1. The document describes an analysis of response surface methodology to model two responses (Y1 and Y2) based on three factors (A, B, C). 2. A central composite design with 17 runs was used to collect data on the responses across varying levels of the factors. Response surface regressions were then used to model each response as a function of the factors and their interactions. 3. For response Y1, the regression identified factors B and C as significant, while for response Y2, factors C and B*B were found to be significant based on a 95% confidence level. Contour and surface plots of the responses are also presented.

1. Elvira Dian Safire (06211840000011)
DESAIN EKSPERIMEN – A
ANALISIS RESPON SURFACE

2. NOMOR 2i Pengolahan pada setiap respon tanpa interpretasi
RESPON KE-1 (Y1)
StdOrder RunOrder PtType Blocks A B C y1
1 5 1 1 -1 -1 -1 5.56
2 18 1 1 1 -1 -1 5.87
3 12 1 1 -1 1 -1 4.7
4 3 1 1 1 1 -1 4.72
5 2 1 1 -1 -1 1 5.38
6 11 1 1 1 -1 1 5.44
7 7 1 1 -1 1 1 4.14
8 1 1 1 1 1 1 4.29
9 17 -1 1 -1.682 0 0 4.4
10 14 -1 1 1.6818 0 0 4.63
11 6 -1 1 0 -1.682 0 6.02
12 4 -1 1 0 1.6818 0 4.72
13 15 -1 1 0 0 -1.682 5.4
14 10 -1 1 0 0 1.6818 4.23
15 20 0 1 0 0 0 4.55
16 13 0 1 0 0 0 4.43
17 8 0 1 0 0 0 4.4
WORKSHEET27
Optimal Design: A, B, C
Response surface design selected according to D-optimality
Number of candidate design points: 17
Number of design points in optimal design: 12
Model terms: A, B, C, AA, BB, CC, AB, AC, BC
Initial design generated by Sequential method
Initial design improved by Exchange method
Number of design points exchanged is 1
Optimal Design
Row number of selected design points: 8, 12, 14, 2, 3, 15, 4, 1, 6, 5, 7, 9
Condition number: 4.07702
D-optimality (determinant of XTX): 683181311
A-optimality (trace of inv(XTX)): 2.42939
G-optimality (avg leverage/max leverage): 0.838181
V-optimality (average leverage): 0.833333
Maximum leverage: 0.994217
OptDesign 12 'A' 'B' 'C' ;
Indicator 'OptPoint2';
Design;
Brief 3.

3. Data Matrix
Run A B C
1 -1.000 -1.000 -1.000
8 1.000 1.000 1.000
2 1.000 -1.000 -1.000
3 -1.000 1.000 -1.000
4 1.000 1.000 -1.000
5 -1.000 -1.000 1.000
6 1.000 -1.000 1.000
7 -1.000 1.000 1.000
15 0.000 0.000 0.000
9 -1.682 0.000 0.000
10 1.682 0.000 0.000
11 0.000 -1.682 0.000
Response Surface Regression: Y1 versus A, B, C
Coded Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 4.454 0.101 44.10 0.000
A 0.0679 0.0474 1.43 0.196 1.00
B -0.4823 0.0474 -10.17 0.000 1.00
C -0.2612 0.0474 -5.51 0.001 1.00
A*A 0.0385 0.0522 0.74 0.485 1.16
B*B 0.3408 0.0522 6.53 0.000 1.16
C*C 0.1446 0.0522 2.77 0.028 1.16
A*B -0.0250 0.0620 -0.40 0.699 1.00
A*C -0.0150 0.0620 -0.24 0.816 1.00
B*C -0.0475 0.0620 -0.77 0.469 1.00
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.175314 96.30% 91.54% 72.56%
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Model 9 5.59708 0.62190 20.23 0.000
Linear 3 4.17133 1.39044 45.24 0.000
A 1 0.06290 0.06290 2.05 0.196
B 1 3.17641 3.17641 103.35 0.000
C 1 0.93202 0.93202 30.32 0.001
Square 3 1.40090 0.46697 15.19 0.002
A*A 1 0.01671 0.01671 0.54 0.485
B*B 1 1.30922 1.30922 42.60 0.000
C*C 1 0.23559 0.23559 7.67 0.028
Command line :
RSRegress;
Response C8;
Factors C5 C6 C7;
Terms C5 C6 C7 C5*C5 C6*C6
C7*C7 C5*C6 C5*C7 C6*C7;
Confidence95.000000;
IType 0;
InUnit 0;
Levels -1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743;
GPareto;
GModel;
RType 2;
GFourpack C10;
NoDefault;
TSimple;
TMethod;
TANOVA;
TSummary;
TCoefficient;
NoFull;
TEquation;
Separate;
TDiagnostics 0.

