Paul L. Fishbein, Ph.D.23 MAR 2015
1
Optimization Without Statistical DOE
• What is the “optimum”?
• What are the techniques?
Paul L. Fishbein, Ph.D.23 MAR 2015
2
The Optimum is the Best Compromise Among the Best Possible Outcomes for
Each Measured Result.
Walters, F.H., et al.
Paul L. Fishbein, Ph.D.23 MAR 2015
3
Desirability Functions Combine Multiple Criteria into One Number
D = (d1d2...dn)1/n
Walters, F.H., et al.
Paul L. Fishbein, Ph.D.23 MAR 2015
4
Before Finding the Optimum, the System Noise Must Be Reduced
• SPC techniques• Some DOE techniques
Wheeler, D.J., Chambers, D.S. Understanding Process Control, 2nd ed. (Knoxville, TN: SPC Press, 1992)
Paul L. Fishbein, Ph.D.23 MAR 2015
5
Rounding Reminder
• When converting units, follow NIST 1038A. 60.5 miles x 1.609347 km/mile = 97.36549 km
9 ≥ 6 97.4 kmB. 66 miles x 1.609347 km/mile = 106.2169 km
1 < 6 106 km
This procedure makes sure the relative error (RE) in the rounded result is the same or slightly less than the RE in the unconverted number so information in the unconverted number is not lost.
Paul L. Fishbein, Ph.D.23 MAR 2015
6
Rounding Reminder (Cont)If data have many points where the last significant
digit is 5 such as 5.5, 7.5, 6.5, 9.5, etc., consider rounding using the round half to even method:
• Round 5 to nearest even number:– 7.5 rounds up to 8 (because 8 is an even number)– 6.5 rounds down to 6 (because 6 is an even number)
This procedure ensures that all the rounding does not go in the same direction producing a bias.
Paul L. Fishbein, Ph.D.23 MAR 2015
7
One Factor at a Time Only Works When the Factors Do Not Interact
Paul L. Fishbein, Ph.D.23 MAR 2015
8
Order of Addition / Operations
• (number of constituents)!• 1) ABCD
2) DABC3) CDAB4) BCDA
5) BDAC
6) ABDC
7) BADC
Carlson, R,; Nordahl, A. Kraus, W. Acta Chim. Scand. 1991, 45, 46-48
Paul L. Fishbein, Ph.D.23 MAR 2015
9
Random EVOP
• Run 10-20 experiments at random. A total of 13 works well.
• Rank the results from lowest to highest.• Calculate 100 -100 * (Rank/(N+1)) where
– Rank = ranking from above– N = number of experiments
• The result equals the probability of finding conditions better than the results corresponding to that rank within the experimental space.
Hendrix, C. ChemTech 1980, 10(8), 488-497
Paul L. Fishbein, Ph.D.23 MAR 2015
10
Random EVOP (Cont)Yield (%) Rank 100-100*(Rank/(N+1))
30 1 92.935 2 85.738 3 21.444 4 78.646 5 35.750 6 64.353 7 50.054 8 42.959 9 35.765 10 28.566 11 21.567 12 14.369 13 7.2
Paul L. Fishbein, Ph.D.23 MAR 2015
11
Random EVOP (Cont)
1. Define the experimental space.2. Run 5 random experiments.3. Define a new experimental space centered about the
best of those 5 experiments. Make this new space smaller than the one before perhaps by cutting each dimension by one-half.
4. Run 5 more random experiments in this new space.5. Repeat steps 3 and 4 until no further improvement is
observed or you run out of time / money.
Paul L. Fishbein, Ph.D.23 MAR 2015
12
Simplex Optimization
• Self-directing EVOP.• Potentially provides a better result with each successive
experiment.• Can be stopped at any time.• Calculations can be done by hand or in a spreadsheet.• Many variations tailored to special needs – optimum at
the experimental space border, multiple optima, experiments run one at a time or in simultaneous groups, etc.
• Can be used in the plant.
Paul L. Fishbein, Ph.D.23 MAR 2015
13
A Simplex is a Geometric Figure Having the Number of Corners Equal to One More Than
the Number of Variables.
• With 2 variables, the simplex is a triangle.
• With 3 variables, the simplex is a tetrahedron.
Paul L. Fishbein, Ph.D.23 MAR 2015
14
Fixed Size Simplex
Walters, F.H., et al.
Paul L. Fishbein, Ph.D.23 MAR 2015
15
Variable Size Simplex
Walters, F.H., et al.
Paul L. Fishbein, Ph.D.23 MAR 2015
16
Some Simplex Variations
• Big starting simplex• Multiple move simplex• Second order reflection
Walters, F.H., et al.
Paul L. Fishbein, Ph.D.23 MAR 2015
17
References
• Hendrix, C. ChemTech 1980, 10(8), 488-497.
• Carlson, R,; Nordahl, A. Kraus, W. Acta Chim. Scand. 1991, 45, 46-48.
• Walters, F.H., et al. Sequential Simplex Optimization (Boca Raton: CRC Press, 1991).
Top Related