Evolutionary Algorithms and their Applications in Civil Engineering - 1
Modul 4. doe rcbd
1. Materi : DOE Minggu IV
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 2 k Factorial Design
8. Two-Level Fractional Factorial Design
9. Nested or Hierarchial Design
10. Response Surface Methods
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2. Chapter 4. Randomized Blocks …
Controllable Factors
X 1 , X 2 , …, X q
Input Process Output (Y)
Randomization
Z 1 , Z 2 , …, Z q
unknown Uncontrollable Factors known
A A design factor that probably has an
effect on the response, but we are
Nuisance not interested in that effect
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3. Chapter 4. Randomized Blocks … (continued)
A A design factor that probably has an
effect on the response, but we are
Nuisance not interested in that effect
Factors
unknown Controllable Factors known
X 1 , X 2 , …, X q
blocking
Input Process Output (Y)
Z 1 , Z 2 , …, Z q
unknown Uncontrollable Factors known
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4. The Randomized Complete Block Design (RCBD)
When the nuisance source of variability is known
and controllable,
blocking can be used to systematically eliminate its
effect on the statistical comparisons among treatments
Situations for which the RCBD is appropriate:
Units of test equipment or machinery (often different in
their operating characteristics and would be a typical
bloking factor)
Batches of raw material, people, and time (common
nuisane sources of variability in an experiment)
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5. Desain penggunaan 4 merk mesin … (Is it right ?)
Hari Kerja atau Operator
1 2 3 4
A B C D
Mesin yang A B C D
digunakan
A B C D
(A,B,C,D)
A B C D
Tidak dapat dipisahkan antara rata-rata
produktifitas mesin dari rata-rata
produktifitas hari ataupun operator
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6. Desain penggunaan 4 merk mesin … (Right
design )
Hari Kerja atau Operator -> BLOK
1 2 3 4
A B C D
Mesin yang B C D A
digunakan
C D A B
(A,B,C,D)
D A B C
Randomisasi secara lengkap dilakukan dalam
BLOK yang sama, sehingga rata-rata produktifitas
mesin dapat dipisahkan dari rata-rata produktifitas
hari ataupun operator
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7. The Randomized Complete Block Design (RCBD)
Block 1 Block 2 Block 3 Block b
Y11 Y12 Y13 Y1b
Y21 Y22 Y23 Y2b
…
Y31 Y32 Y33 Y3b
… … … …
Ya1 Ya2 Ya3 Yab
There is one observation per treatment (1, 2, …, a) in
each block, and the order in which the treatments are
run within each block is determined randomly.
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8. The ANOVA: Structure Data and Model RCBD
Treatment Block (j) Total Average
(level i) 1 2 … b Yi. Yi.
1 Y11 Y12 … Y1n Y1. Y1.
2 Y21 Y22 … Y2n Y2. Y2.
... … … … … … …
a Ya1 Ya2 … Yan Ya. Ya.
Total Y.j Y.1 Y.2 … Y.b Y.. Y..
Statistical model for the RCBD: yij
= µij + εij, , i = 1, 2, …, a; j = 1, 2, …, b atau
yij
= µ + τi + βj + εij
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9. The ANOVA Table for a RCBD Model
Source of Sum of Mean
DF F
Variation Squares Square
Treatments SST a−1 MST FT = MST / MSE
Blocks SSB b–1 MSB FB = MSB / MSE
Error SSE (a-1)(b-1) MSE
Total SSTotal N−1
a b Y..2
SS Total = ∑∑ 2
Yij −
N
i =1 j =1
1 a 2 Y..2 1 b Y..2
SS T = ∑Yi. − ; SSB = ∑Y j2. − N
b i =1 N a j =1
SSE = SS Total − SS T − SSB
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10. Chapter 4. Randomized Blocks …
People, Machine,
and other control-
Type of Tip Controllable Factors able factors are inthe
SAME conditions
1, 2, 3, 4 X 1 , X 2 , …, X q
Input Process Output (Y)
Metal coupon Z 1 , Z 2 , …, Z q The hardness
testing machine
Uncontrollable Factors
We wish to determine whether or not four different tips produce
different readings on a hardness testing machine ?
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11. Data from the Hardness Testing Experiment …
Test Coupon (Block)
Type of Tip
1 2 3 4
1 9.3 9.4 9.6 10.0
2 9.4 9.3 9.8 9.9
3 9.2 9.4 9.5 9.7
4 9.7 9.6 10.0 10.2
The metal coupon differ slightly in their hardness, as might
happen if they are taken from ingots that are product in
different heats, the experiment units (the coupon) will
contribute to the variabiliy observed in the hardness data.
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17. Graphical comparison of means …
This plot indicates that tip
1, 2, and 3 probably
produce identical average
hardness measurements
but that tip 4 produces a
much higher mean
hardness.
Tip 3 Tip 1 Tip 2 Tip 4
9.4 9.6 9.8 10.0
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