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Design of Experiments

Design of Experiments. Hongyan Zhang Dept. of MIME The University of Toledo Fall 2011. Why is this trip necessary? Goals of the course An abbreviated history of DOX Some basic principles and terminology The strategy of experimentation

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Design of Experiments

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  1. Design of Experiments Hongyan Zhang Dept. of MIME The University of Toledo Fall 2011

  2. Why is this trip necessary? 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 Design of Engineering ExperimentsPart 1 – IntroductionChapter 1, Text

  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” Introduction to DOX

  4. Engineering Experiments Some of the objectives • Reduce time to design/develop new products & processes • Improve performance of existing processes • Improve reliability and performance of products • Achieve product & process robustness • Evaluation of materials, design alternatives, setting component & system tolerances, etc.

  5. The agricultural origins, 1918 – 1940s 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 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 Four Eras in the History of DOX

  6. Taguchi’s Method For quality improvement • Robust parameter design • Making processes insensitive to difficult-to-control variables • Making products insensitive to variation transmitted from components • Determining the variable levels to meet required mean and variability requirements • Notes • Different opinions between engineers and statisticians • There were substantial problems with his experimental strategy and methods of data analysis

  7. 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? Blocking Dealing with nuisance factors The Basic Principles of DOX

  8. “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 Statistically designedexperiments Based on Fisher’s factorial concept Strategy of Experimentation

  9. Factorial Designs • 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…

  10. Factorial Design

  11. Factorial Designs with Several Factors

  12. Factorial Designs with Several FactorsA Fractional Factorial

  13. 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 Planning, Conducting & Analyzing an Experiment

  14. Get statisticalthinking involved early Your non-statistical knowledge is crucial to success Pre-experimental planning (steps 1-3) vital Think and experiment sequentially Planning, Conducting & Analyzing an Experiment

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