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Statistical Experimental Design

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.

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Statistical Experimental Design

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  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 Let’s 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? 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.

  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 <>+/-1 std. dev. 94% of area us <>+/- 2 std. dev. 99% of area is <>+/- 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 Student’s t-test.

  16. Means Testing • If the means are the same, the things are of the same population. Use Welch’s 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 interacte.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?

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