Design and Analysis of Experiments Dr. Tai-Yue Wang Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN, ROC 1/33

Introduction Dr. Tai-Yue Wang Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN, ROC 2/33

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 3/33

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” 4/33

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? 5/33

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,…? 6/33

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. 7/33

Engineering Experiments(2/4) 8/33

Engineering Experiments(3/4) Some of the process variables and material properties, x 1, …, x p are controllable. Some of them are uncontrollable (although they may be controllable for purposes of a test). 9/33

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 z 1, …., z q are minimized. 10/33

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 ……. 11/33

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 12/33

Strategy of Experimentation(3/5) 13/33

Strategy of Experimentation(4/5) 14/33

Strategy of Experimentation(5/5) Statistically designed experiments Based on Fisher’s factorial concept 15/33

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… 16/33

Factorial Design(2/4) Results 17/33

Factorial Design(3/4) 18/33

Factorial Design(4/4) 19/33

Factorial Designs with Several Factors(1/2) 20/33

Factorial Designs with Several Factors(2/2) 21/33

Factorial Designs with Several Factors A Fractional Factorial 22/33

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 23/33

Typical Applications of Experimental Design(2/2) Evaluate material alternatives Select design parameters Determine key product design parameters Formulate new product 24/33

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? 25/33

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 26/33

The Basic Principles of DOX(3/3) Blocking Dealing with nuisance factors 27/33

Planning, Conducting & Analyzing an Experiment(1/3) 1.Recognition of & statement of problem 2.Choice of factors, levels, and ranges 3.Selection of the response variable(s) 4.Choice of design 5.Conducting the experiment 6.Statistical analysis 7.Drawing conclusions, recommendations 28/33

Planning, Conducting & Analyzing an Experiment(2/3) 29/33

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 principle) See Coleman & Montgomery (1993) Technometrics paper + supplemental text material 30/33

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 31/33

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 /33

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