Statistical Experimental Design

1
Statistical Experimental Design

• A Primer
• by
• H. B. Oblad (Bruce)

2
Getting Answers Easier - Overview

• The Old Method
• The Better Method
• Simple Statistics for the Lab
• Lets Try It Out!

3
The Old Method

• Experiments one variable at a time in sequence.
  Effect of Temperature on Yield

Pressure 1000 psi Time 20 min
Yield, wt
Temperature, C
4
Next Set of Experiments

• Effect of Pressure

Temperature 300 C Time 20 min
Yield, wt
Pressure, psi
5
More Experiments

• Effect of Time on Yield

Temperature 300 C Pressure 1000 psi
Yield, wt
Time, min
6
What Have We Learned?

• 13 Experiments in 3 Factors

Pressure
Time
Temp
7

• What combinations of conditions have we covered?
  Whats still unknown?
• Do we know anything about the repeatability of
  our lab technique?
• Are the responses straight or curved?
• Can we build a meaningful model that leads to a
  mechanism?
• Could we have done less work and gotten more
  information?
• Minor information about effects of factors.
• Know nothing about interactions.

8
A Smarter Way
Pressure
Time
Temp
9
2-Level Factorial Design

• 8 Tests (XY X levels, Y factors)
• Now know what happens over a large experimental
  volume.
• Now know the effects of factors at two surfaces.
  Effect of factors tested 4 x each
• Some information about interactions between
  factors.
• Repeatability is still unknown.
• Curvature?

10
An Even Smarter Way
Pressure
Time
Temp
11
2-Level Factorial Design w/ Center Points

• 11 Tests (3 cntr pts), 13 Tests (5 cntr pts)
• Now know the effects of factors at two surfaces
  and within the volume.
• More information about interactions between
  factors.
• Repeatability is now estimated or known.
• Curvature can be estimated.
• Predictive model is easy to create.

12
Box-Behnken Design 3 Factor, 3 Level
A fractional factorial design
Spherical, so extrapolation is less risky. 15
tests (3 cp), 17 tests (5 cp)
13
Simple Statistics

• Bell Curve Normal Dist. Gaussian Dist.
• Total population or very large sample
• Errors in lab methodology are assumed random and
  normally distributed except for time. Must
  randomize order to bury effect of time into
  error.
• Repeated tests may be pooled to estimate std.
  dev. and variance.

14
Bell Curve Normal Dist.
68 of area is ltgt/-1 std. dev. 94 of area us
ltgt/- 2 std. dev. 99 of area is ltgt/- 3 std. dev.
15
Means Testing

• If the means and standard deviations of the
  measurements are equal, the things being measured
  are of the same population. Opposite is true
  also (null hyp.) Use Students t-test.

16
Means Testing

• If the means are the same, the things are of the
  same population. Use Welchs t-test

17
Analysis of Variance(ANOVA)

• Variance (standard deviation2) of means of
  several sample groups is determined by F-test.
  Probability criterion is used for pass/fail or
  probability of F being equal is given.

18
Factors, Responses and Interactions

• Numeric Factors are variable inputs to a process
  e.g. feed rate, temperature, pressure, component
  concentration, knobs, levers
• Categorical Factors are discrete inputs e.g.
  catalyst type, feed material, operator
• Responses are effects of changes in factors e.g.
  Reaction rate increases w/ temp.
• Factors that affect each other are said to
  interact e.g. drinking, driving, vs drunken
  driving

19
Rubber Band Experiment

• What affects the distance traveled?
• Factors? How many?
• Numeric or categorical?
• Which design to use?
• Can we make a predictive model?
• Any interaction of factors?
• Can we understand the problem better?