l12-smaller-the-better-template - department of …apte/l12_small_taguch… · xls file · web...

Title of the problem Optimization of the painting process

Write an Introduction to the problem (1) Water vapor permeability to be smaller(2) Particle size / thickness to be nominal(3) Scrub resistance to be maximized

Team members

Duration star27-Sep-06

Date today08-May-23

Last Modified on 31-May-2007

password info for P. R. Apte: L12**** ==> L12 :- upto 11 control factors with 2-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

Optimization of the painting process

(1) Water vapor permeability to be smaller(2) Particle size / thickness to be nominal(3) Scrub resistance to be maximized

YOU MAY OVER-WRITE ON THE 'orange' TEXT

IN ALL THE SHEETS

USERNAMESTART DATE

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

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

27-Dec-2005 TYPE THE DATE HERE

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

Various processes - of mixing, applying and drying the paint - have a lot many NoIsY parameters

The objective of the Taguchi experimentation is to increase "Scrub resistance" and to reduce the "Water vapor permeability".

Control Factors are (1) agitator rpm, (2) type of agitator and (3) type of buffer etc etcTheir levels are taken as far apart as possible

L12 array is chosen upto 11 control factors with 2 levels each are allowed. Interaction among the control factors is evenly distributed, However, interactions can not be studied,

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

TODAY08-May-23

Painting Process

Various processes - of mixing, applying and drying the paint - have a lot many

The objective of the Taguchi experimentation is to increase "Scrub resistance" and to reduce the "Water vapor permeability".

Control Factors are (1) agitator rpm, (2) type of agitator and (3) type of buffer

Their levels are taken as far apart as possible

L12 array is chosen upto 11 control factors with 2 levels each are allowed. Interaction among the control factors is evenly distributed, However, interactions can not be studied,

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

Water vapor permeability YES

Type YES or NOType Quality

Characteristic name/identifier

Repetitions in each row of expt (due to NoIsE Factor

combinations)

no. of times the "confirmation experiment"

is repeated

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

CONTROL FACTORS AND THEIR LEVELS

Agitator-rpm A1 A2B B1 B2C C1 C2D D1 D2E E1 E2F F1 F2

Granules G1 G2H H1 H2- - -J J1 J2K K1 K2

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

Control Factor name

Level 1 name

Level 2 name

"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)

Fill in the factor names and level names

NoIsE Level 3

U3 3 Type 2 or 3 V3 3

NUMBER OF LEVELS

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

WHICH OUTER-

ARRAY IS REQUIRED =

L12 Array

Control FactorsA B C D E F G H I J

1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 2 2 2 2 23 1 1 2 2 2 1 1 1 2 24 1 2 1 2 2 1 2 2 1 15 1 2 2 1 2 2 1 2 1 26 1 2 2 2 1 2 2 1 2 17 2 1 2 2 1 1 2 2 1 28 2 1 2 1 2 2 2 1 1 19 2 1 1 2 2 2 1 2 2 1

10 2 2 2 1 1 1 1 2 2 111 2 2 1 2 1 2 1 1 1 212 2 2 1 1 2 1 2 1 2 2

Total number of expts = 12REPETITIONS FOR EACH LEVEL = 6

Expt No.

Control FactorsK122211121221

L9 Array is always the same

Hence no need to change this - EVER

Experimenter's Log

Expt. No.

CONTROL FACTOR ASSIGNEMNT TO 11 COLUMNS

B C D E F Granules H - J

1 A1 B1 C1 D1 E1 F1 G1 H1 - J12 A1 B1 C1 D1 E1 F2 G2 H2 - J2

3 A1 B1 C2 D2 E2 F1 G1 H1 - J24 A1 B2 C1 D2 E2 F1 G2 H2 - J15 A1 B2 C2 D1 E2 F2 G1 H2 - J2

12 A2 B2 C1 D1 E2 F1 G2 H1 - J2

Repetition number for each level = 6

NUMBER OF MEASUREMENTS

Agitator-rpm

No need to feed anything here.

