Transcript PENDEKATAN NEURAL NETWORK UNTUK PEMODELAN TIME …

Materi : DOE Minggu V
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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
The Latin Squares Design
 When the TWO nuisance sources of variability is
known and controllable,
 blocking in two directions can be used to
systematically eliminate its effect on the statistical
comparisons among treatments
 The rows and columns actually represent two
restriction on randomization.
 In general, a Latin square for p factors, or a pxp Latin Square,
is asquare containing p rows and p columns.
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Desain penggunaan 4 merk mesin …
Operator
Hari Kerja
1
2
3
4
1
A
B
C
D
2
B
C
D
A
3
C
D
A
B
4
D
A
B
C
Rata-rata produktifitas mesin (A,B,C,D)
dapat dipisahkan dari rata-rata produktifitas
hari kerja dan operator
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The ANOVA: Structure Data and Model Latin Squares
Column (j)
Rows
(i)
p
Total
Yi..
Average
Yi..
1
2
…
1
Y1A1
Y1B2
…
Y1Pn
Y1..
Y1..
2
Y2B1
Y2C2
…
Y2An
Y2..
Y2..
...
…
…
…
…
…
…
p
YpP1
YpA2
…
YpOn
Yp..
Yp..
Total Y.k
Y..1
Y..2
…
Y..p
Y...
Y...
Statistical model for the Latin Squares:
yijk =  + i + j + k + ijk
dengan
i = 1,2,…,p; j = 1,2,…,p; dan k = 1,2,…,p
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The ANOVA Table for a Latin Squares Model
Source of
Variation
Sum of
Squares
DF
Mean
Square
F
Treatments
SST
p1
MST
FT = MST / MSE
Rows
SSR
p–1
MSR
FR = MSR / MSE
Column
SSC
p–1
MSC
FC = MSC / MSE
Error
SSE
(p-2)(p-1)
MSE
Total
SSTotal
p
p
p
SST otal    
2
Yijk
i 1 j 1 k 1
1
SST 
p
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p

Y. 2j.
j 1
p2  1
Y...2

N
Y...2

;
N
1 p 2 Y...2
SSC   Y..k 
;
p k 1
N
1 p 2 Y...2
SSR   Yi.. 
p i 1
N
SSE  SST otal  SST  SSR  SSC
Latin Square Design for the Rocket Propellant Problem
Type of Formulation
Controllable Factors
Operators
A, B, C, D, E
X1, X2, …, Xq
1, 2, 3, 4, 5
Input
Process
Output (Y)
Batch of Raw
Material
Z1, Z2, …, Zq
The burning rate
Uncontrollable Factors
An experimenter is studying the effects of five different formulations of a rocket
propellant used in aircrew escape systems on the observed burning rate ?
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Data from the Rocket Propellant experiment …
Operators
Batches of
Raw Material
1
2
3
4
5
1
A = 24
B = 20
C = 19
D = 24
E = 24
2
B = 17
C = 24
D = 30
E = 27
A = 36
3
C = 18
D = 38
E = 26
A = 27
B = 21
4
D = 26
E = 31
A = 26
B = 23
C = 22
5
E = 22
A = 30
B = 20
C = 29
D = 31
We see that both batches of raw material (ROWS) and
operators (COLUMNS) are orthogonal to treatments.
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Graphical Analysis: Box-Plot Data …
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Graphical Analysis: Main Effect Plot …
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ANOVA of Latin Squares: MINITAB output …

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Tukey comparison: MINITAB output …
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Data structure in MINITAB
Data
structure
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(The 20th data …)
Output
MINITAB
MINITAB command for Latin Squares Design Analysis
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