4. 2-Way Interaction 3 0.02485 0.00828 0.27 0.846
A*B 1 0.00500 0.00500 0.16 0.699
A*C 1 0.00180 0.00180 0.06 0.816
B*C 1 0.01805 0.01805 0.59 0.469
Error 7 0.21514 0.03073
Lack-of-Fit 5 0.20254 0.04051 6.43 0.140
Pure Error 2 0.01260 0.00630
Total 16 5.81222
Regression Equation in Uncoded Units
y1 = 4.454 + 0.0679 A - 0.4823 B - 0.2612 C + 0.0385 A*A + 0.3408 B*B
+ 0.1446 C*C
- 0.0250 A*B - 0.0150 A*C - 0.0475 B*C
Fits and Diagnostics for Unusual Observations
Obs Y1 Fit Resid
Std
Resid
5 5.380 5.169 0.211 2.09 R
R Large residual

5. Contour Plots of y1

6. WORKSHEET1
Surface Plots of y1
WORKSHEET1
Response Optimization: y1
Parameters
Response Goal Lower Target Upper Weight Importance
y1 Target 3.5 4 4.5 1 1
Starting Values
Variable Setting
A 1
B 1
C 1
Solution
Solution A B C
y1
Fit
Composite
Desirability
1 -0.424695 0.764451 1.00228 4.12456 0.750879
Multiple Response Prediction
Variable Setting
A -0.424695
B 0.764451
C 1.00228

7. Response Fit SE Fit 95% CI 95% PI
y1 4.125 0.102 (3.884, 4.366) (3.645, 4.604)
MMOpt 'y1';
Goal 2;
MinAccept 3.5;
Target 4;
MaxAccept 4.5;
UTWeight 1;
Importance 1;
Start 1 1 1;
IType 0;
OptiPlot;
NoDefault;
TParameter;
TSolution 1;
TPrediction;
TStart;
DStore 'DESIR_3';
DLevels A B C.

