SOAL NO 1

temp RH storage TensileElongation

modulus

-1 -1 0 27,15 13,5 938,921 -1 0 16,25 5,17 499,8

-1 1 0 35,91 24,56 4001 1 0 20,7 4,65 869,33

-1 0 -1 19,02 10,97 4651 0 -1 21,4 5,2 555,25

-1 0 1 30,6 19,9 681,41 0 1 5,5 1,3 682,20 -1 -1 31,3 29,84 858,330 1 -1 23,53 39,89 548,250 -1 1 24,5 34,53 835,040 1 1 29,16 22,97 624,750 0 0 40 23,2 623,220 0 0 38,7 22,25 624,750 0 0 38 22,91 623,22

TENSILE

Response Surface Regression: Tensile versus temp; RH; storage

The analysis was done using coded units.

Estimated Regression Coefficients for Tensile

Term Coef SE Coef T PConstant 38,9000 1,5923 24,431 0,000temp -6,1038 0,9751 -6,260 0,002RH 1,2625 0,9751 1,295 0,252storage -0,6862 0,9751 -0,704 0,513temp*temp -10,9450 1,4352 -7,626 0,001RH*RH -2,9525 1,4352 -2,057 0,095storage*storage -8,8250 1,4352 -6,149 0,002temp*RH -1,0775 1,3789 -0,781 0,470temp*storage -6,8700 1,3789 -4,982 0,004RH*storage 3,1075 1,3789 2,254 0,074

RH*temp storage*temp1,00,50,0-0,5-1,0

1,0

0,5

0,0

-0,5

-1,0storage*RH

1,00,50,0-0,5-1,0

1,0

0,5

0,0

-0,5

-1,0

temp 0RH 0storage 0

Hold Values

> – – – – – < 6

6 1212 1818 2424 3030 36

36

Tensile

Contour Plots of Tensile

20

30

-1 0

40

-11

01

Tensile

RH

temp

102030

-1 0

3040

10

-11

Tensile

storage

temp

253035

-10

3540

10

-11

Tensile

storage

RH

temp 0RH 0storage 0

Hold Values

Surface Plots of Tensile

ELOGATION

Response Surface Regression: Elongation versus temp; RH; storage

The analysis was done using coded units.

Estimated Regression Coefficients for Elongation

Term Coef SE Coef T PConstant 22,7867 1,962 11,615 0,000temp -6,5763 1,201 -5,474 0,003RH 1,1287 1,201 0,940 0,391storage -0,9000 1,201 -0,749 0,488temp*temp -16,6408 1,768 -9,410 0,000RH*RH 5,8242 1,768 3,293 0,022storage*storage 3,1967 1,768 1,808 0,130temp*RH -2,8950 1,699 -1,704 0,149temp*storage -3,2075 1,699 -1,888 0,118RH*storage -5,4025 1,699 -3,180 0,025

S = 3,39809 PRESS = 917,241R-Sq = 96,93% R-Sq(pred) = 51,22% R-Sq(adj) = 91,40%

Analysis of Variance for Elongation

Source DF Seq SS Adj SS Adj MS F PRegression 9 1822,82 1822,82 202,54 17,54 0,003 Linear 3 362,65 362,65 120,88 10,47 0,014 temp 1 345,98 345,98 345,98 29,96 0,003 RH 1 10,19 10,19 10,19 0,88 0,391 storage 1 6,48 6,48 6,48 0,56 0,488 Square 3 1268,74 1268,74 422,91 36,63 0,001 temp*temp 1 1115,44 1022,46 1022,46 88,55 0,000 RH*RH 1 115,58 125,25 125,25 10,85 0,022 storage*storage 1 37,73 37,73 37,73 3,27 0,130 Interaction 3 191,42 191,42 63,81 5,53 0,048 temp*RH 1 33,52 33,52 33,52 2,90 0,149 temp*storage 1 41,15 41,15 41,15 3,56 0,118 RH*storage 1 116,75 116,75 116,75 10,11 0,025Residual Error 5 57,73 57,73 11,55 Lack-of-Fit 3 57,26 57,26 19,09 80,52 0,012

Pure Error 2 0,47 0,47 0,24Total 14 1880,55

RH*temp storage*temp1,00,50,0-0,5-1,0

1,0

0,5

0,0

-0,5

-1,0storage*RH

1,00,50,0-0,5-1,0

1,0

0,5

0,0

-0,5

-1,0

temp 0RH 0storage 0

Hold Values

> – – – < 0

0 1010 2020 30

30

Elongation

Contour Plots of Elongation

01020

-1 0

2030

-11

01

Elongation

RH

temp

010

20

-1 0

2030

-11

01

Elongation

storage

temp

253035

-1-10

-1

3540

-11

01

Elongation

storage

RH

temp 0RH 0storage 0

Hold Values

Surface Plots of Elongation

MODULUS

Response Surface Regression: modulus versus temp; RH; storage

The analysis was done using coded units.

