Modul kuliah desain eksperimen - Teknik Industri - pertemuan 4 -desain blok acak

1. Randomized
Complete Block
Design
ARIF RAHMAN
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2. Experiments
Hypothesis/
Conjecture
Design of
Experiment
Conduct
Experiment
Analysis of
Data
Discussion &
Conclusion
Refine
the Model
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3. Elements of Design of
Experiments
1. Conjecture or hypothesis
2. Response variable
3. Factors, levels and ranges
4. Treatments of factors
5. Blockings
6. Tools and methods for experiments and
measurements
7. Effect models (independent or interaction factors)
8. Replication, randomization and local factor
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4. P Diagram
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Signal
Factors
(m)
Noise
Factors
(x)
Control
Factors
(z)
Scaling
Factors
(r)
Response
Variables
(y)
F(x,m,z,r)
Inputs
Controllable Factors
(x)
Uncontrollable Factors
(z)
Output
(y)
F(x,z)

5. Blocking Principles and Nuisance
Factors
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6. Blocking Principles and Nuisance
Factors
 Blocking is a technique for dealing with nuisance factors
 A nuisance factor is a factor that probably has some
effect on the response, but it’s of no interest to the
experimenter…however, the variability it transmits to the
response needs to be minimized
 Typical nuisance factors include batches of raw material,
operators, pieces of test equipment, time (shifts, days,
etc.), different experimental units
 Many industrial experiments involve blocking (or should)
 Failure to block is a common flaw in designing an
experiment (consequences?)
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7. Blocking Principles and Nuisance
Factors
 If the nuisance variable is known and controllable, we
use blocking
 If the nuisance factor is known and uncontrollable,
sometimes we can use the analysis of covariance to
remove the effect of the nuisance factor from the analysis
 If the nuisance factor is unknown and uncontrollable (a
“lurking” variable), we hope that randomization
balances out its impact across the experiment
 Sometimes several sources of variability are combined in
a block, so the block becomes an aggregate variable
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8. Randomized Complete Block
Design (RCBD)
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9. Randomized Complete Block
Design (RCBD)
Randomized Complete Block Design is a
type of experimental design to remove the
variability between blocks from experimental
errors by testing each experimental units on
each blocks. Each block contains all
treatments. The blocks form a more
homogeneous experimental unit on which to
compare the treatments. Within a block, the
order in which the treatments are tested is
randomly determined.
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10. Randomized Complete Block
Design (RCBD)
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11. Statistical Analysis of the RCBD
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12. Statistical Analysis of the RCBD
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13. Statistical Analysis of the RCBD
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14. Statistical Analysis of the RCBD
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15. Statistical Analysis of the RCBD
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16. Statistical Analysis of the RCBD
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17. Statistical Analysis of the RCBD
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18. Model Adequacy Checking
Normal Probability Plot of the Residuals
Plot of Residuals in Time Sequence
Plot of Residuals versus Fitted Values
Plot of Residuals versus Other Variables
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19. an Example: The Hardness
Testing Experiment
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20. an Example: The Hardness
Testing Experiment
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21. an Example: The Hardness
Testing Experiment
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22. an Example: The Hardness
Testing Experiment
 We wish to determine whether 4 different tips produce
different (mean) hardness reading on a Rockwell
hardness tester
 Assignment of the tips to an experimental unit; that is, a
test coupon. The machine operates by pressing the tip
into a metal test coupon, and from the depth of the
resulting depression, the hardness of the coupon can be
determined
 The test coupons are a source of nuisance variability.
The metal coupons may differ slightly in their hardness,
since they are taken from ingots that may be produced in
different heats.
 The test coupons will contribute to the variability
observed in the hardness data.
22

23. an Example: The Hardness
Testing Experiment
 To conduct this experiment as a RCBD, assign all 4 tips to
each coupon
 Each coupon is called a “block”; that is, it’s a more
homogenous experimental unit on which to test the tips
 Variability between blocks can be large, variability within
a block should be relatively small
 In general, a block is a specific level of the nuisance factor
 A complete replicate of the basic experiment is conducted
in each block
 A block represents a restriction on randomization
 All runs within a block are randomized
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24. an Example: The Hardness
Testing Experiment
24
Test Coupon
1 2 3 4
tip 1 tip 2 tip 3 tip 4
tip 1 tip 2 tip 3 tip 4
tip 1 tip 2 tip 3 tip 4
tip 1 tip 2 tip 3 tip 4
Test Coupon
1 2 3 4
tip 1 tip 1 tip 1 tip 1
tip 2 tip 2 tip 2 tip 2
tip 3 tip 3 tip 3 tip 3
tip 4 tip 4 tip 4 tip 4
NO RANDOMIZATION

25. an Example: The Hardness
Testing Experiment
25
Random Order Experimental Units on Blocks
1 2 3 4 5 6 7 8 9 10 11 12
tip 1 tip 1 tip 1 tip 1 tip 1 tip 1 tip 2 tip 2 tip 2 tip 2 tip 2 tip 2
tip 2 tip 2 tip 3 tip 3 tip 4 tip 4 tip 1 tip 1 tip 3 tip 3 tip 4 tip 4
tip 3 tip 4 tip 2 tip 4 tip 2 tip 3 tip 3 tip 4 tip 1 tip 4 tip 1 tip 3
tip 4 tip 3 tip 4 tip 2 tip 3 tip 2 tip 4 tip 3 tip 4 tip 1 tip 3 tip 1
Randomization Alternatives of four Experimental Units (tips) on Blocks (coupon)
24
!
4
4
4 

P
Random Order Experimental Units on Blocks
13 14 15 16 17 18 19 20 21 22 23 24
tip 3 tip 3 tip 3 tip 3 tip 3 tip 3 tip 4 tip 4 tip 4 tip 4 tip 4 tip 4
tip 1 tip 1 tip 2 tip 2 tip 4 tip 4 tip 1 tip 1 tip 2 tip 2 tip 3 tip 3
tip 2 tip 4 tip 1 tip 4 tip 1 tip 2 tip 2 tip 3 tip 1 tip 3 tip 1 tip 2
tip 4 tip 2 tip 4 tip 1 tip 2 tip 1 tip 3 tip 2 tip 3 tip 1 tip 2 tip 1

26. an Example: The Hardness
Testing Experiment
Test Coupon
1 2 3 4
tip 3 tip 3 tip 2 tip 1
tip 1 tip 4 tip 1 tip 4
tip 4 tip 2 tip 3 tip 2
tip 2 tip 1 tip 4 tip 3
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Test Coupon
1 2 3 4
9.2 9.4 9.8 10.0
9.3 9.6 9.6 10.2
9.7 9.3 9.5 9.9
9,4 9.4 10.0 9.7

27. an Example: The Hardness
Testing Experiment
Test Coupon
1 2 3 4
9.3 9.4 9.6 10.0
9.4 9.3 9.8 9.9
9.2 9.4 9.5 9.7
9.7 9.6 10.0 10.2
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28. an Example: The Extrusion
Pressure Experiment
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29. an Example: The Extrusion
Pressure Experiment
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30. an Example: The Extrusion
Pressure Experiment
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31. an Example: The Extrusion
Pressure Experiment
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32. an Example: The Extrusion
Pressure Experiment
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33. an Example: The Extrusion
Pressure Experiment
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34. 34
That’s all
... Any Questions ???