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Engineering.
Lampiran 1. Alias interaksi dua faktor untuk tiga rancangan 2
IV7-2Alias interaksi dua faktor Interaksi
2 faktor D1 D2 D3
AB CF + ACDG + BDFG CF + BDEG + ACDEFG CDF + DEG + ABCEFG AC BF + ABDG + ACDFG BF + CDEG + ABDEFG BDF + BCDEG + AEFG AD BCDF + BCG + FG BCDF + EG + ABCEFG BCF + BEG + ACDEFG AE BCF + ABCDEG + DEFG BCEF + D G + ABCDFG BCDEF + BDG + ACFG AF BC + ABCDFG + DG BC + DEFG + ABCDG BCD + BDEFG + ACEG AG BCFG + ABCD + DF BCFG + DE + ABCDEF BCDFG + BDE + ACEF BC AF + DG + ABCDFG AF + ABCDEG + DEFG ADF + ACDEG + BEFG BD ACDF + CG + ABFG ACDF + ABEG + CEFG ACF + AEG + BCDEFG BE ACEF + CDEG + ABDEFG ACEF + ABDG + CDFG ACDEF + ADG + BCFG BF AC + CDFG + ADG AC + ABDEFG + CDEG ACD + ADEFG + BCEG BG ACFG + CD + ABDF ACFG + ABE + CDEF ACDFG + ADE + BCEF CD ABDF + BG + ACFG ABDF + ACEG + BEFG ABF + ABCEG + DEFG CE ABEF + BDEG + ACDEFG ABEF + ACDG + BDFG ABDEF + ABCDG + FG CF AB + BDFG + ACDG AB + ACDEFG + BDEG ABD + ABCDEFG + EG CG ABFG + BD + ACDF ABFG + ACDE + BDEF ABDFG + ABCDE + EF DE ABCDEF + BCEG + AEFG ABCDEF + AG + BCFG ABCEF + ABG + CDEG DF ABCD + BCFG + AG ABCD + AEFG + BCEG ABC + ABEFG + CDEG D G ABCDFG + BC + AF ABCDFG + AE + BCEF ABCFG + ABE + CDEF EF ABCE + BCDEFG + ADEG ABCE + ADFG + BCDG ABCDE + ABDFG + CG EG ABCEFG + BCDE + ADEF ABCEFG + AD + BCDF ABCDEFG + ABD + CF FG ABCG + BCDF + AD ABCG + ADEF + BCDE ABCDG + ABDEF + CE
No
Generator &
defining relation
Alias
Pengaruh yg
dianalisis
A = BD = BE = ADEB = AD = AE = BDE C = ABCD = ABCE = CDE D = AB = ABDE = E AC = BCD = BCE = ACDE BC = ACD = ACE = BCDE CD = ABC = ABCDE = CE A = BD = BE B = AD = AE C D = E = AB AC BC CD = CE 1 D = AB ; E = AB I = ABD = ABE = DE
AB terpaut dengan D&E; AD terpaut dengan B A = BD = CE = ABCDE B = AD = ABCE = CDE C = ABCD = AE = BDE D = AB = ACDE = BCE E = ABDE = AC = BCD BC = ACD = ABE = DE BE = AD E = ABC = CD A = BD = CE B = AD C = AE D = AB E = AC BC = DE BE = CD 2 D = AB ; E = AC
I = ABD = ACE = BCDE (Resolusi III)
(sesuai kriteria resolusi maksimum dan minimum
aberration) AB terpaut dengan D; AD terpaut dengan B A = BD = ABCE = CDE B = AD = CE = ABCDE C = ABCD = BE = ADE D = AB = BCDE = ACE E = ABDE = BC = ACD AC = BCD = ABE = DE AE = BDE = ABC = CD A = BD B = AD = CE C = BE D = AB E = BC AC = DE AE = CD 3 D = AB ; E = BC
I = ABD = BCE = ACDE (Resolusi III)
Isomorphic dari no 2
(A à B ; B à A)
AB terpaut dengan D; AD terpaut dengan B; BC terpaut dengan E A = BD = BCE = ACDE B = AD = ACE = BCDE C = ABCD = ABE = DE D = AB = ABCDE = CE E = ABDE = ABC =CD AC = BCD = BE = ADE AE = BDE = BC = ACD A = BD B = AD C = DE D = AB = CE E = CD AC = BE AE = BC 4 D = AB ; E = ABC