All 'text' is linked to entries in the sheet "Control-NoIsE Factors & Levels"

CHOSEN FACTORIAL OR ORTHOGONAL ARRAY

1 2 3 4 5 6 7 8 9

U NoIsE FACTOR 1 U1 U1 U1 U2 U2 U2 U3 U3 U3V NoIsE FACTOR 2 V1 V2 V3 V1 V2 V3 V1 V2 V3

CONTROL FACTOR ASSIGNEMNT TO 11 COLUMNS

K1 6.00E-02 6.50E-02 6.02E-02 6.25E-02 6.25E-02 6.53E-02 6.41E-02 6.11E-02 6.20E-02

K2 1.20E-01 1.30E-01 1.20E-01 1.23E-01 1.21E-01 1.25E-01 1.21E-01 1.25E-01 1.27E-01

K2 1.80E-01 1.95E-01 1.90E-01 1.81E-01 1.94E-01 1.86E-01 1.85E-01 1.90E-01 1.83E-01

K2 6.00E-01 6.57E-01 6.54E-01 6.29E-01 6.24E-01 6.50E-01 6.52E-01 6.52E-01 6.11E-01

K1 1.20E-01 1.31E-01 1.30E-01 1.28E-01 1.31E-01 1.26E-01 1.25E-01 1.31E-01 1.23E-01

K1 9.00E-02 9.17E-02 9.52E-02 9.33E-02 9.24E-02 9.62E-02 9.21E-02 9.13E-02 9.57E-02

K1 2.40E-01 2.53E-01 2.57E-01 2.41E-01 2.53E-01 2.62E-01 2.51E-01 2.50E-01 2.50E-01

K2 6.00E-02 6.45E-02 6.18E-02 6.29E-02 6.37E-02 6.54E-02 6.17E-02 6.06E-02 6.11E-02

K1 9.00E-02 9.72E-02 9.59E-02 9.69E-02 9.60E-02 9.23E-02 9.58E-02 9.60E-02 9.26E-02

K2 1.80E-01 1.98E-01 1.97E-01 1.91E-01 1.93E-01 1.85E-01 1.94E-01 1.84E-01 1.91E-01

K2 9.00E-02 9.42E-02 9.70E-02 9.72E-02 9.53E-02 9.86E-02 9.83E-02 9.38E-02 9.77E-02

K1 1.50E-01 1.61E-01 1.55E-01 1.50E-01 1.56E-01 1.58E-01 1.57E-01 1.64E-01 1.53E-01

CHOSEN FACTORIAL OR ORTHOGONAL

ARRAY==>L9

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

L4 / F4 F6 F8 / L8 L9 L12 F16 F16

REPETITIONS

NoIsE FACTOR names

meas # 1

meas # 2

meas # 3

meas # 4

meas # 5

meas # 6

meas # 7

meas # 8

meas # 9

No need to feed anything here.

All 'text' is linked to entries in the sheet "Control-NoIsE Factors & Levels"

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 2BCD

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 2 3BCD

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 2 2B 1 2 1 2CD

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 1 2 2 2B 1 2 3 1 2 3CD

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 1 1 2 2 2 2B 1 1 2 2 1 1 2 2C 1 2 1 2 1 2 1 2D

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 1 1 1 1 2 2 2B 1 1 1 2 2 2 1 1 1C 1 2 3 1 2 3 1 2 3D

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 1 1 1 1 1 1 2B 1 1 1 1 2 2 2 2 1C 1 1 2 2 1 1 2 2 1D 1 2 1 2 1 2 1 2 1

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 2 2B 1 2 1 2C 1 2 2 1D

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 1 1 2 2 2 2B 1 1 2 2 1 1 2 2C 1 2 1 2 1 2 1 2D 1 2 1 2 2 1 2 1

