Design and Analysis of Experiments

1. Design and Analysis of Experiments Dr. Tai-Yue Wang Department of Industrial and InformationManagement National Cheng Kung University Tainan, TAIWAN, ROC

2. Introduction Dr. Tai-Yue Wang Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN, ROC

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, …, xpare 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, allpossiblecombinations 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 statisticalthinking 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)