I = ABD = ABCE = CDE (Resolusi III)
(sesuai kriteria resolusi maksimum dan minimum
aberration) AB terpaut dengan D; AD terpaut dengan B A = CD = BE = ABCDE B = ABCD = AE = ABCD C = AD = ABCE = BDE D = AC = ABDE = BCE E = ACDE = AB = BCD BC = ABD = ACE = DE BD = ABC = ADE = CE A = CD = BE B = AE C = AD D = AC E = AB BC = DE BD = CE 5 D = AC ; E = AB
I = ACD = ABE = BCDE (Resolusi III)
Isomorphic dari no 2
(C à B ; B à C)
AB terpaut dengan E; AD terpaut dengan C A = CD = CE = ADE
B = ABCD = ABCE = BDE C = AD = AE = CDE D = AC = ACDE = E AB = BCD = BCE = ABDE BC = ABD = ABE = BCDE BD = ABC = ABCDE = BE A = CD = CE B C = AD = AE D = AC = E AB BC BD = BE 6 D = AC ; E = AC I = ACD = ACE = DE AD terpaut dengan C
Lampiran 2. (lanjutan)
No
Generator &
defining relation
Alias
Pengaruh yg
dianalisis
A = CD = ABCE = BDE B = ABCD = CE = ADE C = AD = BE = ABCDE D = AC = BCDE = ABE E = ACDE = BC = ABD AB = BCD = ACE = DE AE = CDE = ABC = BD A = CD B = CE C = AD = BE D = AC E = BC AB = DE AE = BD 7 D = AC ; E = BCI = ACD = BCE = ABDE (Resolusi III)
Isomorphic dari no 2
(AàB ; BàC ; CàA)
AD terpaut dengan C ; BC terpaut dengan E A = CD = BCE = ABDE B = ABCD = ACE = DE C = AD = ABE = BCE D = AC = ABCDE = BE E = ABDE = ABC = BD AB = BCD = CE = ADE AE = CDE = BC = ABD A = CD B = DE C = AD D = AC = BE E = BD AB = CE AE = BC 8 D = AC ; E = ABC
I = ACD = ABCE = BDE (Resolusi III) Isomorphic dari no 4 (B à C ; C à B) AD terpaut dengan C A = ABCD = BE = CDE B = CD = AE = ABCDE C = BD = ABCE = ADE D = BC = ABED = ACE E = BCDE = AB = ACD AC = ABD = BCE = DE AD = ABC = BED = CE A = BE B = CD = AE C = BD D = BC E = AB AC = DE AD = CE 9 D = BC ; E = AB I = BCD = ABE = ACDE (Resolusi III) Isomorphic dari no 2 (AàC ; CàB ; BàA)
AB terpaut dengan E; BC terpaut dengan D A = ABCD = CE = BDE B = CD = ABCE = ADE C = BD = AE = ABCDE D = BC = ACED = ABE E = BCDE = AC = ABD AB = ACD = BCE = DE AD = ABC = CDE = BE A = CE B = CD C = BD = AE D = BC E = AC AB = DE AD = BE 10 D = BC ; E = AC I = BCD = ACE = ABDE (Resolusi III) Isomorphic dari no 2 (CàA ; AàC) BC terpaut dengan D A = ABCD = ABCE = ADE B = CD = CE = BDE C = BD = BE = CDE D = BC = BCDE = E AB = ACD = ACE = ABDE AC = ABD = ABE = ACDE AD = ABC = ABCDE = AE A B = CD = CE C = BD = BE D = BC = E AB AC AD = AE 11 D = BC ; E = BC I = BCD = BCE = DE Isomorphic dari no 1 (C à A)
BC terpaut dengan D&E A = ABCD = BCE = DE B = CD = ACE = ABDE C = BD = ABE = ACDE D = BC = ABCDE = AE E = BCDE = ABC = AD AB = ACD = CE = BDE AC = ABD = BE = CDE A = DE B = CD C = BD D = BC = AE E = AD AB = CE AC = BE 12 D = BC ; E = ABC I = BCD = ABCE = ADE (Resolusi III) Isomorphic dari no 4 (A à C ; C à A)
No
Generator &
defining relation
Alias