8. RESPON KE-2 (Y2)
StdOrder RunOrder PtType Blocks A B C y2
1 17 1 1 -1 -1 -1 22.92
2 13 1 1 1 -1 -1 11.94
3 9 1 1 -1 1 -1 46.49
4 12 1 1 1 1 -1 5.41
5 15 1 1 -1 -1 1 55.4
6 16 1 1 1 -1 1 51.05
7 1 1 1 -1 1 1 67.44
8 8 1 1 1 1 1 33.47
9 5 -1 1 -1.6818 0 0 48.65
10 2 -1 1 1.68179 0 0 56.54
11 18 -1 1 0 -1.6818 0 5.58
12 10 -1 1 0 1.68179 0 47.2
13 7 -1 1 0 0 -1.6818 21.75
14 14 -1 1 0 0 1.68179 60.71
15 4 0 1 0 0 0 56.6
16 19 0 1 0 0 0 53.75
17 20 0 1 0 0 0 56.54
WORKSHEET19
Optimal Design: A, B, C
Response surface design selected according to D-optimality
Number of candidate design points: 17
Number of design points in optimal design: 12
Model terms: A, B, C, AA, BB, CC, AB, AC, BC
Initial design generated by Sequential method
Initial design improved by Exchange method
Number of design points exchanged is 1
Optimal Design
Row number of selected design points: 4, 12, 13, 1, 2, 15, 3, 5, 6, 7, 8, 9
Condition number: 4.07702
D-optimality (determinant of XTX): 115.182
A-optimality (trace of inv(XTX)): 10.6709
G-optimality (avg leverage/max leverage): 0.838181
V-optimality (average leverage): 0.833333
Maximum leverage: 0.994217
Data Matrix
Run A B C
4 1.000 1.000 -1.000
RSRegress;
Response C8;
Factors C5 C6 C7;
Terms C5 C6 C7 C5*C5 C6*C6 C7*C7
C5*C6 C5*C7 C6*C7;
Confidence95.000000;
IType 0;
InUnit 1;
Levels -1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743;
GPareto;
GModel;
RType 1;
NoDefault;
TSimple;
TMethod;
TANOVA;
TSummary;
TCoefficient;
NoFull;
TEquation;
Separate;
TDiagnostics 0.

9. 12 0.000 1.682 0.000
13 0.000 0.000 -1.682
1 -1.000 -1.000 -1.000
2 1.000 -1.000 -1.000
15 0.000 0.000 0.000
3 -1.000 1.000 -1.000
5 -1.000 -1.000 1.000
6 1.000 -1.000 1.000
7 -1.000 1.000 1.000
8 1.000 1.000 1.000
9 -1.682 0.000 0.000
Response Surface Regression: y2 versus A, B, C
Coded Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 55.78 7.15 7.81 0.000
A -5.65 3.36 -1.68 0.136 1.00
B 5.97 3.36 1.78 0.119 1.00
C 13.63 3.36 4.06 0.005 1.00
A*A -1.60 3.69 -0.43 0.678 1.16
B*B -10.86 3.69 -2.94 0.022 1.16
C*C -5.62 3.69 -1.52 0.172 1.16
A*B -7.46 4.38 -1.70 0.132 1.00
A*C 1.72 4.38 0.39 0.707 1.00
B*C -2.82 4.38 -0.64 0.540 1.00
Model Summary
S R-sq R-sq(adj) R-sq(pred)
12.4020 83.51% 62.32% 0.00%
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Model 9 5453.96 606.00 3.94 0.042
Linear 3 3458.29 1152.76 7.49 0.014
A 1 435.39 435.39 2.83 0.136
B 1 486.32 486.32 3.16 0.119
C 1 2536.58 2536.58 16.49 0.005
Square 3 1462.53 487.51 3.17 0.094
A*A 1 28.77 28.77 0.19 0.678
B*B 1 1330.19 1330.19 8.65 0.022
C*C 1 355.52 355.52 2.31 0.172
2-Way Interaction 3 533.14 177.71 1.16 0.392
A*B 1 445.81 445.81 2.90 0.132
A*C 1 23.60 23.60 0.15 0.707
B*C 1 63.73 63.73 0.41 0.540
Error 7 1076.66 153.81
Lack-of-Fit 5 1071.36 214.27 80.81 0.012
Command line :
CCDesign 3;
Center 6;
Randomize;
SOrder 'StdOrder' 'RunOrder';
PtType 'PtType';
Brief 3;
XMatrix 'Blocks' 'A' 'B' 'C'.