EXPT NO. 1 2 3 4 5 6 7 8 9A 1 1 1 2 2 2 3 3 3B 1 2 3 1 2 3 1 2 3C 1 2 3 2 3 1 3 1 2D 1 2 3 3 1 2 2 3 1

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

L4 / F4 F6 F8 / L8 L9 L12

10 11 12 13 14 15 16

10 11 12 13 14 15 162 2 22 2 21 2 3

10 11 12 13 14 15 162 2 2 2 2 2 21 1 1 2 2 2 21 2 2 1 1 2 22 1 2 1 2 1 2

10 11 12 13 14 15 16

Expt No. 1 2 3 4 5 6 7 8

1 6.0E-02 1.2E-01 1.8E-01 6.0E-01 1.2E-01 9.0E-02 2.4E-01 6.0E-022 6.5E-02 1.3E-01 2.0E-01 6.6E-01 1.3E-01 9.2E-02 2.5E-01 6.4E-023 6.0E-02 1.2E-01 1.9E-01 6.5E-01 1.3E-01 9.5E-02 2.6E-01 6.2E-024 6.3E-02 1.2E-01 1.8E-01 6.3E-01 1.3E-01 9.3E-02 2.4E-01 6.3E-025 6.3E-02 1.2E-01 1.9E-01 6.2E-01 1.3E-01 9.2E-02 2.5E-01 6.4E-026 6.5E-02 1.3E-01 1.9E-01 6.5E-01 1.3E-01 9.6E-02 2.6E-01 6.5E-027 6.4E-02 1.2E-01 1.9E-01 6.5E-01 1.2E-01 9.2E-02 2.5E-01 6.2E-028 6.1E-02 1.3E-01 1.9E-01 6.5E-01 1.3E-01 9.1E-02 2.5E-01 6.1E-029 6.2E-02 1.3E-01 1.8E-01 6.1E-01 1.2E-01 9.6E-02 2.5E-01 6.1E-0210 6.3E-02 1.2E-01 2.0E-01 6.0E-01 1.3E-01 9.6E-02 2.4E-01 6.1E-0211 6.1E-02 1.2E-01 1.9E-01 6.4E-01 1.3E-01 9.7E-02 2.6E-01 6.4E-0212 6.3E-02 1.3E-01 1.8E-01 6.6E-01 1.3E-01 9.3E-02 2.5E-01 6.5E-0213141516

3.9E-03 1.5E-02 3.5E-02 4.0E-01 1.6E-02 8.8E-03 6.3E-02 3.9E-03

S/N Ratio 24.0864 18.12829 14.5104 3.933314 17.88276 20.56571 12.00547 24.06332

Repetitions for each expt

MEAN of sum of squares

You can have upto 16 measurements per expt

How to use NoIsE Factors for generating

repetitions for each expt

2 NF with 2-levels each = 3 NF with 2-levels each = 1 NF with 2-levels 1 NF with 3-levels= 2-4 NF with 3-levels each =

9 10 11 12

9.0E-02 1.8E-01 9.0E-02 1.5E-019.7E-02 2.0E-01 9.4E-02 1.6E-019.6E-02 2.0E-01 9.7E-02 1.6E-019.7E-02 1.9E-01 9.7E-02 1.5E-019.6E-02 1.9E-01 9.5E-02 1.6E-019.2E-02 1.8E-01 9.9E-02 1.6E-019.6E-02 1.9E-01 9.8E-02 1.6E-019.6E-02 1.8E-01 9.4E-02 1.6E-019.3E-02 1.9E-01 9.8E-02 1.5E-019.8E-02 1.9E-01 9.9E-02 1.5E-019.4E-02 2.0E-01 9.9E-02 1.6E-019.5E-02 1.9E-01 9.9E-02 1.6E-01

9.0E-03 3.6E-02 9.3E-03 2.4E-02

20.45574 14.3953 20.30193 16.12777

4 factorial

4 L4 Orthogonal Array

6 factorial

9 L9 Orthogonal Array

Feed the data in these rows and columns

Blanks will not affect the results of mean, Variance and

SN Ratio

2 NF with 2-levels each = 3 NF with 2-levels each = 1 NF with 2-levels 1 NF with 3-levels= 2-4 NF with 3-levels each =

Expt No. 1 2 3 4 5 6 7

1 6.00E-02 1.20E-01 1.80E-01 6.00E-01 1.20E-01 9.00E-02 2.40E-012 6.50E-02 1.30E-01 1.95E-01 6.57E-01 1.31E-01 9.17E-02 2.53E-013 6.02E-02 1.20E-01 1.90E-01 6.54E-01 1.30E-01 9.52E-02 2.57E-014 6.25E-02 1.23E-01 1.81E-01 6.29E-01 1.28E-01 9.33E-02 2.41E-015 6.25E-02 1.21E-01 1.94E-01 6.24E-01 1.31E-01 9.24E-02 2.53E-016 6.53E-02 1.25E-01 1.86E-01 6.50E-01 1.26E-01 9.62E-02 2.62E-017 6.41E-02 1.21E-01 1.85E-01 6.52E-01 1.25E-01 9.21E-02 2.51E-018 6.11E-02 1.25E-01 1.90E-01 6.52E-01 1.31E-01 9.13E-02 2.50E-019 6.20E-02 1.27E-01 1.83E-01 6.11E-01 1.23E-01 9.57E-02 2.50E-01