Pengaruh yg
dianalisis
A = BCD = BE = ACDE B = ACD = AE = BCDE C = ABD = ABCE = DE D = ABC = ABDE = CE E = ABCDE = AB = CD AC = BD = BCE = ADE AD = BC = BDE = ACE A = BE B = AE C = DE D = CE E = AB = CD AC = BD AD = BC 13 D = ABC ; E = ABI = ABCD = ABE = CDE (Resolusi III)
Isomorphic dari no 4
(D à E ; E à D)
AB terpaut dengan E ; AD terpaut dengan BC A = BCD = CE = ABDE B = ACD = ABCE = DE C = ABD = AE = BCDE D = ABC = ACDE = BE E = ABCDE = AC = BD AB = CD = BCE = ADE AD = BC = CDE = ABE A = CE B = DE C = AE D = BE E = AC = BD AB = CD AD = BC 14 D = ABC ; E = AC
I = ABCD = ACE = BDE (Resolusi III) Isomorphic dari no 4 (D à E ; E à D) (B à C ; C à B) AD terpaut dengan BC A = BCD = ABCE = DE B = ACD = CE = ABDE C = ABD = BE = ACDE D = ABC = BCDE = AE E = ABCDE = BC = AD AB = CD = ACE = BDE AC = BD = ABE = CDE A = DE B = CE C = BE D = AE E = BC = AD AB = CD AC = BD 15 D = ABC ; E = BC
I = ABCD = BCE = ADE (Resolusi III)
Isomorphic dari no 4
(D à E ; E à D)
(A à C ; C à A) AD terpaut dengan BC & E A = BCD = BCE = ADE B = ACD = ACE = BDE C = ABD = ABE = CDE D = ABC = ABCDE = E AB = CD = CE = ABDE AC = BD = BE = ACDE AD = BC = BCDE = AE A B C D = E AB = CD = CE AC = BD = BE AD = BC = AE 16 D = ABC ; E = ABC I = ABCD = ABCE = DE AD terpaut dengan BC
Lampiran 3. Penggunaan SAS 9.1 untuk pembentukan struktur rancangan FF
Tahapan pembentukan struktur rancangan FF dengan SAS 9.1 adalah sebagai
berikut :
1. Pilih menu SOLUTIONS à Analysis à Design of Experiments
2. untuk membuat rancangan FF yang baru, pilih menu FILE à Create New
Design à Two-level…
3. Klik Define Variables.
Klik Add> untuk menentukan banyaknya faktor yang akan dicobakan ,
untuk contoh ini dipilih 5 faktor yang digunakan.
Kemudian klik OK untuk kembali ke kotak dialog sebelumnya.
4. Klik Select Design.
Pilih Fractional factorial designs pada show designs of type.
Tentukan fraksi percobaan dengan memilih type rancangan yang tersedia,
dalam contoh ini pilih rancangan dengan fraksi ¼.
Lampiran 3. (lanjutan)
5. Klik Design Details... untuk mengetahui struktur rancangan yang
terbentuk.
Pada Design Information dapat diketahui informasi tentang resolusi
maksimum yang bisa dicapai, didapat resolusi III sebagai resolusi
maksimum
6. Pada Confounding Rules didapatkan generator yang terpilih sebagai
pembentuk struktur rancangan terbaik.
Dengan menekan panah ke bawah pada Principal : ++ dapat ditentukan
seperempat bagian yang mana yang akan dicobakan, hal ini berkaitan
dengan fold over.
7. Pada Alias Structure dap at diketahui susunan pengaruh faktor yang saling
terpaut.
8. Klik tanda silang untuk menutup kotak Design Details dan kembali pada
kotak dialog Two-Level design spesifications.
