Formulation Simplified: Finding the Sweet Spot via Design and Analysis of Experiments with Mixtures 1200 1000 800
Turbidity
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By Mark J. Anderson, PE, CQE Stat‐Ease, Inc., Minneapolis, MN
[email protected] 1
Formulation Simplified
Reference: Formulation Simplified Now in 3rd edition.*
2nd edition 2016.
1st edition 2018!
Formulation SIMPLIFIED Finding the Sweet Spot via Design and Analysis of Experiments with Mixtures A: Apple
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B: Cinnamon
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C: Lemon
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A Primer on Mixture Design: What’s In It for Formulators? www.statease.com/ pubs/MIXprimer.pdf
* Productivity Press CRC, Taylor & Francis New York, June 2015.
Formulation Simplified
Copyright ©2017 Stat‐Ease, Inc. Do not copy or redistribute in any form.
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The WIIFM for this Webinar Introduce tools for multi‐component product development and optimization. Brief formulators on tailored tools that hone in on optimal recipes. Via real‐world examples, lay out experiment‐designs and models for mixtures that ultimately lead to the “sweet spot” —a formulation meeting all product specifications.
See how Stat‐Ease makes formulation optimization easy for its users! Please press the raise hand now if you are with me. Formulation Simplified
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Mixture Design* *(Pioneered by Henry Scheffé, U Cal., 1957)
Considerations: Factors are ingredients of a mixture. The response is a function of proportions, not amounts. Given these two conditions, fixing the total (an equality constraint) facilitates modeling of the response as a function of component proportions. Let’s try forcing a factorial design onto a mixture. Formulation Simplified
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Forcing (squeezing?) factorial design on a mixture:
Glasses of sugar water
Lemonade
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1
Lemons
2 5
Formulation Simplified
Mixture Design and Modeling (sweet!) Two components: Quadratic (synergistic) Yˆ 1x1 2 x 2 12 x1x 2
12 0
Response
1 4 12
2 Lemons plus water taste better than either one alone .
1 X1 1
3/4
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X2 0
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Formulation Simplified
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Three‐Component Mixture Factorial
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Mixture
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Formulation Simplified
Ternary Diagram for Mixture Composition (for example, stainless steel flatware) x1 + x2 + x3 = 1
X1 90
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10 90
90
X2
This geometry is called a simplex.
X3
Formulation Simplified
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Mixture Design: Solid Rocket Fuel 1060
Elasticity
860 660 460 260
A (1) B (0)
Special cubic model: Elasticity= + 351 * A + 446 * B + 653 * C 6 * AB +1008 * AC +1597 * BC +6141 * ABC
C (1) C (0)
A (0)
B (1)
Formulation Simplified
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Mixture Case Study Three detergent components are varied: 3% A (water) 5% 2% B (alcohol) 4% 2% C (urea) 4% The sum of the three active components always equals 9% of the final formulation (all other components held constant at 91%). A + B + C = 9%
Detergent mix Using v11 Rebuild,* Run, Analyze *(With Water at 8% high) Formulation Simplified
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Complex Constraints (Non‐Simplex) Cornell’s Fruit Juice In Example 4.5 (p. 140‐141), Cornell details an experiment on a tropical beverage formulated from juices of: A. Watermelon B. Orange C. Pineapple D. Grapefruit The formulators decided to restrict watermelon to 80% at most, but they wanted mixtures in this region because this juice is so much cheaper than the others. Formulation Simplified
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Formulation Simplified
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Complex Constraints
Cornell’s Fruit Juice This complex constraint forms a frustrum of the simplex tetrahedron (top cut off).
Fruit juice* *Apple added as 5th component Slice 3D on pineapple & grapefruit
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Categorical Factors Combined In this study a paint chemist working for an automobile manufacturer was tasked to choose: Monomer vendor M1 or M2. Crosslinker type CL1, CL2 or CL3. The optimal mix of A. Monomer, 5 ‐ 20 % B. Crosslinker, 25 ‐ 40 % C. Resin, 55 ‐ 70 % With these goals for two key response measures: 1. Knoop hardness > 10. 2. Solids content > 50%.
Autocoat
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Formulation Simplified
Categorical Factors Combined: Split Plot In this study a paint chemist working for an automobile manufacturer was tasked to choose: Monomer vendor M1 or M2. <=Hard to Change! Crosslinker type CL1, CL2 or CL3. The optimal mix of A. Monomer, 5 ‐ 20 % B. Crosslinker, 25 ‐ 40 % C. Resin, 55 ‐ 70 % With these goals for two key response measures: 1. Knoop hardness > 10. Autocoat 2. Solids content > 50%. Rebuild w vendor HTC Go with 6 added groups Formulation Simplified
Copyright ©2017 Stat‐Ease, Inc. Do not copy or redistribute in any form.
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The WIIFM for this Webinar Introduce tools for multi‐component product development and optimization. Brief formulators on tailored tools that hone in on optimal recipes. Via real‐world examples, lay out experiment‐designs and models for mixtures that ultimately lead to the “sweet spot” —a formulation meeting all product specifications.
See how Stat‐Ease makes formulation optimization easy for its users! Now you know. 15
Formulation Simplified
Stat‐Ease Training: Sharpen Up via Computer‐Intensive Workshops Shari Kraber, Workshop Manager & Master Statistician
[email protected]
PreDOE Web‐Based (optional) Stat‐Ease Academy
Basic Statistics for Design of Experiments Designed Experiments for Pharma, Life Sciences, Assay Optimization, Food Science
Experiment Design Made Easy
Modern DOE for Process Optimization Factorial Split‐Plot Designs Stat‐Ease Academy
Response Surface Methods for Process Optimization
Robust Design and Tolerance Analysis
Plus more classes here! Mixture and Combined Designs for Optimal Formulations
www.statease.com/training/stat‐ease‐academy.html
Formulation Simplified
Copyright ©2017 Stat‐Ease, Inc. Do not copy or redistribute in any form.
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Statistics Made Easy®
Best of luck for your experimenting! Thanks for listening! ‐‐ Mark
[email protected]
“Chemistry is necessarily an experimental science: its conclusions are drawn from data, and its principles supported by evidence from facts.” ‐ Michael Faraday Formulation Simplified
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