1. Experimental Design and Statistical Analysis Seth Price Department of Chemical Engineering New Mexico Tech Rev. 11/4/14

2. Designing Experiments Find what variables have been important (literature, past data, etc.) Find what “knobs to turn” Run screening experiments to determine appropriate ranges Identify what cannot be controlled

3. Factorial Analysis Once ranges of variables are established, set up a test matrix –One test at each “corner” of the data, plus one center point –For a 2D analysis: 5 tests –For a 3D analysis: 9 tests

4. Optimization Example There is an RF enhanced CVD reactor of a certain design (constant). You can control: –RF power: (100 mW to 500 mW) –Gas flow rate: (0.5 L/min to 1.5 L/min) Find the optimal range for maximizing coating thickness rate (μm/s)

5. Factorial Analysis

6. Optimum Area

7. Close Enough? If more time is available, choose: –Another factorial analysis, using current area as new corners –Repeated experiments for statistical analysis

8. Simple Statistics Average (Mean) Variance Standard Deviation Range

9. Process Engineering Likely involves statistical analysis –Why is our result not what was expected? –Is the new equal or better than the old way? Important skills –Pattern recognition –Decision making

10. Pattern Recognition?

11. Types of Problems Is this process in control? We made a change to one part of the process. Has it influenced another part? We did equipment maintenance to a machine. Has it fixed the problem? Does ambient air pressure influence our process?

12. Is This Process In Control? In Control: –We know exactly how this system behaves –What output to expect with changes to input Example: –If a flow rate upstream changes, what change in our output can we expect?

13. SPC Chart Mean chart –Plot data vs. time –Center line is mean (or target) –Define zones of concern Sigma chart –Target line is 0 –Define control limits

14. SPC Mean Chart

15. Western Electric Rules http://www.infinityqs.com/resources/spc-tools

16. Western Electric Rules A good starting point: –Zone A: 2σ – 3σ, -2σ to -3σ –Zone B: 1σ -2σ, -1σ to -2σ –Zone C: Mean to 1σ, Mean to -1σ Can redefine these as process develops Does not have to be symmetric Also look for patterns in data

17. In Control?

18. NO! (8pts on one side)

19. In Control?

20. NO! (2 of 3 in Zone A)

21. In Control?

22. Yes (W.E. Rules) and No (Cyclic)

23. Comparison Did the changes to my process affect something downstream? –Make a “null hypothesis” –Test it. You cannot compare averages directly –Reject the null hypothesis, or “fail to reject” the null hypothesis

24. Comparison Methods One sample T/Z-tests: –Test to see if a sample is from a certain population Two sample T/Z-tests: –Test two samples to see if they came from the same population Dependent T/Z tests: –Same samples used before/after treatment ANOVA: ANalysis Of VAriance –Testing if multiple samples (3+) are from the same population

25. Rather than evaluating each method… No-Frills Statistics: A Guide for the First-Year Student –Susan H. Gray –ISBN 0822603802 –Amazon: $2.49 (used)

26. Linear Regression Is there a correlation between two variables? –This is when you guys dump data into Excel and do a best fit line. How correlated are these variables? –“R squared value”, range 0 to 1 –0 is no correlation at all –1 is a perfectly positive linear correlation

27. Correlation and Causation Correlation does not prove causation

28. Still didn’t get it? Correlation does not prove causation

29. Proof http://www.venganza.org/images/PiratesVsTemp.png

30. If Correlation Proved Causation… Climate change caused by lack of pirates

31. If Correlation Proved Causation… Climate change caused by lack of pirates Solution to climate change is more pirates