Lampiran 4. Penggunaan ADX SAS 9.1 untuk Pengacakan Rancangan FF.
Teknik pengacakan pada rancangan FF dapat dilakukan dengan klik edit
response kemudian memilih menu Design à Randomized Design...
No
Defining contrast
subgroups AP
Alias
Pengaruh yg
dianalisis
A = PQ = PR = AQR B = ABPQ = ABPR = BQR AB = BPQ = BPR = ABQR P = AQ = AR = PQR Q = AP = APQR = R BP = ABQ = ABR = BPQR BQ = ABP = ABPQR = BR A = PQ = PR B AB P = AQ = AR Q = AP = R BP BQ = BR 1 Q = AP ; R = AP I = APQ = APR = QR Q terpaut dengan R A = PQ = ABPR = BQR B = ABPQ = PR = AQR AB = BPQ = APR = QR P = AQ = BR = ABPQR Q = AP = BPQR = ABR R = APQR = BP = ABQ AR = PQR = ABP = BQ A = PQ B = PR AB = QR P = AQ = BR Q = AP R = BP AR = BQ 2 Q = AP ; R = BP I = APQ = BPR = ABQR (terbaik menurut kriteria resolusi maksimum danminimum aberration) Tidak ada pengaruh utama yang terpaut dengan pengaruh utama lain A = PQ = BPR = ABQR B = ABPQ = APR = QR AB = BPQ = PR = AQR P = AQ = ABR = BPQR Q = AP = ABPQR = BR R = APQR = ABP = BQ AR = PQR = BP = ABQ A = PQ B = QR AB = PR P = AQ Q = QP = BR R = BQ AR = BP 3 Q = AP ; R = ABP I = APQ = ABPR = BQR (Resolusi III)
Tidak ada pengaruh utama yang terpaut dengan pengaruh utama lain A = ABPQ = PR = BQR B = PQ = ABPR = AQR AB = APQ = BPR = QR P = BQ = AR = ABPQR Q = BP = APQR = ABR R = BPQR = AP = ABQ AQ = ABP = PQR = BR A = PR B = PQ AB = QR P = BQ = AR Q = BP R = AP AQ = BR 4 Q = BP ; R = AP I = BPQ = APR = ABQR (Resolusi III) Isomorphic dari no 2
(A à B ; B à A) Tidak ada pengaruh utama yang terpaut dengan pengaruh utama lain
A = ABPQ = ABPR = AQ R B = PQ = PR = BQR AB = APQ = APR = ABQR P = BQ = BR = PQR Q = BP = BPQR = R AP = ABQ = ABR = APQR AQ = ABP = ABPQR = AR A B = PQ = PR AB P = BQ = BR Q = BP = R AP AQ = AR 5 Q = BP ; R = BP I = BPQ = BPR = QR Q terpaut dengan R A = ABPQ = BPR = QR B = PQ = APR = AQR AB = APQ = PR = BQR P = BQ = ABR = APQR Q = BP = ABPQR = AR R = BPQR = ABP = AQ AP = ABQ = BR = PQR A = QR B = PQ AB = PR P = BQ Q = BP = AR R = AQ AP = BR 6 Q = BP ; R = ABP I = BPQ = ABPR = AQR (Resolusi III) Isomorphic dari no 3
(A à B ; B à A) Tidak ada pengaruh utama yang terpaut dengan pengaruh utama lain
Lampiran 5. (Lanjutan)
No
Defining contrast
subgroups AP
Alias
Pengaruh yg
dianalisis
A = BPQ = PR = ABQR B = APQ = APR = QR AB = PQ = BPR = AQR P = ABQ = AR = BPQR Q = ABP = APQR = BR R = ABPQR = AP = BQ AQ = BP = PQR = ABR A = PR B = QR AB = PQ P = AR Q = BR R = AP = BQ AQ = BP 7 Q = ABP ; R = AP I = ABPQ = APR = BQR (Resolusi III) Isomorphic dari no 3(Q à R ; R à Q) Tidak ada pengaruh utama yang terpaut dengan pengaruh utama lain A = BPQ = ABPR = QR B = APQ = PR = ABQR AB = PQ = APR = BQR P = ABQ = BR = APQR Q = ABP = BPQR = AR R = ABPQR = BP = AQ AP = BQ = ABR = PQR A = QR B = PR AB = PQ P = BR Q = AR R = BP = AQ AP = BQ 8 Q = ABP ; R = BP I = ABPQ = BPR = AQR (Resolusi III) Isomorphic dari no 3 (A à B ; B à A) (Q à R ; R à Q)
Tidak ada pengaruh utama yang terpaut dengan pengaruh utama lain A = BPQ = BPR = AQR B = APQ = APR = BQR AB = PQ = PR = ABQR P = ABQ = ABR = PQR Q = ABP = ABPQR = R AP = BQ = BR = APQR AQ = BP = BPQR = AR A B AB = PQ = PR P Q = R AP = BQ = BR AQ = BP = AR 9 Q = ABP ; R = ABP I = ABPQ = ABPR = QR Q terpaut dengan R
FFSP
Tahapan pembentukan struktur rancangan FFSP dengan SAS 9.1 adalah sebagai
berikut :
