04/10/23
Materi : DOE Minggu II
1. Introduction 2. Simple Comparative Experiments 3. Experiments with a Single Factor 4. The Randomized Complete Block Design 5. The Latin Square Design 6. Factorial Design 7. The 2k Factorial Design 8. Two-Level Fractional Factorial Design 9. Nested or Hierarchial Design10. Response Surface Methods
04/10/23
Reference :
. Montgomery, D.C. (2003) Design and Analysis of Experiments Fifth Edition, John Wiley & Sons.
Chapter 2. Simple Comparative Experiments
Inferences About the Defferences in Means : Randomized Designs
Paired Comparison Designs Inferences About the Variances of Normal Distributions
Chapter 3. Experiments with a Single Factor: The Analysis of Variance
Completely Randomized Designs
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Problem 1: Simple Comparative Experiments
ProcessInput Output (Y)
Z1, Z2, …, Zq
X1, X2, …, Xq
Uncontrollable Factors
Controllable Factors
Bahan baku produk
Metode perakitan
produk
Prosedur STANDA
R
Prosedur BARU
Manusia, Mesin dan faktor lain yang
dapat dikontrol dalam kondisi
SAMA
Waktu perakitan
produk
Apakah ada perbedaan rata-rata waktu perakitan produk antara prosedur STANDAR dan BARU ?
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Problem 1: Data Eksperimen ... (dalam menit)
jProsedur
STANDARProsedur BARU
1. 32 35
2. 37 31
3. 35 29
4. 38 25
5. 41 34
6. 42 30
7. 40 27
8. 36 32
9. 34 31
9 pekerja
9 pekerja
18 pekerja
Dari 18 pekerja baru yang ada, 9 orang dilatih dengan prosedur STANDAR dan 9 orang yang lain dengan prosedur BARU. RANDOMIZED DESIGNS
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Problem 1: Data Analysis ... (MINITAB output)
Data BARU Berdistribusi NORMAL
Data STANDAR
Berdistribusi NORMAL
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Problem 1: Data Analysis ... (MINITAB output)
MTB > TwoSample 'STANDAR' 'BARU';SUBC> Pooled.
Two-sample T for STANDAR vs BARU
N Mean StDev SE MeanSTANDAR 9 37.22 3.35 1.1BARU 9 30.44 3.17 1.1
Difference = mu STANDAR - mu BARUEstimate for difference: 6.7895% CI for difference: (3.52, 10.03)
T-Test of difference = 0 (vs not =): T-Value = 4.41 P-Value = 0.000 DF = 16
Both use Pooled StDev = 3.26
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Problem 1: Data Analysis ... (continued)
MTB > AOVOneway 'STANDAR' 'BARU'.
One-way ANOVA: STANDAR, BARU
Analysis of VarianceSource DF SS MS F PFactor 1 206.7 206.7 19.48 0.000Error 16 169.8 10.6Total 17 376.5
Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ----------+---------+---------+------STANDAR 9 37.222 3.346 (-----*------) BARU 9 30.444 3.167 (------*------) ----------+---------+---------+------Pooled StDev = 3.257 31.5 35.0 38.5
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Problem 2: Simple Comparative Experiments
ProcessInput Output (Y)
Z1, Z2, …, Zq
X1, X2, …, Xq
Uncontrollable Factors
Controllable Factors
Bahan baku BAN mobil
Dua Merk BAN
Ban A Ban B
Manusia, Mesin, Mobil, Jalan dan faktor lain yang dapat dikontrol dalam kondisi TIDAK SAMA
Jarak tempuh sampai ban
rusak
Apakah ada perbedaan rata-rata jarak tempuh (keawetan) ban antara ban merk A dan merk B ?
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Problem 2: Data Eksperimen ... (dalam km)
jBan Merk A
Ban Merk B
1. 106 102
2. 98 94
3. 123 118
4. 97 91
5. 88 83
kiri-kanan acak
kiri-kanan acak
5 mobil
Ada 5 mobil dengan merk, tahun, rute, sopir, model dan kondisi mesin yang TIDAK SAMA RANDOMIZED BLOCK DESIGN
Posisi ban
belakang
Ban A
Ban B
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Problem 2: Data Analysis ... (continued)
MTB > Paired 'Ban A' 'Ban B'.
