Design and Analysis of
Experiments
Dr. Tai-Yue Wang
Department of Industrial and Information Management
National Cheng Kung University
Tainan, TAIWAN, ROC
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Introduction
Dr. Tai-Yue Wang
Department of Industrial and Information Management
National Cheng Kung University
Tainan, TAIWAN, ROC
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Outline
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Goals of the course
An abbreviated history of DOX
Some basic principles and terminology
The strategy of experimentation
Guidelines for planning, conducting and
analyzing experiments
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Introduction to DOX(1/3)
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An experiment is a test or a series of tests
Experiments are used widely in the engineering
world
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Process characterization & optimization
Evaluation of material properties
Product design & development
Component & system tolerance determination
“All experiments are designed experiments, some
are poorly designed, some are well-designed”
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Introduction to DOX(2/3)
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Experimentation is a vital part of scientific (or
engineering) method
For any experiment, questions to be asked:
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Are only these methods available?
Are there any other factors that might affect the
results?
How many samples are needed for the experiment?
How should the samples be assigned to each
experiment?
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Introduction to DOX(3/3)
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What is the order that the data should be collected?
What method of data analysis should be used?
What difference in average observed results
between method, material, machines,…?
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Engineering Experiments(1/4)
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In general, experiments are used to study the process
and systems.
The system or process can be represented by next
figure.
The process can be the combination of operations,
machines, methods, people, and other resources
(often materials) that transfer some input into output
that has one or more observable response variables y.
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Engineering Experiments(2/4)
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Engineering Experiments(3/4)
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Some of the process variables and material properties,
x1, …, xp are controllable.
Some of them are uncontrollable (although they may
be controllable for purposes of a test).
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Engineering Experiments(4/4)
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The objectives of the experiment may include the
following:
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Determining which variables are most influential on the
response y
Determining where to set the influential x’s so that y is
almost always near the desired nominal value.
Determining where to set the influential x’s so that
variability in y is small.
Determining where to set the influential x’s so that the
effects of the uncontrollable variables z1, …., zq are
minimized.
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Strategy of
Experimentation(1/5)
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Golf example-factor to influence the
score
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Driver– oversized or regular
Ball– balata or three piece
Mode of travel—walking or riding a golf cart
Beverage– water or beer
…….
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Strategy of
Experimentation(2/5)
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“Best-guess” experiments
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Used a lot
 More successful than you might suspect, but
there are disadvantages…
One-factor-at-a-time (OFAT) experiments
 Sometimes associated with the “scientific” or
“engineering” method
 Devastated by interaction, also very inefficient
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Strategy of
Experimentation(3/5)
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Strategy of
Experimentation(4/5)
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Strategy of
Experimentation(5/5)
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Statistically designed experiments
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Based on Fisher’s factorial concept
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Factorial Design(1/4)
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In a factorial experiment, all
possible combinations of
factor levels are tested
The golf experiment:
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Type of driver
Type of ball
Walking vs. riding
Type of beverage
Time of round
Weather
Type of golf spike
Etc, etc, etc…
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Factorial Design(2/4)
Results
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Factorial Design(3/4)
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Factorial Design(4/4)
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Factorial Designs with Several
Factors(1/2)
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Factorial Designs with Several
Factors(2/2)
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Factorial Designs with Several
Factors A Fractional Factorial
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Typical Applications of
Experimental Design(1/2)
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Improve process yield
Reduce variability and closer conformance
to nominal or target requirements
Reduce development time
Reduce overall costs
Evaluate and compare basic design
configurations
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Typical Applications of
Experimental Design(2/2)
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Evaluate material alternatives
Select design parameters
Determine key product design parameters
Formulate new product
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The Basic Principles of
DOX(1/3)
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Randomization
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Running the trials in an experiment in random
order
Notion of balancing out effects of “lurking”
variables
Replication
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Sample size (improving precision of effect
estimation, estimation of error or background noise)
Replication versus repeat measurements?
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The Basic Principles of
DOX(2/3)
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Replication
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Replication reflects sources of variability both
between runs and within runs
Repeat measurement examples
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A wafer is measured three times
Four wafers are processed simultaneously and measured
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The Basic Principles of
DOX(3/3)
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Blocking
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Dealing with nuisance factors
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Planning, Conducting &
Analyzing an Experiment(1/3)
1.
2.
3.
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6.
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Recognition of & statement of problem
Choice of factors, levels, and ranges
Selection of the response variable(s)
Choice of design
Conducting the experiment
Statistical analysis
Drawing conclusions, recommendations
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Planning, Conducting &
Analyzing an Experiment(2/3)
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Planning, Conducting &
Analyzing an Experiment(3/3)
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Get statistical thinking involved early
Your non-statistical knowledge is crucial to
success
Pre-experimental planning (steps 1-3) vital
Think and experiment sequentially (use the
KISS principle)
See Coleman & Montgomery (1993)
Technometrics paper + supplemental text
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material
Four Eras in the History of
DOX(1/3)
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The agricultural origins, 1908 – 1940s
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W.S. Gossett and the t-test (1908)
R. A. Fisher & his co-workers
Profound impact on agricultural science
Factorial designs, ANOVA
The first industrial era, 1951 – late 1970s
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Box & Wilson, response surfaces
Applications in the chemical & process industries
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Four Eras in the History of
DOX(2/3)
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The second industrial era, late 1970s – 1990
 Quality improvement initiatives in many
companies
 Taguchi and robust parameter design, process
robustness
The modern era, beginning circa 1990
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R. A. Fisher (1890 – 1962)
George E. P. Box
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