Modul kuliah desain eksperimen - Teknik Industri - pertemuan 1 - pengantar desain eksperimen

1. Introduction to
Design of
Experiments
ARIF RAHMAN
1

2. Industrial Engineering
...is concerned with the design, improvement, and
installation of integrated systems of men,
materials, information, energy, and equipment. It
draws upon specialized knowledge and skill in the
mathematical, physical and social sciences
together with the principles and methods of
engineering analysis and design to specify, predict
and evaluate the result to be obtained from such
systems
2

3. Industrial Engineering
Mathematical
Physical Sciences
Social Sciences
Engineering
Knowledge & Skill
Industrial
Engineering
Integrated
Systems
Design
Improvement Installation
Specify
Predict
Evaluate
Optimal
Result
3

4. What is SYSTEM ?
 A set of interdependent things (parts or elements) forming a unified
whole and performing a set of rules to carry out a specific purpose.
 An organized, purposeful structure that consists of interrelated and
interdependent elements (components, entities, factors, members,
parts etc.). These elements continually influence one another (directly
or indirectly) to maintain their activity and the existence of the system,
in order to achieve the goal of the system.
(http://www.businessdictionary.com/definition/)
 A regularly interacting or interdependent group of items forming a
unified whole (https://www.merriam-webster.com/dictionary/)
 A set of things working together as parts of a mechanism or an
interconnecting network; a complex whole
(https://en.oxforddictionaries.com/definition/)
 A set of connected things or devices that operate together
(http://dictionary.cambridge.org/dictionary/english/)

5. What is SYSTEM ?
(a) a functional perspective,
(b) a structural perspective,
(c) a hierarchical perspective
5

6. System Analysis
6

7. Statistical Inference
7

8. Process Improvement - SIPOC
Diagram
Customers
Process
Suppliers
Inputs Outputs
S I P O C
8

9. Process Improvement - SIPOC
Diagram
Customers
Process
Suppliers
Inputs Outputs
Process Management
and Improvement
Supplier
Performance
Input
Measures
Process
Measures
Output
Measures
Customer
Feedback
Process
Changes
9

10. Statistical Design and Analysis of
Experiments
10

11. References
 Montgomery, DC, Design and Analysis of Experiments,
John Wiley & Sons
 Hicks, CR & Turner, KV, Fundamental Concepts in the
Design of Experiments. Oxford University Press
 Cochran, WG & Cox, G, Experimental Designs, John
Wiley & Sons
 Fisher, RA, The Design of Experiments, Oliver and Boyd
 Taguchi, G, Systems of Experimental Design, Unipub
Kraus International
 Sudjana. Desain dan Analisis Eksperimen, Tarsito
 Suwanda, Desain Eksperimen untuk Penelitian Ilmiah,
Alfabeta
11

12. References
12

13. Learning Outcomes
Students can comprehend the basic principles of
experimental design, such as randomization,
replication and local control (blocking, balancing
and grouping).
Students can construct an appropriate design of
experiments with a minimal risk of bias
Students can analyze the results of experiments
with statistical inference
13

14. Deductive – Inductive Reasoning
Theory Observation
General Specific
Population Sample
Hypothesis Prediction
Estimation Hypothesis
R
E
A
S
O
N
I
N
G
INDUCTIVE
DEDUCTIVE
14

15. Deductive – Inductive Reasoning
DEDUCTIVE
REASONING
INDUCTIVE
REASONING
PREMISES Stated as facts or
general principles
Based on
observations of
specific cases
CONCLUSION Conclusion is more
special than the
information the
premises provide. It is
reached directly by
applying logical
rules to the premises
Conclusion is more
general than the
information the
premises provide. It is
reached by
generalizing the
premises information
VALIDITY If the premises are
true, the conclusion
must be true
If the premises are
true, the conclusion is
probably true
USAGE More difficult to use
(mainly in logical
problems). One needs
facts which are
definitely true
Used often in
everyday life (fast and
easy). Evidence is
used instead of proved
facts.
15

