experimental design and statistical analysis seth price department of chemical engineering new...
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Experimental Design and Statistical Analysis
Seth PriceDepartment of Chemical Engineering
New Mexico TechRev. 11/4/14
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
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
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)
Factorial Analysis
Optimum Area
Close Enough?
• If more time is available, choose:– Another factorial analysis, using current
area as new corners– Repeated experiments for statistical
analysis
Simple Statistics
• Average (Mean)
• Variance
• Standard Deviation
• Range
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
Pattern Recognition?
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?
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?
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
SPC Mean Chart
Western Electric Rules
http://www.infinityqs.com/resources/spc-tools
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
In Control?
NO! (8pts on one side)
In Control?
NO! (2 of 3 in Zone A)
In Control?
Yes (W.E. Rules) and No (Cyclic)
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
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
Rather than evaluating each method…
• No-Frills Statistics: A Guide for the First-Year Student– Susan H. Gray– ISBN 0822603802
– Amazon: $2.49 (used)
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
Correlation and Causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
Still didn’t get it?
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
• Correlation does not prove causation
Proof
http://www.venganza.org/images/PiratesVsTemp.png
If Correlation Proved Causation…
• Climate change caused by lack of pirates
If Correlation Proved Causation…
• Climate change caused by lack of pirates
• Solution to climate change is more pirates