Paired T-Test and CI: Ban A, Ban B
Paired T for Ban A - Ban B
N Mean StDev SE MeanBan A 5 102.40 13.16 5.89Ban B 5 97.60 13.28 5.94Difference 4.80 0.837 0.374
95% CI for mean difference: (3.761, 5.839)
T-Test of mean diff. = 0 (vs not = 0): T-Value = 12.83 P-Value = 0.000
MTB > TwoSample 'Ban A' 'Ban B';SUBC> Pooled.
Two-Sample T-Test and CI: Ban A, Ban B
Two-sample T for Ban A vs Ban B N Mean StDev SE MeanBan A 5 102.4 13.2 5.9Ban B 5 97.6 13.3 5.9
Difference = mu Ban A - mu Ban BEstimate for difference: 4.8095% CI for difference: (-14.48, 24.08)T-Test of difference = 0 (vs not =):
T-Value = 0.57 P-Value = 0.582 DF = 8
Both use Pooled StDev = 13.2
difference conclusion !!!
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Experiments with a Single Factor
ProcessInput Output (Y)
Z1, Z2, …, Zq
X1, X2, …, Xq
Uncontrollable Factors
Controllable Factors
Material
Cotton Weight Percentge
15, 20, 25, 30, 35, 40
People, Machine, Method and other
controbllable factors are inthe SAME
conditions
The tensile strength
Engineer suspects that increasing the cotton content will increase the tensile strength ?
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Experimental Run Number
Cotton Weigth Percentage Experimental Run Number
15 1 2 3 4 5
20 6 7 8 9 10
25 11 12 13 14 15
30 16 17 18 19 20
35 21 22 23 24 25
Select a random number between 1 and 25.
A completely randomized design
1
25
2
Factor
Level Factor
Use compute
r software
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The Test Sequence obtained …
Test sequence
Run Number
Cotton Weight Percentage
Test sequence
Run Number
Cotton Weight
Percentage
1 8 20 14 7 20
2 18 30 15 1 15
3 10 20 16 24 35
4 23 35 17 21 35
5 17 30 18 11 25
6 5 15 19 2 15
7 14 25 20 13 25
8 6 20 21 22 35
9 15 25 22 16 30
10 20 30 23 25 35
11 9 20 24 19 30
12 4 15 25 3 15
13 12 25
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Data from the Tensile Strength Experiment …
Cotton Weight Percent
ObservationsTotal Average1 2 3 4 5
15 7 7 15 11 9 49 9.8
20 12 17 12 18 18 77 15.4
25 14 18 18 19 19 88 17.6
30 19 25 22 19 23 108 21.6
35 7 10 11 15 11 54 10.8
Total - - - - - 376 15.04
First data
25th data
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Data Analysis …
Cotton weight percentage
Ten
sile s
tren
gth
(l
b/i
n2)
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Data Analysis … (continued)
MTB > AOVOneway '15%'-'35%'
One-way ANOVA: 15%, 20%, 25%, 30%, 35%
Analysis of VarianceSource DF SS MS F PFactor 4 475.76 118.94 14.76 0.000Error 20 161.20 8.06Total 24 636.96 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ------+---------+---------+---------+15% 5 9.800 3.347 (-----*----) 20% 5 15.400 3.130 (----*----) 25% 5 17.600 2.074 (----*----) 30% 5 21.600 2.608 (----*----) 35% 5 10.800 2.864 (-----*----) ------+---------+---------+---------+Pooled StDev = 2.839 10.0 15.0 20.0 25.0
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Data Analysis … (continued)
Tukey's pairwise comparisons
Family error rate = 0.0500Individual error rate = 0.00722
Critical value = 4.23
Intervals for (column level mean) - (row level mean)
15 20 25 30
20 -10.971 -0.229
25 -13.171 -7.571 -2.429 3.171
30 -17.171 -11.571 -9.371 -6.429 -0.829 1.371
35 -6.371 -0.771 1.429 5.429 4.371 9.971 12.171 16.171
BERBEDA
SAMA
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Data Analysis … (continued)
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Tiga tahap utama dalam Desain Eksperimen
The Planning Phase
The Conducting Phase
The Analysis Phase
Product and/or process experts
Product, process and DOE experts
DOE experts or statistician
