Transcript PENDEKATAN NEURAL NETWORK UNTUK PEMODELAN TIME …

Materi : DOE Minggu II
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Introduction
Simple Comparative Experiments 
Experiments with a Single Factor 
The Randomized Complete Block Design
The Latin Square Design
Factorial Design
The 2k Factorial Design
Two-Level Fractional Factorial Design
Nested or Hierarchial Design
Response Surface Methods
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

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Completely Randomized Designs
Problem 1: Simple Comparative Experiments
Metode perakitan
produk
Prosedur
STANDAR
Prosedur
BARU
Controllable Factors
X1, X2, …, Xq
Manusia, Mesin dan
faktor lain yang dapat
dikontrol dalam kondisi
SAMA
Input
Process
Output (Y)
Bahan baku
produk
Z1, Z2, …, Zq
Waktu perakitan
produk
Uncontrollable Factors
Apakah ada perbedaan rata-rata waktu perakitan produk antara
prosedur STANDAR dan BARU ?
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Problem 1: Data Eksperimen ... (dalam menit)
j
Prosedur
STANDAR
Prosedur
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
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Dari 18 pekerja baru yang ada, 9 orang
dilatih dengan prosedur STANDAR dan 9
orang yang lain dengan prosedur BARU.
RANDOMIZED DESIGNS
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
STANDAR
BARU
N
9
9
Mean
37.22
30.44
StDev
3.35
3.17
SE Mean
1.1
1.1
Difference = mu STANDAR - mu BARU
Estimate for difference: 6.78
95% CI for difference: (3.52, 10.03)
T-Test of difference = 0 (vs not =):
T-Value = 4.41 P-Value = 0.000
Both use Pooled StDev = 3.26
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DF = 16
Problem 1: Data Analysis ...
(continued)
MTB > AOVOneway 'STANDAR' 'BARU'.
One-way ANOVA: STANDAR, BARU
Analysis of Variance
Source
DF
SS
Factor
1
206.7
Error
16
169.8
Total
17
376.5
MS
206.7
10.6
F
19.48
P
0.000
Individual 95% CIs For Mean
Based on Pooled StDev
Level
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
X1, X2, …, Xq
Manusia, Mesin,
Mobil, Jalan dan
faktor lain yang dapat
dikontrol dalam kondisi
TIDAK SAMA
Input
Process
Output (Y)
Bahan baku
BAN mobil
Z1, Z2, …, Zq
Jarak tempuh
sampai ban rusak
Dua Merk BAN
Ban A
Ban B
Controllable Factors
Uncontrollable Factors
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)
Ada 5 mobil dengan merk, tahun, rute, sopir,
model dan kondisi mesin yang TIDAK SAMA
RANDOMIZED BLOCK DESIGN
j
Ban
Merk A
Ban
Merk B
1.
106
102
2.
98
94
3.
123
118
4.
97
91
5.
88
83
Posisi ban
belakang
kiri-kanan
acak
kiri-kanan
acak
5 mobil
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

Ban A
Ban B

Problem 2: Data Analysis ...
MTB > Paired
'Ban A' 'Ban B'.

Paired T-Test and CI: Ban A, Ban B
Paired T for Ban A - Ban B
Ban A
Ban B
Difference
N
5
5
Mean
102.40
97.60
4.80
StDev SE Mean
13.16
5.89
13.28
5.94
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
N
Ban A 5
Ban B 5
for Ban A vs Ban B
Mean StDev SE Mean
102.4
13.2
5.9
97.6
13.3
5.9
Difference = mu Ban A - mu Ban B
Estimate for difference: 4.80
95% 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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(continued)
Experiments with a Single Factor
People, Machine,
Method and other
controbllable factors are
inthe SAME conditions
Cotton Weight
Percentge
Controllable Factors
15, 20, 25, 30, 35, 40
X1, X2, …, Xq
Input
Process
Output (Y)
Material
Z1, Z2, …, Zq
The tensile
strength
Uncontrollable Factors
Engineer suspects that increasing the cotton content will increase
the tensile strength ?
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Experimental Run Number
Factor
1
2
Level
Factor
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
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25
Use
computer
software
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
1
2
3
4
5
15
7
7
15
11
20
12
17
12
25
14
18
30
19
35
Total
Observations
Total
Average
9
49
9.8
18
18
77
15.4
18
19
19
88
17.6
25
22
19
23
108
21.6
7
10
11
15
11
54
10.8
-
-
-
-
-
376
15.04
First data
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25th data
Tensile strength (lb/in2)
Data Analysis …
Cotton weight percentage
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Data Analysis …
MTB > AOVOneway
(continued)
'15%'-'35%'
One-way ANOVA: 15%, 20%, 25%, 30%, 35%
Analysis of Variance
Source
DF
SS
Factor
4
475.76
Error
20
161.20
Total
24
636.96
Level
15%
20%
25%
30%
35%
N
5
5
5
5
5
Mean
9.800
15.400
17.600
21.600
10.800
StDev
3.347
3.130
2.074
2.608
2.864
Pooled StDev = 2.839
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MS
118.94
8.06
F
14.76
P
0.000
Individual 95% CIs For Mean
Based on Pooled StDev
------+---------+---------+---------+
(-----*----)
(----*----)
(----*----)
(----*----)
(-----*----)
------+---------+---------+---------+
10.0
15.0
20.0
25.0
Data Analysis …
(continued)
BERBEDA
Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.00722
SAMA
Critical value = 4.23
Intervals for (column level mean) - (row level mean)
15
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20
25
20
-10.971
-0.229
25
-13.171
-2.429
-7.571
3.171
30
-17.171
-6.429
-11.571
-0.829
-9.371
1.371
35
-6.371
4.371
-0.771
9.971
1.429
12.171
30
5.429
16.171
Data Analysis …
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(continued)
Tiga tahap utama dalam Desain Eksperimen


Product and/or
process experts
The Conducting Phase
Product, process
and DOE experts
The Analysis Phase
DOE experts or
statistician

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The Planning Phase