16. System Approach
16

17. Engineering Method
Scientific Method
•Identify
problem
•Explore
requirements
•Trace
constraints
•Diagnose
causes
•Define
objectives
•Plan program
schedule
•Drawings
•Schematics
•Models
•Algorithms
•Proof of
concepts
•Prototypes
•Experiments
•Validation
and
verification
•Summary
results
•Conduct
implementa-
tion
Phase 1
Idea
Phase 2
Concept
Phase 3
Planning
Phase 4
Design
Phase 5
Development
Phase 6
Launch
Step 1
Ask A
Question
Step 2
Do
Background
Research
Step 3
Construct
A Hypothesis
Step 4
Test
Hypothesis
Step 5
Analyze Data &
DrawConclusion
Step 6
Communicate
17

18. Observations and Experiments
In an observational study, the engineer observes
the process or population, disturbing it as little as
possible, and records the quantities of interest.
In a designed experiment the engineer makes
deliberate or purposeful changes in the controllable
variables of the system or process, observes the
resulting system output data, and then makes an
inference or decision about which variables are
responsible for the observed changes in output
performance.
18

19. Observations and Experiments
19

20. Observations and Experiments
20

21. Observations and Experiments
21

22. Random Experiments
Designed experiment is an experiment in which
the tests are planned in advance and the plans
usually incorporate statistical models
Random experiment is an experiment that can
result in different outcomes, even though it is
repeated in the same manner each time.
Outcome is an element of a sample space.
Event is a subset of a sample space.
Sample space is the set of all possible outcomes
of a random experiment.
22

23. Factors and Treatment
Factors are the potential sources of variability that
influence the performance of a process or system.
Treatments are specific levels of the design
factors (factors of interest). They are deliberate
changes of a set of design factors at various level
to observe the changes in the system
performance.
Factor level is the settings (or conditions) used
for a factor in an experiment.
23

24. Factors and Treatment
Effects are the impact of treatment to response
variables. They are the mean change to the
response due to the presence of the treatment.
Interaction is interdependence of several factors.
Two factors are said to interact if the effect of one
variable is different at different levels of the other
variables. In general, when variables operate
independently of each other, they do not exhibit
interaction. An interaction is the failure of one
factor to produce the same effect on the response
at different levels of another factor.
24

25. Factors and Treatment
The potential design factors are those factors
that the experimenter may wish to vary in the
experiment.
Design factors are the factors actually selected for
study in the experiment.
Held-constant factors are variables that may exert
some effect on the response, but for purposes of the
present experiment these factors are not of interest, so
they will be held at a specific level.
Allowed-to-vary factors are variables that are usually
nonhomogeneous, but for ignoring this unit-to-unit
variability, it relies on randomization to balance out any
effect.
25

26. Factors and Treatment
Nuisance factors may have large effects that
must be accounted for, yet the experimenter may
not be interested in them in the context of the
present experiment.
A controllable nuisance factor is one whose levels
may be set by the experimenter
An uncontrollable nuisance factor is a nuisance
factor that is uncontrollable in the experiment, but it can
be measured. An analysis procedure called the analysis
of covariance can be used to compensate for its effect.
A noise factor is a factor that varies naturally and
uncontrollably in the process.
26

27. Factors and Treatment
Fixed effect factor is a design factor of
experiment with specific treatment at certain
levels. All the levels of interest for the factor are
included in the experiment.
Random effect factor is a design factor of
experiment with treatment by random sample from
some population of factor levels. There may be
unknown levels between treatment (level numbers
are only nominal).
27

28. Factors and Treatment
28

29. P Diagram
29

30. P Diagram
Signal
Factors
(m)
Noise
Factors
(x)
Control
Factors
(z)
Scaling
Factors
(r)
Response
Variables
(y)
F(x,m,z,r)
30
Inputs
Controllable Factors
(x)
Uncontrollable Factors
(z)
Output
(y)
F(x,z)

31. P Diagram
 Response variables (y) are the dependent variables (that are affected
some factors) as observed output characteristics (that are designed to meet
the target).
 Signal factors (M) are the parameter values set by the user at specified
point or within an acceptable range to attain the desired output.
 Control factors (Z) are the parameter values set by the engineer at least at
two-levels to select the best level for the desired output.
 Noise factors (X) are not controllable by the engineer or the user. However,
for the purpose of optimization, these factors may be set at one or more levels.
 Scaling factors (R) are special cases of control factors that are adjusted to
achieve the desired functional relationship as a ratio between the signal factor
and the response.
 Leveling factors (D) are special cases of control factors that are adjusted
to achieve the desired functional relationship as a constant between the signal
factor and the response.
31