10111213141516

3.9E-03 1.5E-02 3.5E-02 4.1E-01 1.6E-02 8.7E-03 6.3E-02

S/N Ratio 24.08 18.15 14.54 3.92 17.91 20.62 12.01

Repetitions for each expt

MEAN of sum of squares

8 9 10 11 12

6.00E-02 9.00E-02 1.80E-01 9.00E-02 1.50E-016.45E-02 9.72E-02 1.98E-01 9.42E-02 1.61E-016.18E-02 9.59E-02 1.97E-01 9.70E-02 1.55E-016.29E-02 9.69E-02 1.91E-01 9.72E-02 1.50E-016.37E-02 9.60E-02 1.93E-01 9.53E-02 1.56E-016.54E-02 9.23E-02 1.85E-01 9.86E-02 1.58E-016.17E-02 9.58E-02 1.94E-01 9.83E-02 1.57E-016.06E-02 9.60E-02 1.84E-01 9.38E-02 1.64E-016.11E-02 9.26E-02 1.91E-01 9.77E-02 1.53E-01

3.9E-03 9.0E-03 3.6E-02 9.2E-03 2.4E-02

24.09 20.47 14.41 20.37 16.13

data has been 'linked' from the sheet:"Input measured

data" in these rows and columns

S-N RATIOs for each expariment ARE CALCULATED

Main EffectsAgitator-rpm B C D

Expt. No. S/N Ratio A1 A2 B1 B2 C1 C2 D1 D21 24.08 24.08 24.08 24.08 24.082 18.15 18.15 18.15 18.15 18.153 14.54 14.54 14.54 14.54 14.544 3.92 3.92 3.92 3.92 3.925 17.91 17.91 17.91 17.91 17.916 20.62 20.62 20.62 20.62 20.627 12.01 12.01 12.01 12.01 12.018 24.09 24.09 24.09 24.09 24.099 20.47 20.47 20.47 20.47 20.4710 14.41 14.41 14.41 14.41 14.4111 20.37 20.37 20.37 20.37 20.3712 16.13 16.13 16.13 16.13 16.13

Sum 99.22 107.49 113.34 93.36 103.12 103.59 114.77 91.93Factor Effects 16.54 17.91 18.89 15.56 17.19 17.26 19.13 15.32

ov mean 17.23 check= 17.23 check= 17.23 check= 17.23 check= 17.23

3560.61

3908.44

347.84

SUM OF SQ DUE TO MEAN

GRAND TOTAL SUM OF SQTotal sum of squares =

E F Granules H - JE1 E2 F1 F2 G1 G2 H1 H2 - - J1 J2

24.08 24.08 24.08 24.08 24.08 24.0818.15 18.15 18.15 18.15 18.15 18.15

14.54 14.54 14.54 14.54 14.54 14.543.92 3.92 3.92 3.92 3.92 3.92

17.91 17.91 17.91 17.91 17.91 17.9120.62 20.62 20.62 20.62 20.62 20.6212.01 12.01 12.01 12.01 12.01 12.01

24.09 24.09 24.09 24.09 24.09 24.0920.47 20.47 20.47 20.47 20.47 20.47

14.41 14.41 14.41 14.41 14.41 14.4120.37 20.37 20.37 20.37 20.37 20.37

16.13 16.13 16.13 16.13 16.13 16.13

109.64 97.07 85.10 121.61 111.78 94.93 119.83 86.87 102.38 104.32 107.58 99.1218.27 16.18 14.18 20.27 18.63 15.82 19.97 14.48 17.06 17.39 17.93 16.52