10. Pure Error 2 5.30 2.65
Total 16 6530.63
Regression Equation in Uncoded Units
y2 = 55.78 - 5.65 A + 5.97 B + 13.63 C - 1.60 A*A - 10.86 B*B - 5.62 C*C
- 7.46 A*B
+ 1.72 A*C - 2.82 B*C
RSRegress;
Response C8;
Factors C5 C6 C7;
Terms C5 C6 C7 C5*C5 C6*C6
C7*C7 C5*C6 C5*C7 C6*C7;
Confidence95.000000;
IType 0;
InUnit 0;
Levels -1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743;
GPareto;
GModel;
RType 2;
GFourpack C10;
NoDefault;
TSimple;
TMethod;
TANOVA;
TSummary;
TCoefficient;
NoFull;
TEquation;
Separate;
TDiagnostics 0.

11. WORKSHEET5
Contour Plots of y2

12. WORKSHEET5
Surface Plots of y2
WORKSHEET5
Response Optimization: y2
Parameters
Response Goal Lower Target Upper Weight Importance
y2 Maximum 67 67.42 1 1
Solution
Solution A B C
y2
Fit
Composite
Desirability
1 -1.68179 0.764451 0.764451 71.8498 1
Multiple Response Prediction
Variable Setting
A -1.68179
B 0.764451
C 0.764451
Response Fit SE Fit 95% CI 95% PI
y2 71.8 13.2 (40.6, 103.1) (29.0, 114.7)

13. MMOpt 'y2';
Goal 3;
MinAccept 67;
Target 67.42;
MaxAccept 67.42;
UTWeight 1;
Importance 1;
IType 0;
OptiPlot;
NoDefault;
TParameter;
TSolution 1;
TPrediction;
DStore 'DESIR_5';
DLevels A B C.

14. RESPON KE-3 (Y3)
StdOrder RunOrder PtType Blocks A B C y3
1 10 1 1 -1 -1 -1 19.17
2 19 1 1 1 -1 -1 -2.39
3 15 1 1 -1 1 -1 13.73
4 17 1 1 1 1 -1 5.94
5 3 1 1 -1 -1 1 10.29
6 13 1 1 1 -1 1 -4.02
7 4 1 1 -1 1 1 12.28
8 8 1 1 1 1 1 5.58
9 20 -1 1 -1.6818 0 0 26.78
10 1 -1 1 1.68179 0 0 -2.57
11 2 -1 1 0 -1.6818 0 13.91
12 9 -1 1 0 1.68179 0 5.76
13 12 -1 1 0 0 -1.6818 30.04
14 18 -1 1 0 0 1.68179 10.11
15 14 0 1 0 0 0 18.44
16 6 0 1 0 0 0 16.45
17 16 0 1 0 0 0 15
WORKSHEET20
Optimal Design: A, B, C
Response surface design selected according to D-optimality
Number of candidate design points: 17
Number of design points in optimal design: 12
Model terms: A, B, C, AA, BB, CC, AB, AC, BC
Initial design generated by Sequential method
Initial design improved by Exchange method
Number of design points exchanged is 1
Optimal Design
Row number of selected design points: 4, 12, 13, 1, 2, 15, 3, 5, 6, 7, 8, 9
Condition number: 4.07702
D-optimality (determinant of XTX): 115.182
A-optimality (trace of inv(XTX)): 10.6709
G-optimality (avg leverage/max leverage): 0.838181
V-optimality (average leverage): 0.833333
Maximum leverage: 0.994217
Data Matrix
Run A B C
4 1.000 1.000 -1.000
OptDesign 12 ;
ResModel C5 C6 C7 C5*C5 C6*C6 C7*C7
C5*C6 C5*C7 C6*C7;
InUnit 1;
Levels -1.68179 1.68179 -1.68179 1.68179 -
1.68179 1.68179;
Exchange 1;
Sequential;
Indicator 'OptPoint';
Design;
Brief 3.

