type 'NEW' levels as 1,2 or 3

L18 ASSIGNMENT

Control Factor Names

Opt Level % Factor Effect "F" after Pooling

- - 0 -

T1 43 21.14 18.48

P1 34 17.81 14.25

N1 10 6.34 4.30

- - 0.00 -

- - 0.00 -Ov-Mean -45.36

S/N Ratio -0.08

Defects

1.01E+00

Contribution of SELECTed Level to S/N Ratio (in dB)

"+-" prediction error (95% confidence) in dB

RangeCenter Value

neutral/negligible-

D O M I N A N T

SIGNIFICANT

neutral/negligible-

D O M I N A N T orSIGNIFICANT orneutral/negligible

Interaction between Columns 1 X 2

LEVELSColumn # CONTROL FACTORS \ LEVELS 1 2 3

1 empty -48.02 -42.702 Temperature -24.23 -50.10 -61.76

1x2 empty (1) x Temperature (1,2,3) -0.43 2.59 -2.151x2 empty (2) x Temperature (1,2,3) 0.43 -2.59 2.15

Ov-Mean -45.36 -45.36 -45.36

The Contribution of SETTINGS empty (1) X Temperature (1) The Contribution of SETTINGS empty (1) X Temperature (2) The Contribution of SETTINGS empty (1) X Temperature (3)

The Contribution of SETTINGS empty (2) X Temperature (1) The Contribution of SETTINGS empty (2) X Temperature (2) The Contribution of SETTINGS empty (2) X Temperature (3)

to objective function for Defects = 18.0 dBto objective function for Defects = -4.8 dBto objective function for Defects = -21.2 dB

=to objective function for Defects = 24.2 dBto objective function for Defects = -4.7 dBto objective function for Defects = -11.6 dB

Copy of L18 Small Taguchi 1

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