32. Noise or Nuisances Factors
 External noise factors are sources of variation that are external to the
product or process. They include environmental noise factors and load-related
noise factors. The environmental noise factors are temperature, humidity, dust,
electromagnetic interference, etc. The load-related noise factors are the period
of time the product works continuously, the pressures to which it is subjected
simultaneously..
 Internal noise factors are sources of variation that are internal to the
product or process. They include time-dependent deterioration factors such as
wear of components, spoilage of materials, fatigue of parts, and operational
errors, such as improper settings on product or equipment.
 Unit-to-unit noise factors are inherent random variations in the process or
product caused by variability in raw materials, machinery and human
participation.
32

33. Sources of Errors
33

34. Sources of Errors
random error is an uncontrollable difference from one
trial to another due to environment, equipment, or other
issues that reduce the repeatability of an observation
systematic error is a reproducible deviation of an
observation that biases the results, arising from
procedures, instruments, or ignorance
illegitimate error is an error introduced when an
engineer does mistakes, blunders, or miscalculations (e.g.
measures at the wrong time, notes the wrong value)
34

35. Measurement Errors
unusual value (outlier) is an observation in a
sample that are so far from the main body of data
that they give rise to the question that they may be
from another population.
missing value is any relevant data which are
missing, since there may be transcription or
recording errors or may not have been collected
and archived.
bias is an effect that systematically distorts a
statistical result or estimate, preventing it from
representing the true quantity of interest.
35

36. Errors on Statistical Analysis
Type I Error () is rejecting the true null
hypothesis
Type II Error () is failing to reject the false
null hypothesis
 
36

37. Application of Experiments
37

38. Application of Experiments
38

39. Objectives of Experiments
39

40. Objectives of Experiments
40

41. Objectives of Experiments
41

42. Objectives of Experiments
42

43. Guidelines for Designing an
Experiment
43

44. Guidelines for Designing an
Experiment
44

45. Guidelines for Designing an
Experiment
45

46. Guidelines for Designing an
Experiment
46

47. Guidelines for Designing an
Experiment
47

48. Guidelines for Designing an
Experiment
48

49. Guidelines for Designing an
Experiment
49

50. Guidelines for Designing an
Experiment
50

51. Experiments
Hypothesis/
Conjecture
Design of
Experiment
Conduct
Experiment
Analysis of
Data
Discussion &
Conclusion
Refine
the Model
51

52. 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
52

53. Tentative Empirical Model
Linear
Quadratic
Cubic
Polynomial



 
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 2
2
1
1
0 x
x
y


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
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
 2
2
22
2
1
11
2
1
12
2
2
1
1
0 x
x
x
x
x
x
y


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 3
2
222
3
1
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2
2
22
2
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2
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0 ...
... x
x
x
x
x
x
y



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
 k
k
x
x
x
x
y 2
...
2
1
...
1
2
2
1
1
0 ...
53

54. Strategies of Experimentation
Best-guess experiments
One-factor-at-a-time (OFAT) experiments
Statistically-designed experiments
Factorial experiments
Fractional factorial experiments
54

55. Best-guess Experiments
Advantages
 The experimenter reasonably
selects an arbitrary combination
of the design factors, test them,
and see what happens
 The experimenter switches the
levels of one or two (or perhaps
several) factors for the next test,
based on the outcome of the
current test.
 There is a great deal of
technical or theoretical
knowledge of the system, as
well as considerable practical
experience.
Disadvantages
 The approach could be
continued almost indefinitely.
 The initial best-guess does not
produce the desired results. So
the experimenter has to take
another guess at the correct
combination of factor levels.
This could continue for a long
time, without any guarantee of
success.
 The initial best-guess produces
an acceptable result. And the
experimenter is tempted to stop
testing, although there is no
guarantee that the best solution
has been found.
55

56. One-factor-at-a-time (OFAT)
Experiments
Advantages
 The experimenter selects a
starting point, or baseline set of
levels, for each factor, and then
successively varying each factor
over its range with the other
factors held constant at the
baseline level.
 The experimenter analyzes how
the response variable is
affected by varying each factor
with all other factors held
constant.
 The interpretation is
straightforward, conclude the
interaction.
Disadvantages
 It assumes factors were
independent. If the
experimenter varies a factor, he
assumes that the other factors
have virtually no effect.
 It fails to consider any possible
interaction between the factors.
A factor may produce the
different effect on the response
at different levels of another
factor.
 If the interactions between
factors occur, it will usually
produce poor results
56