1. Pilih menu FILE à Create New Design à Split-plot…
2. Klik Define Variables.
Pada Whole Plot Factor Klik Add> untuk menentukan banyaknya faktor
petak utama yang akan dicobakan,untuk contoh ini dipilih 2.
Lampiran 6 (lanjutan)
Pada Sub -plot Factor klik Add> untuk menentukan banyaknya faktor anak
petak yang dicobakan, untuk contoh ini dipilih 3. kemudian klik OK untuk
kembali pada kotak dialog sebelumnya.
3. Klik Select Design.
Pilih type rancangan yang diinginkan, untuk contoh ini dipilih rancangan
dengan 8 run.
4. Klik Design Details... untuk mengetahui struktur rancangan yang
terbentuk.
Pada Design Information dapat diketahui informasi tentang resolusi
maksimum yang bisa dicapai, didapat resolusi III sebagai resolusi
maksimum. Defining relation yang terbaik adalah APQ=BPR dengan
WLP {2,1,0}
Lampiran 7. Penggunaan SAS 9.1 untuk pembentukan pengacakan struktur
rancangan FFSP
Pilih Edit Respon kemudian klik Design à Randomize Design...
percobaan pada contoh kasus rancangan FF
•
Tahap 1 : Pengaruh faktor E masuk ke dalam model, R
2model = 76.44%
Analysis of Variance Source DF Sum of Squares Mean Square F Value P r > F Model 1 7921.000 0 7921.0000 45.41 <.0001 Error 14 2442.0000 174.4286 Corrected Total 15 10363.0000 Variable Parameter Estimate Standard Error Type II SS F Value P r > F Intercept 54.2500 3.3018 47089 .0000 269.96 <.0001 E -22.2500 3.3018 7921.0000 45.41 <.0001•
Tahap 2 : Pengaruh faktor B masuk ke dalam model, R
2model = 91.49%
Analysis of Variance Source DF Sum of Squares Mean Square F Value P r > F Model 2 9481.2500 4740.6250 69.89 <.0001 Error 13 881.7500 67.8269 Corrected Total 15 10363.0000 Variable Parameter Estimate Standard Error Type II SS F Value P r > F Intercept 54.2500 2.0589 47089.0000 694.25 <.0001 B 9.8750 2.0589 1560.2500 23.00 0.0003 E -22.2500 2.0589 7921.000 0 116.78 <.0001 No other variable met the 0.0500 significance level for entry into the model.Lampiran 9. Data percobaan pada contoh kasus rancangan FFSP
