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 Pressure = 1000 psi Time = 20 min Yield, wt % Temperature, °C

Next Set of Experiments Effect of Pressure Temperature = 300 °C Time = 20 min Yield, wt % Pressure, psi

More Experiments Effect of Time on Yield Temperature = 300 °C Pressure = 1000 psi Yield, wt % Time, min

What Have We Learned? 13 Experiments in 3 Factors Pressure Time 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.

A Smarter Way Pressure Time 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?

An Even Smarter Way Pressure Time 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 F-test. 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 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?