57. Statistically-designed (Factorial)
Experiments
Advantages
 All possible combinations of the
design factors across their
levels are used in the design
 A reasonable plan would be at
each combination of factor
levels
 The experimental design would
enable the experimenter to
investigate the individual effects
of each factor (or the main
effects) and to determine
whether the factors interact.
Disadvantages
 The number of factors of
interest increases, the number
of runs required increases
rapidly.
57

58. an Example: Playing Golf
58

59. an Example: Playing Golf
59

60. an Example: Playing Golf
60

61. an Example: Playing Golf
61

62. an Example: Playing Golf
62

63. an Example: Playing Golf
63

64. an Example: Playing Golf
64

65. an Example: Playing Golf
65

66. Experimental Units
Experimental unit or trial is a single testing in
scientific investigation through observations or
experiments that is reproducible in the same
condition or treatment to observe the response
variable. It is an entity which is the primary unit of
interest in a specific research objective for
researcher to make inferences about (in the
population) based on the sample (in the
experiment). Thus it needs adequate replication of
experimental units. The sample size is the number
of experimental units per group.
66

67. Basic Principles of Experimental
Design
Replication, to provide an estimate of
experimental error;
Randomization, to ensure that this estimate is
statistically valid; and
Local control, to reduce experimental error by
making the experiment more efficient
67

68. Basic Principles of Experimental
Design
Replication is an independent repeat run of each factor
combination. It is the repetition of experiment under identical
conditions. It refers to the number of distinct experimental
units under the same treatment.
 Replikasi bermanfaat untuk mendapatkan data yang homogen.
 Replikasi meningkatkan akurasi taksiran response dengan memetakan
confidence interval pada significance level tertentu.
 Replikasi membantu mendeteksi outlier akibat kekeliruan eksperimen,
kekeliruan pengukuran atau faktor pengganggu lainnya.
68

69. Basic Principles of Experimental
Design
Randomization is the cornerstone underlying the use of
statistical methods in experimental design to randomly
determine the order in which the individual runs of the
experiment are to be performed. Through randomization,
every experimental unit will have the same chance of
receiving any treatment.
 Pengacakan bermanfaat untuk memastikan setiap percobaan bersifat
independen, dan pengaruh faktor pengganggu terkurangi.
 Pengacakan mengurangi resiko bias eksperimentasi akibat faktor
pengganggu memberikan pengaruh sama dan berulang pada
perlakuan eksperimentasi yang sama.
 Pengacakan membantu menambah keyakinan dari analisa statistik
hasil eksperimentasi
69

70. Basic Principles of Experimental
Design
Local control is the control of all factors except the design
factors which are investigated. It refines the relatively
heterogeneous experimental subset into homogeneous
subset by removing extraneous sources of variability. It refers
to the amount of balancing, blocking and grouping of the
experimental units.
 Pengelompokan (grouping) yaitu penempatan sekumpulan percobaan
yang homogen dalam kelompok-kelompok yang mendapatkan
perlakuan yang sama.
 Pemblokan (blocking) yaitu pengalokasian percobaan dalam blok,
agar setiap blok berisikan percobaan-percobaan bersifat homogen.
 Penyeimbangan (balancing) yaitu pengendalian proses
pengelompokan dan pemblokan agar percobaan dalam konfigurasi
atau formasi yang seimbang.
70

71. Engineering Method
Scientific Method
•Identify
problem
•Explore
requirements
•Trace
constraints
•Diagnose
causes
•Define
objectives
•Plan program
schedule
•Drawings
•Schematics
•Models
•Algorithms
•Proof of
concepts
•Prototypes
•Experiments
•Validation
and
verification
•Summary
results
•Conduct
implementa-
tion
Phase 1
Idea
Phase 2
Concept
Phase 3
Planning
Phase 4
Design
Phase 5
Development
Phase 6
Launch
Step 1
Ask A
Question
Step 2
Do
Background
Research
Step 3
Construct
A Hypothesis
Step 4
Test
Hypothesis
Step 5
Analyze Data &
DrawConclusion
Step 6
Communicate
71

72. Keep The Following Points In
Mind
Use your non-statistical knowledge of the
problem.
Keep the design and analysis as simple as
possible.
Recognize the difference between practical and
statistical significance.
Experiments are usually iterative.
72

73. 73
That’s all
... Any Questions ???