Statistical Experimental
Design
A Primer
by
H. B. Oblad (Bruce)
Getting Answers Easier - Overview
The Old Method
The Better Method
Simple Statistics for the Lab
Let’s Try It Out!
The Old Method
Experiments one variable at a time in
sequence. Effect of Temperature on Yield
Yield, wt %
Pressure = 1000 psi
Time = 20 min
Temperature, °C
Next Set of Experiments
Yield, wt %
• Effect of Pressure
Temperature = 300 °C
Time = 20 min
Pressure, psi
More Experiments
Yield, wt %
• Effect of Time on Yield
Temperature = 300 °C
Pressure = 1000 psi
Time, min
What Have We Learned?
Pressure
• 13 Experiments in 3 Factors
Temp
• What combinations of conditions have we
covered? What’s 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.
Pressure
A Smarter Way
Temp
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?
Pressure
An Even
Smarter Way
Temp
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.
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)
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.
Bell Curve = Normal Dist.
68% of area is
<>+/-1 std. dev.
94% of area us
<>+/- 2 std. dev.
99% of area is
<>+/- 3 std. dev.
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 Student’s t-test.
Means Testing
• If the means are the same, the things are
of the same population. Use Welch’s t-test
Analysis of Variance
(ANOVA)
• Variance (standard deviation2) of means of
several sample groups is determined by Ftest. Probability criterion is used for
pass/fail or probability of F being equal is
given.
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
Rubber Band Experiment
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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?