0 25 7 6.5 6 75 5.5 5 A: Apple 0 00 2 4.5 00 75 25 B: Cinnamon C: Lemon 2 4 3.5 4 00 2 2 3.5 25 3 75 0 : Finding the Sweet Spot via Design and Analysis of Experiments with Mixtures Making the most of this learning opportunity Stat Ease worldwide webinars attract many attendees, so, to prevent audio disruptions, all must be muted by the presenter. Also, to avoid interruptions and keep the presentation to about one hour, please hold all questions until afterwards and address them to stathelp@statease.com. Mark P.S. Find slides posted now at www.statease.com/webinar.html and, barring technical issues, a recording put up afterwards. Turbidity 200 000 800 600 400 200 A (5) C (2) B (4) B (2) A (3) C (4) By Mark J. Anderson, PE, CQE Stat Ease, Inc., Minneapolis, MN mark@statease.com Reference: Now in 3 rd edition.* 2 nd edition 206. st edition 208! Formulation SIMPLIFIED Finding the Sweet Spot via Design and Analysis of Experiments with Mixtures * Productivity Press CRC, Taylor & Francis New York, June 205. A Primer on Mixture Design: What s In It for Formulators? www.statease.com/ pubs/mixprimer.pdf 2 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form.
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. 3 Mixture Design* *(Pioneered by Henry Scheffé, U Cal., 957) 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. 4 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 2
Forcing (squeezing?) factorial design on a mixture: Lemonade Glasses of sugar water 2 Lemons 2 5 Mixture Design and Modeling (sweet!) Two components: Quadratic (synergistic) Ŷ x 2x2 2xx 2 2 0 2Response 4 2 Lemons plus water taste better than either one alone. 2 X 3/4 /2 /4 0 X 0 /4 /2 3/4 6 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 3
Three Component Mixture B Factorial B Mixture A A C C 7 Ternary Diagram for Mixture Composition (for example, stainless steel flatware) x + x 2 + x 3 = X 90 70 0 0 30 30 30 70 70 0 90 90 X 2 X 3 This geometry is called a simplex. 8 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 4
Mixture Design: Solid Rocket Fuel 060 860 Elasticity 660 460 260 A () B (0) Special cubic model: Elasticity= + 35 * A + 446 * B + 653 * C - 6 * AB +008 * AC +597 * BC +64 * ABC C (0) B () A (0) C () 9 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 9%). A + B + C = 9% Detergent mix Using v Rebuild,* Run, Analyze *(With Water at 8% high) 0 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 5
Complex Constraints (Non Simplex) Cornell s Fruit Juice In Example 4.5 (p. 40 4), 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. Complex Constraints Cornell s Fruit Juice This complex constraint forms a frustrum of the simplex tetrahedron (top cut off). Fruit juice* *Apple added as 5 th component Slice 3D on pineapple & grapefruit 2 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 6
Categorical Factors Combined In this study a paint chemist working for an automobile manufacturer was tasked to choose: Monomer vendor M or M2. Crosslinker type CL, 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:. Knoop hardness > 0. 2. Solids content > %. Autocoat 3 Categorical Factors Combined: Split Plot In this study a paint chemist working for an automobile manufacturer was tasked to choose: Monomer vendor M or M2. <=Hard to Change! Crosslinker type CL, 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:. Knoop hardness > 0. 2. Solids content > %. Autocoat Rebuild w vendor HTC Go with 6 added groups 4 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 7
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. 5 Stat Ease Training: Sharpen Up via Computer Intensive Workshops Shari Kraber, Workshop Manager & Master Statistician shari@statease.com PreDOE Web Based (optional) Stat Ease Academy Basic Statistics for Design of Experiments Experiment Design Made Easy Designed Experiments for Pharma, Life Sciences, Assay Optimization, Food Science Factorial Split Plot Designs Stat Ease Academy Modern DOE for Process Optimization Response Surface Methods for Process Optimization Mixture and Combined Designs for Optimal Formulations Plus more classes here! Robust Design and Tolerance Analysis www.statease.com/training/stat ease academy.html 6 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 8
Statistics Made Easy Best of luck for your experimenting! Thanks for listening! Mark mark@statease.com Chemistry is necessarily an experimental science: its conclusions are drawn from data, and its principles supported by evidence from facts. Michael Faraday 7 Copyright 207 Stat Ease, Inc. Do not copy or redistribute in any form. 9