applied statistics
Design of Experiments
Spring 2017
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Design of Engineering Experiments
Part 1 – Introduction
Chapter 1, Text
- 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
Introduction to DOX
- 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”
Engineering Experiments
- 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.
Some of the objectives
Four Eras in the History of DOX
- 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
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
The Basic Principles of DOX
- 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
Strategy of Experimentation
- “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 designed experiments
- Based on Fisher’s factorial concept
Factorial Designs
- 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…
Factorial Design
Factorial Designs with Several Factors
Factorial Designs with Several Factors
A Fractional Factorial
Planning, Conducting & Analyzing an Experiment
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
- Get statistical thinking involved early
- Your non-statistical knowledge is crucial to success
- Pre-experimental planning (steps 1-3) vital
- Think and experiment sequentially