15. 12 0.000 1.682 0.000
13 0.000 0.000 -1.682
1 -1.000 -1.000 -1.000
2 1.000 -1.000 -1.000
15 0.000 0.000 0.000
3 -1.000 1.000 -1.000
5 -1.000 -1.000 1.000
6 1.000 -1.000 1.000
7 -1.000 1.000 1.000
8 1.000 1.000 1.000
9 -1.682 0.000 0.000
WORKSHEET6
Response Surface Regression: y3 versus A, B, C
Coded Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 17.03 3.64 4.68 0.002
A -7.30 1.71 -4.28 0.004 1.00
B 0.06 1.71 0.03 0.974 1.00
C -3.36 1.71 -1.97 0.090 1.00
A*A -2.99 1.88 -1.59 0.155 1.16
B*B -3.80 1.88 -2.02 0.083 1.16
C*C -0.17 1.88 -0.09 0.929 1.16
A*B 2.67 2.23 1.20 0.270 1.00
A*C 1.04 2.23 0.47 0.655 1.00
B*C 1.09 2.23 0.49 0.641 1.00
Model Summary
S R-sq R-sq(adj) R-sq(pred)
6.31131 80.98% 56.54% 0.00%
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Model 9 1187.53 131.948 3.31 0.064
Linear 3 882.04 294.014 7.38 0.014
A 1 728.15 728.147 18.28 0.004
B 1 0.04 0.044 0.00 0.974
C 1 153.85 153.852 3.86 0.090
Square 3 230.19 76.731 1.93 0.214
A*A 1 100.96 100.956 2.53 0.155
B*B 1 162.37 162.368 4.08 0.083
C*C 1 0.34 0.344 0.01 0.929
2-Way Interaction 3 75.29 25.098 0.63 0.618
A*B 1 57.14 57.138 1.43 0.270
Name C1 "StdOrder" C2
"RunOrder" C3 "PtType" C4
"Blocks" C5 "A" C6 "B" C7 "C"
CCDesign 3;
Center 6;
Randomize;
SOrder 'StdOrder' 'RunOrder';
PtType 'PtType';
Brief 3;
XMatrix 'Blocks' 'A' 'B' 'C'.
RSRegress;
Response C8;
Factors C5 C6 C7;
Terms C5 C6 C7 C5*C5 C6*C6
C7*C7 C5*C6 C5*C7 C6*C7;
Confidence95.000000;
IType 0;
InUnit 0;
Levels -1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743 -
1.68179283050743
1.68179283050743;
GPareto;
GModel;
RType 2;
GFourpack C10;
NoDefault;
TSimple;
TMethod;
TANOVA;
TSummary;
TCoefficient;
NoFull;
TEquation;
Separate;
TDiagnostics 0.

16. A*C 1 8.69 8.694 0.22 0.655
B*C 1 9.46 9.461 0.24 0.641
Error 7 278.83 39.833
Lack-of-Fit 5 272.86 54.573 18.30 0.053
Pure Error 2 5.97 2.983
Total 16 1466.36
Regression Equation in Uncoded Units
y3 = 17.03 - 7.30 A + 0.06 B - 3.36 C - 2.99 A*A - 3.80 B*B - 0.17 C*C + 2.67 A*B
+ 1.04 A*C
+ 1.09 B*C

17. WORKSHEET6
Contour Plots of y3

18. WORKSHEET6
Surface Plots of y3
WORKSHEET6
Response Optimization: y3
Parameters
Response Goal Lower Target Upper Weight Importance
y3 Maximum 25 31 1 1
Solution
Solution A B C
y3
Fit
Composite
Desirability
1 -1.68179 -0.832403 -1.68179 31.5367 1
Multiple Response Prediction
Variable Setting
A -1.68179
B -0.832403
C -1.68179
Response Fit SE Fit 95% CI 95% PI
y3 31.5 10.8 (6.0, 57.1) (1.9, 61.1)

19. MMOpt 'y3';
Goal 3;
MinAccept 25;
Target 31;
MaxAccept 31;
UTWeight 1;
Importance 1;
IType 0;
OptiPlot;
NoDefault;
TParameter;
TSolution 1;
TPrediction;
DStore 'DESIR_4';
DLevels A B C.