1. Design and Analysis of Experiments
Dr. Tai-Yue Wang
Department of Industrial and Information Management
National Cheng Kung University
Tainan, TAIWAN, ROC
This is a basic course blah, blah, blah…

2. Introduction Dr. Tai-Yue Wang
Department of Industrial and Information Management
National Cheng Kung University
Tainan, TAIWAN, ROC
This is a basic course blah, blah, blah…

3. Outline 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

4. Introduction to DOX(1/3)
An experiment is a test or a series of tests
Experiments are used widely in the engineering world
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”

5. Introduction to DOX(2/3)
Experimentation is a vital part of scientific (or engineering) method
For any experiment, questions to be asked:
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?

6. Introduction to DOX(3/3)
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,…?

7. Engineering Experiments(1/4)
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.

8. Engineering Experiments(2/4)

9. Engineering Experiments(3/4)
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).

10. Engineering Experiments(4/4)
The objectives of the experiment may include the following:
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.

11. Strategy of Experimentation(1/5)
Golf example-factor to influence the score
Driver– oversized or regular
Ball– balata or three piece
Mode of travel—walking or riding a golf cart
Beverage– water or beer
…….

12. Strategy of Experimentation(2/5)
“Best-guess” experiments
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

13. Strategy of Experimentation(3/5)

14. Strategy of Experimentation(4/5)

15. Strategy of Experimentation(5/5)
Statistically designed experiments
Based on Fisher’s factorial concept

16. Factorial Design(1/4)
In a factorial experiment, all possible combinations of factor levels are tested
The golf experiment:
Type of driver
Type of ball
Walking vs. riding
Type of beverage
Time of round
Weather
Type of golf spike
etc, etc, etc…

17. Factorial Design(2/4)
Results

18. Factorial Design(3/4)

19. Factorial Design(4/4)

20. Factorial Designs with Several Factors(1/2)

21. Factorial Designs with Several Factors(2/2)

22. Factorial Designs with Several Factors A Fractional Factorial

23. Typical Applications of Experimental Design(1/2)
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

24. Typical Applications of Experimental Design(2/2)
Evaluate material alternatives
Select design parameters
Determine key product design parameters
Formulate new product

25. The Basic Principles of DOX(1/3)
Randomization
Running the trials in an experiment in random order
Notion of balancing out effects of “lurking” variables
Replication
Sample size (improving precision of effect estimation, estimation of error or background noise)
Replication versus repeat measurements?

26. The Basic Principles of DOX(2/3)
Replication
Replication reflects sources of variability both between runs and within runs
Repeat measurement examples
A wafer is measured three times
Four wafers are processed simultaneously and measured

27. The Basic Principles of DOX(3/3)
Blocking
Dealing with nuisance factors
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

28. Planning, Conducting & Analyzing an Experiment(1/3)
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

29. Planning, Conducting & Analyzing an Experiment(2/3)

30. Planning, Conducting & Analyzing an Experiment(3/3)
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(Keep it Simple, Stupid) principle)
See Coleman & Montgomery (1993) Technometrics paper + supplemental text material

31. Four Eras in the History of DOX(1/3)
The agricultural origins, 1908 – 1940s
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
Box & Wilson, response surfaces
Applications in the chemical & process industries

32. Four Eras in the History of DOX(2/3)
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

33. George E. P. Box
R. A. Fisher (1890 – 1962)