check= 17.23 check= 17.23 check= 17.23 check= 17.23 check= 17.23 check= 17.23

KK1 K2

24.0818.1514.543.92

17.9120.6212.01

24.0920.47

14.4120.37

111.22 95.4818.54 15.91

check= 17.23

Ov Mean 17.2317.23

A1 16.53643 17.23A2 17.91452 17.23

17.23B1 18.89043 17.23B2 15.56053 17.23

17.23C1 17.18608 17.23C2 17.26488 17.23

17.23D1 19.12901 17.23D2 15.32195 17.23

17.23E1 18.27326 17.23E2 16.1777 17.23

17.23F1 14.18292 17.23F2 20.26804 17.23

17.23G1 18.62971 17.23G2 15.82125 17.23

17.23H1 19.97227 17.23H2 14.47869 17.23

17.23- 17.06367 17.23- 17.38729 17.23

17.23J1 17.93044 17.23J2 16.52051 17.23

17.23K1 18.53693 17.23K2 15.91403 17.23

ov mean

YOU CAN MODIFY THE CHART - PARTICULARLY THE Y-AXIS

E2 F1 F2 G1

H2 - -

J1 J2 K1

Main Factor Effects for Quality Char Name

2-Level Control Factors Ov Mean

Control Factors and Their Levels

YOU CAN MODIFY THE CHART - PARTICULARLY THE Y-AXIS

E2 F1 F2 G1

H2 - -

J1 J2 K1

Main Factor Effects for Quality Char Name

Ov Mean 17.2317.23

A1 16.53643 17.23A2 17.91452 17.23

17.23B1 18.89043 17.23B2 15.56053 17.23

17.23C1 17.18608 17.23C2 17.26488 17.23

17.23D1 19.12901 17.23D2 15.32195 17.23

17.23E1 18.27326 17.23E2 16.1777 17.23

17.23F1 14.18292 17.23F2 20.26804 17.23

17.23G1 18.62971 17.23G2 15.82125 17.23

17.23H1 19.97227 17.23H2 14.47869 17.23

17.23- 17.06367 17.23- 17.38729 17.23

17.23J1 17.93044 17.23J2 16.52051 17.23

17.23K1 18.53693 17.23K2 15.91403 17.23

Ov Mean

E2 F1 F2 G1

H2 - -

J1 J2 K1

Main Factor Effects

E2 F1 F2 G1

H2 - -

J1 J2 K1

Main Factor Effects

LEVELS

Control Factors and Levels 1 2

Agitator-rpm 16.54 17.91 1 6 6

B 18.89 15.56 1 33 33

C 17.19 17.26 1 0 0

D 19.13 15.32 1 43 43

E 18.27 16.18 1 13 13

F 14.18 20.27 1 111 111

Granules 18.63 15.82 1 24 24

H 19.97 14.48 1 91 91

- 17.06 17.39 0 0 0

J 17.93 16.52 1 6 6

K 18.54 15.91 1 21 21

Ov-Mean 17.23 17.23

Total sum of Squares due to Factor Effects 348 348

Total sum of Squares = grand Total -12*mean sq 348

Error Variance (unpooled) 1 0

Error Variance (unpooled) per degree of freedom 0.31

(Error Variance pooled)) 4 12

Error Variance per degree of freedom 3.00

Error Bar for each Level of CF = 2*SQRT(error var. per DF / repetition of each level) = 1.41

95% confidence interval for pred. err = +-2*sqrt(pred err) = 4.17

OV-MEAN 3.18 3.18 3.18

Degrees of

Freedom

Sum of Squares

Mean Square

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

2 1813 no pooled - +- 1.41 dB

10 10587 no no 11 +- 1.41 dB

0 6 no pooled - +- 1.41 dB

13 13839 no no 15 +- 1.41 dB

4 4193 no no 4 +- 1.41 dB

32 35356 no no 37 +- 1.41 dB

7 7531 no no 8 +- 1.41 dB

26 28816 no no 30 +- 1.41 dB

- 0 yes yes - +- 1.41 dB

2 1898 no pooled - +- 1.41 dB

5.94 6569 no no 7 +- 1.41 dB

100no. of unpooled CFs = 7

5 0.68965517

Factor Effect (percent)

F before pooling

empty or pooled F=<1.5

F After

pooling

Error Bar on each CF Level

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

nr = no of repeat expts =

1/neff = 1/n + 1/nr

therefore neff =

Level 1 Level 2

Column 1 Agitator-rpm A1 A2 - -

Column 2 B B1 B2 1 B1

Column 3 C C1 C2 - -

Column 4 D D1 D2 1 D1

Column 5 E E1 E2 1 E1

Column 6 F F1 F2 1 F1

Column 7 Granules G1 G2 1 G1

Column 8 H H1 H2 1 H1

Column 9 - - - - -

Column 10 J J1 J2 - -

Column 11 K K1 K2 1 K1

28.43 20.09

3.79E-02 to 9.90E-02

Type 'NEW' levels as 1,2

L12 ASSIGNMENT

Control Factor Names

SELECT LEVEL

LevelName

See the 'RESULTS' here

Opt Level % Factor Effect

- - 0.00 neutral/negligible- -

B1 10 1.66 SIGNIFICANT 11

D1 13 1.90 SIGNIFICANT 15

E1 4 1.05 neutral/negligible 4

F2 32 -3.04 D O M I N A N T 37

G1 7 1.40 SIGNIFICANT 8

H1 26 2.75 D O M I N A N T 30

K1 6 1.31 SIGNIFICANT 7

Ov-Mean 17.23

S/N Ratio 24.26

6.12E-02

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

DOMINANT orSignificant or

neutral/negligible"F" after Pooling

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

Water vapor permeability

Range Center Value

l12-smaller-the-better-template - department of …apte/l12_small_taguch… · xls file · web...

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