Estimated Regression Coefficients for modulus

Term Coef SE Coef T PConstant 623,730 41,94 14,872 0,000temp 15,158 25,68 0,590 0,581RH -86,220 25,68 -3,357 0,020

storage 49,570 25,68 1,930 0,111temp*temp -33,674 37,80 -0,891 0,414RH*RH 86,956 37,80 2,300 0,070storage*storage 5,906 37,80 0,156 0,882temp*RH 227,112 36,32 6,253 0,002temp*storage -22,362 36,32 -0,616 0,565RH*storage 24,948 36,32 0,687 0,523

S = 72,6433 PRESS = 422143R-Sq = 92,51% R-Sq(pred) = 0,00% R-Sq(adj) = 79,02%

Analysis of Variance for modulus

Source DF Seq SS Adj SS Adj MS F PRegression 9 325763 325763 36196 6,86 0,024 Linear 3 80967 80967 26989 5,11 0,055 temp 1 1838 1838 1838 0,35 0,581 RH 1 59471 59471 59471 11,27 0,020 storage 1 19657 19657 19657 3,73 0,111 Square 3 33987 33987 11329 2,15 0,213 temp*temp 1 6065 4187 4187 0,79 0,414 RH*RH 1 27792 27919 27919 5,29 0,070 storage*storage 1 129 129 129 0,02 0,882 Interaction 3 210810 210810 70270 13,32 0,008 temp*RH 1 206320 206320 206320 39,10 0,002 temp*storage 1 2000 2000 2000 0,38 0,565 RH*storage 1 2490 2490 2490 0,47 0,523Residual Error 5 26385 26385 5277 Lack-of-Fit 3 26384 26384 8795 11270,76 0,000 Pure Error 2 2 2 1Total 14 352149

RH*temp storage*temp1,00,50,0-0,5-1,0

1,0

0,5

0,0

-0,5

-1,0storage*RH

1,00,50,0-0,5-1,0

1,0

0,5

0,0

-0,5

-1,0

temp 0RH 0storage 0

Hold Values

> – – – – – < 400

400 500500 600600 700700 800800 900

900

modulus

Contour Plots of modulus

400600800

-1-1 0-1

8001000

-11

01

modulus

RH

temp

500550600

-1-1 0-1

650

10

-11

modulus

storage

temp

600

700

-1-10

-1

800

-11

01

modulus

storage

RH

temp 0RH 0storage 0

Hold Values

Surface Plots of modulus

RESPON YANG PALING SEDERHANA YAITU RESPON TENSILE, SEHINGGA

MENCARI TITIK OPTIMUM UNTUK RESPON TENSILEMencari Titik Stasioner respon Tensile Dengan Pengkodean

Untuk mendapatkan model regresi tensile dengan pengkodean, nilai yang diregresikan adalah

temperature, Rh, dan storage dan yang telah dikodekan. Dilakukan analyze response surface design

dengan minitab pada data sehingga didapatkan model regresi berikut.

Tensile = 38,9- 6,1038 temp+ 1,2625 RH-0,6862 storage-10,9450 tempt*temp -2.9525 RH*RH -8.8250 storage*storage -1.0775 temp*RH-6.8700 temp*storage+3.1075 RH*storage

B =

-10.9450 -0.5387 -3.4350

>> B=[-10.945 -0.53875 -3.435; -0.53875 -2.9525 1.554; -3.435 1.554 -8.825 ]

B =

-10.9450 -0.5387 -3.4350

-0.5387 -2.9525 1.5540

-3.4350 1.5540 -8.8250

>> inv(B)

ans =

-0.1097 0.0468 0.0509

0.0468 -0.3933 -0.0875

0.0509 -0.0875 -0.1485

>> b=[-6.10375;1.2625;-0.68625]

b =

-6.1037

1.2625

-0.6863

>> inv(B)*b

ans =

0.6934

-0.7222

-0.3193

>> -0.5*inv(B)*b

ans =

-0.3467

0.3611

0.1597

x0=[−0.34670.36110.1597 ]

x1=temp−2723

−0,3467= temp−2723

=19,0259

x2= relative−6020

0,3611= relative−6020

=67,22

x3= storage−63

0,1597= storage−63

=6,4791

Dengan memasukkan nilai xo ke persamaan regresi diperoleh respon maksimum tensile sebesar

42,763. nilai respon optimum didapatkan dengan mengatur temperatue sebesar 27 , Rh

sebesar 60% dan storange day sebesar 6.