Introduction to Experimental Design

1
Introduction to Experimental Design

• Engineering Experimental Design
• Winter 2003

2
Fundamentals of Experimentation

• Clearly define the objective
• What question are you trying to answer? How will
  you know you are finished?
• Choose
• the factor(s) of interest - The response to
  measure,
• The data analysis techniques
• Consider the design specifics
• Range - Replication - Repetition
• Randomization - Blocking - Risks
• Collect the data
• Record all conditions carefully. Will you
  understand this later?
• Analyze the data
• Graphs descriptive statistics first -
  Hypothesis testing regression next
• Interpret the results
• Draw conclusions - Make recommendations

3
Advantages of Designed Experiments

• Enable data-based decisions
• Create understanding of a process and how to
  control it
• Take into account the inherent noise in the
  system
• Provide maximum information for the amount of
  effort
• Detect variable interactions

4
A Designed Experiment Should . . .

• Meet the objective
• Allow for simultaneous study of multiple factors
• Cover the region of interest
• Obtain maximum information for minimum cost
• Be simple to analyze and interpret
• Enable the experimenter to
• Distinguish important from unimportant factors
• Develop a mathematical model
• Test for model adequacy
• Estimate experimental uncertainty

5
Terminology

• Controlled variables
• Xs - Factors
• Treatments - Independent variables
• Outputs
• Ys - Responses
• Effects - Dependent variables

6
Types of Experimental Designs

• Factorial
• To distinguish important from unimportant Xs
• To form limited models
• Fractional factorial
• To make a preliminary distinction between
  important and unimportant Xs
• Response Surface
• To determine the relationship between Ys and the
  important Xs (develop a model)
• Regression is a way to analyze data from a
  response-surface experiment

7
Fundamentals of Experimentation

• Clearly define the objective
• What question are you trying to answer? How will
  you know you are finished?
• Choose
• the factor(s) of interest - The response to
  measure,
• The data analysis techniques
• Consider the design specifics
• Range - Replication - Repetition
• Randomization - Blocking - Risks
• Collect the data
• Record all conditions carefully. Will you
  understand this later?
• Analyze the data
• Graphs descriptive statistics first -
  Hypothesis testing regression next
• Interpret the results
• Draw conclusions - Make recommendations

8
Design Specifics - Range

• Cover the region of interest
• Are you in the right flow regime?
• Wide enough to see the effect of interest
• Will the real change in Y be bigger than the
  variability in Y?
• For regression, remember that model parameters
  (adjustable parameters, slope intercept) can be
  determined more precisely from a wide range of
  data than from a narrow range

9
Design Specifics - Replication

• Means coming back to the same conditions at a
  different time
• Allows you to estimate the inherent noise in the
  process
• Allows you to distinguish between a real response
  and normal variability
• Allows you to estimate the overall uncertainty in
  the experiment

10
Design Specifics - Repetition

• Provides an estimate of the variability within a
  given run
• Measurement uncertainty
• Variations in water pressure, temperature
• Provides an opportunity to study the variability
  in Y for a given X

11
Repetition and Replication
12
Replication and Repetition

• In practice, in an experimental situation, it can
  be difficult to achieve true replication.
• Do you really want to spend 30 minutes twiddling
  the valves to get exactly the same flow rate you
  got yesterday?
• How do you decide whether the current conditions
  are close enough to replication?
• Consider uncertainty on flow rate.

13
Design Specifics - Randomization

• An insurance policy
• Helps ensure that the effects of unknown,
  unidentified, or uncontrolled variables do not
  bias our experiments
• Helps ensure the validity of statistical
  assumptions

14
Design Specifics - Blocking

• Allows you to see a difference in Y due to one X,
  in spite of a change in another X
• How do you use blocking to see the effect of
  shell-side flow regime on overall heat transfer
  coefficient, in spite of the effect of tube-side
  flow regime on overall heat transfer coefficient?

15
Design Specifics - Risk

• Not a part of statistics, but something to
  consider to avoid becoming a statistic
• Potential danger to people
• Potential danger to property
• Potential danger to environment