A B P Q R S T U y -1 -1 -1 -1 -1 1 1 1 1.00 1 -1 -1 -1 1 -1 0.50 -1 1 -1 -1 -1 1 37.46 1 1 -1 1 -1 -1 32.26 -1 -1 1 1 -1 -1 36.54 1 -1 1 -1 -1 1 33.34 -1 1 1 -1 1 -1 4.00 1 1 1 1 1 1 2.50 1 -1 -1 -1 -1 1 1 1 1.00 1 -1 -1 -1 1 -1 34.74 -1 1 -1 -1 -1 1 1.20 1 1 -1 1 -1 -1 76.86 -1 -1 1 1 -1 -1 2.10 1 -1 1 -1 -1 1 76.34 -1 1 1 -1 1 -1 1.10 1 1 1 1 1 1 37.66 -1 1 -1 -1 -1 1 1 1 1.90 1 -1 -1 -1 1 -1 2.50 -1 1 -1 -1 -1 1 31.06 1 1 -1 1 -1 -1 37.06 -1 -1 1 1 -1 -1 31.34 1 -1 1 -1 -1 1 40.94 -1 1 1 -1 1 -1 3.20 1 1 1 1 1 1 5.20 1 1 -1 -1 -1 1 1 1 6.10 1 -1 -1 -1 1 -1 37.54 -1 1 -1 -1 - 1 6.00 1 1 -1 1 -1 -1 82.06 -1 -1 1 1 -1 -1 7.10 1 -1 1 -1 -1 1 84.34 -1 1 1 -1 1 -1 2.10 1 1 1 1 1 1 50.46Struktur Alias Pengaruh Faktor
A = APQS = AQRT = APRU = APRST = APQTU = AQRSU 12.87 B = BPQS = BQRT = BPRU = BPRST = BPQTU = BQRSU 3.14
P = QS = PQRT = RU =PRST = QTU = PQRSU 28.82
Q = PS = RT = PQRU = PQRST = PTU = RSU 0.80
R = PQRS = QT = PU = PST = PQRTU = QSU 1.81
S = PQ = QRST = PRSU = PRT = PQSTU = QRU 0.92
T = PQST = QR = PRTU = PRS = PQT = QRSTU -26.53
U = PQSU = QRTU = PR = PRSTU = PQT = QRS 1.59
AB = ABPQS = ABQRT = ABPRU = ABPRST = ABPQTU = ABQRSU 2.44
PT = QST = PQR = RUT = RS = QU = PQRSTU -9.98
AP = AQS = APQRT = ARU = ARST = AQTU = APQRSU 27.84 AQ = APS = ART = APQRU = APQRST = APTU = ARSU 0.22 AR = APQRS = AQT = APU = APST = APQRTU = AQSU 0.15 AS = APQ = AQRST = APRSU = APRT = APQSTU = AQRU 1.57 AT = APQST = AQR = APRTU = APRS = APQU = AQRSTU 5.87 AU = APQSU = AQRTU = APR = APRSTU = APQT = AQRS 0.84 BP = BQS = BPQRT = BRU = BRST = BQTU = BPQRSU 2.59 BQ = BPS = BRT = BPQRU = BPQRST = BPTU = BRSU -0.13 BR = BPQRS = BQT = BPU = BPST = BPQRTU = BQSU 0.74 BS = BPQ = BQRST = BPRSU = BPRT = BPQSTU = BQRU 0.77 BT = BPQST = BQR = BPRTU = BPRS = BPQU = BQRSTU 0.17 BU = BPQSU = BQRTU = BPR = BPRSTU = BPQT = BQRS 1.29 ABP = ABQS = ABPQRT = ABRU = ABRST = ABQTU = ABPQRSU -0.98 ABQ = ABPS = ABRT = ABPQRU = ABPQRST = ABPTU = ABRSU 0.49 ABR = ABPQRS = ABQT = ABPU = ABPST = ABPQRTU = ABQSU 0.37 ABS = ABPQ = ABQRST = ABPRSU = ABPRT = ABAQTU = ABQRU 0.67 ABT = ABPQST = ABQR = ABPRTU = ABPRS = ABPQU = ABQRSTU -0.33 ABU = ABPQSU = ABQRTU = ABPR = ABSTU = ABPQT = ABQRS 0.79 APT = AQST = APQR = ARTU = ARS = AQU = APQRSTU -9.16 BPT = BQST = BPQR = BRTU = BRS = BQU = BPQRSTU -0.83 ABPT = ABQST = ABPQR = ABRTU = ABRS = ABQU = ABPQRSTU 1.59